The multi-source cooperation integrating distributed low-density parity-check codes is investigated to jointly collect data from multiple sensor nodes to the mobile sink in the wireless sensor network. The one-round and two-round cooperative data collection schemes are proposed according to the moving trajectories of the sink node. Specifically, two sparse cooperation models are firstly formed based on geographical locations of sensor source nodes, the impairment of inter-node wireless channels and moving trajectories of the mobile sink. Then, distributed low-density parity-check codes are devised to match the directed graphs and cooperation matrices related with the cooperation models. In the proposed schemes, each source node has quite low complexity attributed to the sparse cooperation and the distributed processing. Simulation results reveal that the proposed cooperative data collection schemes obtain significant bit error rate performance and the two-round cooperation exhibits better performance compared with the one-round scheme. The performance can be further improved when more source nodes participate in the sparse cooperation. For the two-round data collection schemes, the performance is evaluated for the wireless sensor networks with different moving trajectories and the variant data sizes. For traditional wireless sensor networks (WSNs), many static nodes are randomly deployed and the data of active sensor nodes are usually forwarded to the sink node through multiple hops . HoweverMobile sink nodes were introduced to overcome some challenges above for wireless sensor networks ,6,7,8,9.Cooperative communications can achieve the diversity gain to decrease the impairment of wireless fading channels and improve the power efficiency by sharing antennas of different nodes in wireless networks ,14. In cThe investigations above disclose that coded cooperation can achieve significant performance gain for wireless networks. For multi-node coded cooperation, each node usually needs multiple cooperative partners so as to obtain the good performance. However, it is difficult for the complex cooperation relation to be implemented for wireless sensor networks due to the limited energy and processing capability of sensor nodes. Therefore, efficient multi-node coded cooperation schemes with low complexity should be elaborately designed for wireless sensor networks to reduce the energy consumption and improve the lifetime.In this paper, multi-source sparse cooperation schemes with efficient distributed LDPC codes are proposed to transmit data from multiple sources to the mobile sink in WSN. We investigate two cooperation models. In the first model, each source node usually has one parter to help itself and it also assists another partner, where the moving sink traverses one time along the distribution region of the active source nodes. In the second model, each source node is helped by two partners and also participates in the data transmission of two cooperative partners, where the moving sink traverses twice in the region of source nodes. We call the two cooperation models as multi-source sparse cooperation due to the simple cooperation relation especially when a lot of source nodes participate in the cooperation. Specifically, the sparse cooperation models are firstly formed considering the geographical locations of the nodes, the quality of the inter-node wireless channels, and the moving trajectories of the mobile sink node. Here, the neighbors of source nodes can be chosen to serve as the cooperative partners. Then, directed graphs and cooperative matrices are involved to present the cooperation models. Finally, distributed LDPC codes based on the sparse cooperation are devised to jointly transmit the data from multiple sources to the mobile sink node. In this cooperative data collection schemes, the energy consumption of the sensor nodes can be greatly reduced and each source node has very low complexity. If more source nodes participate in the sparse cooperation, the performance can be further improved.This paper is organized as follows. We consider a wireless sensor network consisting of a large quantity of static sensor nodes and a mobile sink node connecting to the remote base station, as shown in d moving along the distribution region of source nodes. Assume that each source node The network model is defined as follows. In a wireless sensor network, multiple sensor nodes N sensor nodes consist a cooperative set d. In this paper, we design two sparse cooperative models according to different moving trajectories of the sink node. In the first model, the moving sink node d moves along the distribution region of the active source nodes one time only. For the other model, the mobile sink d moves twice in the distribution region of the nodes along different routes. Indeed, the two moving trajectories interlace with one another. How to form the cooperative models are explained in the following.For the wireless sensor network above, we investigate cooperative models, where d and its neighbors sequentially when the mobile sink d approaches and awakes it. Specifically, when the source node d listen to d during the data collection. In this way, a cooperative link is formed one by one as shown in d and the reception results In this model, each source node In N increases and the performance can be improved when more source nodes participate in the cooperative link in For the cooperative link, we will design effective coded cooperation scheme with LDPC codes to achieve significant performance with quite low complexity in the next section. Note that the cooperative link in In this model, the moving sink node traverses twice along the distribution region of the active source nodes d should be different from the first one, though the two trajectories both traverse the nodes one by one in the cooperative group In order to obtain the promising performance, the second trajectory of the moving sink node Indeed, each moving round plays different roles in the cooperative data collection. In the next section, an efficient distributed encoding scheme is designed using LDPC codes to further illustrate the two-round cooperation model. Generally, for the first moving round, the sink node collects the information data broadcasted by each source node sequentially and each source node keeps the correctly received information data from its partner according to the dashed line in In this section, distributed low-density parity-check (LDPC) codes are designed based on the multi-source sparse cooperation models above to achieve the diversity gain and coding gain simultaneously. Specifically, the node cooperation models are firstly described using directed graphs. Then, the coded cooperation schemes with LDPC codes are devised based on the directed graphs. In the design, the coding schemes are constructed with the expansion from the basic matrix, which can be derived from the cooperative models. In this way, the data of all the sources in the cooperative group In the following, we represent the cooperation relation using the directed graphs for the two models.S consists of all the nodes in the cooperative link and the edge set E defines the cooperative relation among all the nodes.In this line-like cooperation model, each source node except N is the number of the nodes involved in the cooperation, and N in the one-round cooperation model. Thus, we call it the multi-source sparse cooperation in this paper. In the following, the matrix Then, let define a In this model, the moving sink node traverses twice along the distribution region of the active source nodes. In this way, the source nodes cooperate during the two rounds and the cooperation relation can be also denoted using the directed graphs. Taking the two-round cooperation model in For the directed graph in D. Overall, each source node in the set S jointly encodes its own data and the data successfully received from one or two selected partners according to the cooperation graphs and then forwards the encoded bits to the mobile sink. The detailed procedures for two cooperation models are introduced as follows.When multi-source cooperation graphs are formed, low complex distributed processing schemes using distributed LDPC codes are proposed to match the directed graphs d approaches it. Generally, each source node only receives the information data from its prior node according to the cooperation graph D and combines the data with its own data to generate the parity check data. For the line-like cooperative data collection, the processing at source nodes consists of two phases.For the cooperative data collection with the one-round model, each source node in the cooperative link acts sequentially when the sink node K bits to its selected partner D and the mobile sink node d, when the sink approaches and awakes In the first phase, each source node A is a In the second phase, the selected partner d. Thus, the parity-check data vectors D.The linear time encoding can be implemented at each source node in a distributed manner. The parity-check data vector d collects the data transmitted from all the sources in the set In this way, the mobile sink node Define a sparse matrixd from N cooperative sources during two phases is indeed a codeword of the LDPC code with h as the parity-check matrix and the matrix h can be easily derived from the cooperation matrix N of cooperation graphs. Then, the iterative decoding can be performed at the sink node d to decode the distributed LDPC code and obtain the data of all the sources in S. Moreover, the encoding and transmission are implemented by all the sources in the cooperative group N sources to protect the information data vector m during the first phase, they can be combined with the distributed LDPC code to further improve the performance.Therefore, the whole codeword Equation . Here, td moves two rounds along the region of active sensor nodes in the set S and two different cooperative links of two rounds also play different roles in the data collection. During each round, each source node also acts sequentially when the sink node d approaches it according to its related cooperative link in the graph D. The processing at the source nodes during the two rounds is described as follows, which is different from the one-round model above.In this model, the sink node K bits to the mobile sink node d and the selected partner in the first round according to the directed graph D. Each node just keeps the correctly decoded data from its partner and does not generate the parity check bits during the first round. For example, we assume that the node In the first moving round, each source node d by the node In the second moving round, each node generates and forwards the parity check bits using its own information data, the information data from its partner in the first round, and the parity-check data from its another partner in the second round. Taking the node given bypjT= constellations are employed and the data from each source node undergo independent and identically distributed quasi-static Rayleigh fading. We compare the performance of the one-round cooperation, the two-round cooperation, and the non-cooperation data collection scheme. In the non-cooperation data collection scheme, each source node individually transmits its data to the sink node by employing an LDPC code with the same code code length and code rate with the cooperative schemes, when the sink node approaches and awakes it. The iterative decoding based on message passing with maximum iteration of 30 times is performed at the sink node L in all the schemes equals to 1024 bits and the code rate is N of the source nodes involved in the cooperation set S increases, the data length K of each source decreases with the constraint L for comparison. We simulate three one-round cooperation cases with different N, that is, the cooperation with 4, 8, or 16 nodes. In N. Moreover, the encoding complexity at each source node in the one-round sparse cooperation scheme is lower than the non-cooperation, for distributed encoding is employed in the cooperation scheme.Firstly, the bit error rate (BER) of the one-round cooperation scheme is compared with the non-cooperation scheme in Secondly, the BER performance of the two-round cooperation with different numbers of source nodes is illustrated in Thirdly, the performance of the two multi-source cooperation models is compared in Fourthly, the moving trajectories of the sink node are discussed. We have addressed that the moving trajectory during the second round should be different from the trajectory in the first round so as to construct the distributed LDPC code with good performance. Taking the network with K results in the longer LDPC codes with the code length Finally, the performance of the two-round cooperation schemes with different data sizes is compared in For the large scale wireless sensor networks with one mobile sink node, multi-source sparse cooperation schemes integrating distributed LDPC codes are proposed to jointly collect different source data to the sink node. Specifically, two cooperation models are formed considering the geographical locations of the source nodes, practical channel condition and the moving trajectories of the sink node. Then, directed graphs and cooperation matrices are derived for the one-round and two-round cooperation models and the distributed LDPC codes are designed to match different cooperation models. Finally, simulation results are given to exhibit the significant performance of the proposed one-round and two-round cooperation schemes compared with the non-cooperation, while each source node has very low processing complexity attributed to the distributed encoding and transmission in the cooperation schemes. Furthermore, the performance of the two-round data collection schemes is also evaluated considering different moving trajectories and the variant data sizes.


Pompe disease is a rare disorder producing muscle weakness and progressive impairments in performing daily motor activities, such as walking and standing. Most studies have focused on dysfunctions at cellular level, restricting the examination of gross motor functions to qualitative or subjective rating scales evaluations. With the aim of providing an instrumented quantification of upright standing in Pompe disease, we used a force platform to measure the center of pressure over three foot positions and with eyes open and closed. Amplitude and variability of body sway were measured to determine the level of postural stability, while power spectrum analysis and nonlinear computations were performed to explore the structure of the postural control. In comparison with healthy participants, patients with Pompe disease showed a reduced level of postural stability, but irrelevant variations in frequency content and spatio-temporal structure of the sway motion were detected. Changes in foot position did not increase the postural instability associated with Pompe disease, but prominent worsening occurred in the patients when they stand with eyes closed, particularly along the anterior-posterior direction. These results provide objective elements to monitor deficiencies of upright standing in Pompe disease, emphasizing the specific contributions of sway direction and sensory deficits. Pompe disease (PD) is a very rare disorder caused by mutations of the glucosidase alpha acid gene. These mutations reduce considerably the activity of the acid alpha-glucosidase enzyme, preventing an appropriate breakdown of glycogen to glucose in the lysosomes12Accumulation of lysosomal glycogen may potentially affect all tissues, but the most prominent effects are observable in muscle. In particular, the release of autolytic enzymes from collapsed lysosomes produces an extensive fibers and contractile apparatus degeneration, leading to progressive muscle weakness. However, the clinical spectrum of PD is very heterogeneous, exhibiting a variability with respect to the level of severity, the rate of disease progression, the extent of organs involved, and the age of onset1234561Typically, in late-onset PD, the clinical symptoms may develop between the first and sixth decade, with muscle weakness localized mainly in paraspinal and proximal lower limbs muscles138127710The muscle weakness and respiratory deficits may in part origin from degenerative nervous system processes. In fact, the presence of substantial glycogen storage has been reported in the peripheral and central nervous system457121314151612131471061213155710The functional consequences of this clinical spectrum may lead to important impairments in executing essential everyday motor abilities, such as standing posture and walking. For example, the weakness of trunk and lower limb muscles and the severe alteration of ventilation movements potentially worsen the maintenance of balance, increasing the risk of falls1819Despite the important impact of PD on the basic motor abilities, most of experimental studies have focused on molecular and metabolic disorders or on dysfunctions of single organs or systems. To date, muscular strength and endurance capability have been the most examined motor functions212223Instrumented quantification of essential motor activities in persons with PD would provide more objective and valuable information on the severity of the motor dysfunctions and thus would help to monitor the disease evolution in natural condition and under therapeutic treatment.et al.While McIntosh Following the above line of thought, the main goal of this study was to provide an objective, instrumented quantification of the bipedal standing stability in adult patients with late-onset PD. To accomplish this purpose we addressed the following issues.First, we compared the level of postural stability during quiet standing in patients with PD and healthy people, measuring the standard spatial and temporal parameters (stability-related parameters) of the center of pressure (COP). Based on clinical data, the most straightforward prediction is that the patients should exhibit larger extension and temporal variability of the COP displacement with respect to the healthy persons. However, the contribution of the anterior-posterior (AP) and medial-lateral (ML) components of the COP to the overall stability might show some specificity in persons with PD. In fact, during quiet stance, the oscillations in the ML direction are attenuated by passive anatomical constraints at ankle and knee joints, while the AP direction is controlled most entirely by active muscle contractions. Therefore, the muscle weakness in PD would impair mainly the postural stability along the AP direction.Second, to test the adaptation of the static upright standing in patients with PD, postural changes associated with variations of foot position and visual condition were evaluated. During quite stance, healthy subjects respond to changes in foot configuration or vision condition with a moderate decrease of postural stability. Since the deficits associated with PD involve also the nervous system, we hypothesize that the patients should show more postural difficulties to face biomechanical and/or sensory changes when compared with the healthy subjects. Alternatively, the lack of differences between the two groups would be a sign of functional compensation for the muscle weakness.Finally, in addition to the standard posturography measurements, we explored also the frequency domain and the nonlinear dynamic structure of the spatio-temporal signals produced by the COP motion (structure-related parameters). These analyses capture the level of complexity that is not detected by traditional measures of postural performance and may indicate possible changes in the patterns of controlling upright standing. Muscle weakness or sensory-motor deficits may induce a reorganization of these patterns, but, particularly in the adult form of PD, it is possible that well-consolidated postural schemes prevent adaptive variations.Clinical data from five patients are summarized in The participants experienced standing posture over three foot positions  and withThe analysis of differences between the AP and ML directions for each two-dimensional parameter was modelled as a four-way repeated measures ANOVA with group as between-subjects factor, and foot position, vision condition, and direction as within-subjects factors.The majority of stability-related parameters were sensible in differentiating the patients from the healthy participants . In fact1,8 = 23.19, P = 0.001,  = 0.74) and for the RMS , with the AP direction exhibiting longer SP and more variability with respect to the ML direction, regardless of group, foot position, and vision condition , with the patients showing longer SP in the AP than in ML direction compared with healthy participants . These results suggest that, passing from eyes open to closed, the difference between the two directions increased more in the patients than in healthy subjects, with larger worsening in the AP than ML direction .Most of the balance deficits observed in patients with PD occurred along the AP direction, as it appears comparing SP and RMS measurements for the two directions. Moreover, a consistent postural stability was maintained in the ML direction also when the medial-lateral axis of the feet surface decreased passing from 20 cm (FP20) to 10 cm (FP10) inter-foot distance. On the other hand, when the AP axis was reduced, as in the position with the feet 30 degree rotated (FP30), the largest COP motion among the three foot configurations was observed.Generally, in healthy subjects the sway motion along the AP component of the COP is more instable than the sway in the ML component during both quiet2930et al.On these bases, the additional reduction in motion along the AP direction observed in the patients can be explained by the fact that muscle weakness may produce more impairments along the AP than ML direction as most of the perturbations along the ML direction are compensated by the intrinsic passive joint constraints. This interpretation is supported by the findings of Horlings Proximal muscles (trunk and hip joints muscles) could give a special contribution to the balance deterioration in the patients with PD. In fact, a non-uniform distribution of the level of force over the muscular apparatus was reported in patients with late-onset PD, with the proximal muscles more impaired than the distal muscles1368When studying the factors that influence standing stability, it should be considered that postural perturbations might also originate from the body itself. For example, voluntary limbs movements are the main source for the internal perturbations of upright posture323435710As the central nervous system prevents upright standing perturbations that arise from voluntary movements by accomplishing anticipated postural adjustments3237This compensation could be absent in diseases with breathing cycle impairment. For example, Grimstone and HodgesA signal supporting the lack of postural adaptation associated with breathing impairment in PD might be the limited variations of the structure-related parameters between the two groups observed in the current study. In fact, although we cannot evaluate the level of sensibility of these parameters, the emerging of novel compensatory strategies should determinate changes in frequency domain and/or in the spatio-temporal structure of sway motion.A possible postural adaptation emerging from our data regards the standing behavior associated with the foot position changes from easy to more difficult configurations. Although people with PD showed greater instability than the control group, the variations across the three foot positions were consistent between the two groups. This compensation could depend on the level of muscle force adaptation, since the effect of structure-related parameters was irrelevant for the interaction between foot positions and groups. It is possible that the level of muscle weakness characterizing our sample of patients did not prevent postural compensations for changes in foot position when the stances are restricted within quiet and static postures.On the contrary, an important reduction of the postural performance was associated with the vision condition. Maintaining upright stance relies on the integration of vision, vestibular and proprioceptive sensory signals39Although muscle weakness may be responsible for the further reducing in standing stability during stances with eyes closed in patients with PD, we believe that a suitable interpretation of this outcome could be based on the complex interaction of the sensory channels providing information to the postural control system.Several data suggest that a reduction of visual accuracy produces less postural instability than inaccurate proprioceptive information393943Overall, the reduction in balance stability associated with the visual condition in patients with PD might reflect a failure in sensory reweighting. In other words, possible proprioceptive and/or vestibular deficits in patients with PD may prevent an appropriate sensory integration to compensate for the lack of visual information.Although the information on the contribution of nervous dysfunctions to the clinical features of PD are sparse1213More in general, these findings suggest a reconsideration of neuronal factors influencing gross motor function, such as upright standing or gait movements, in patients with PD457121314The restricted sample size, due to the rarity of Pompe disease, is a limitation to the study design. However, the good level of effect sizes corroborates the reliability of the results observed here. In addition, in We recognize that an objective quantification of muscle force and an evaluation of the respiratory function would have been important for the completeness of the study. However, the main objective of this study was to quantify with an objective approach the impact of PD on the upright posture. Future studies on more specific functional and clinical relationships may benefit from the data provided by this paper.Quantitative analysis of quiet upright standing in patients with PD reveals an overall reduction of the postural stability without changes in the structure of the sway motion. Specific balance impairments associated with the sway direction and with the availability of visual information are discussed in relation to the topographical distribution of muscle weakness, respiratory insufficiencies and proprioceptive input deficits.This study strongly suggests to consider the sensory impairment, poorly documented in the specialized literature on PD, as a potential element affecting the motor performance, especially for multi-segments tasks that require a complex sensory-motor integration.The data of the current work can serve as a base for further investigations on the effects of PD on upright posture and other everyday motor skills. Moreover, we deemed that these results might help to monitor the disease evolution and to improve the accuracy of clinical interventions.Ten male participants took part in the study. Five patients with confirmed diagnosis of PD  recorded the reactive forces during the balance tests and sent the signals to the SMART-D system  for offline processing.Experimental sessions were performed two days before the ERT. Preliminary physical examination allowed to collect anthropometric measures  and range of motion and muscle strength at the hip, knee and ankle joints. Muscles strength was evaluated by using the MRC scaleparallel feet with the heels spaced 20 cm (FP20);parallel feet with the heels spaced 10 cm (FP10);feet extra-rotated with the heels together and opening angle of 30° (FP30).After the physical examination, the participants received adequate explanation concerning the procedure to follow. The postural assessment protocol consisted to perform a sequence of quiet stances with the foot positions configured as follow :parallelThese configurations imply a progressive reduction of the postural stability, since the base of support decreases from FP20 to FP30 . MoreoveFor each foot position, the test was performed with eyes open and closed. The order of presentation of combinations of foot position and vision condition was randomized across the participants.The subjects stood barefoot with their arms placed downward at their sides of the body, and their eyes focusing on a mark placed at a distance of 2.5 m. The feet were placed inside an outline borders to guarantee a consistent foot positioning across the tests. The participants were asked to keep the upright posture as immobile as possible for 50 sec, with an inter-trial interval of 2 min.To prevent fatigue, the participants were instructed to alert the experimenters if they were feeling fatigue, and the experimenters occasionally asked the participants about their fatigue level. However, given the low level of physical performance, and the large fraction of time for the rest (10 min) with respect to the time for the tests (5 min), fatigue was never an issue.The sessions took place in a room at the temperature of 22–24 °C, without external noises and with diffused light.Raw data were low-pass filtered using a zero-lag second-order Butterworth filter with 5-Hz cutoff frequency.The AP and ML coordinates of the COP position were computed from forces and torques values measured by the force platform and elaborated offline by the software Sway . From the AP and ML time series, the two-dimensional trajectory of the COP was reconstructed, and two sets of parameters were obtained.The first set of parameters describes the level of stability of the COP (stability-related parameters):Area: total area covered by the COP trajectory computed as the 95% confidence ellipse;SP: the total length of the COP trajectory computed as the sum of the distances between two consecutive points in the two-dimensional space;SP AP and SP ML: the length of the COP displacement computed as SP, but measured along the AP and ML directions;RMS AP and RMS ML: variability along the AP and ML directions computed as standard deviation from the mean of each time series.The second set of parameters describes the dynamical structure of postural signals in time, space and frequency domain (structure-related parameters):ApEn AP and ApEn-ML: estimation of the level of regularity of oscillations along the AP and ML directions, taking into account the non-stationarity property of the postural signal. The ApEn was computed using input parameters based on our data and former established protocols47FD: a measure of the two-dimensional COP trajectory complexity. The FD was computed using the following equationN is the number of data points ; d = (2a · 2b)1/2 where a and b are the major and minor axes of the 95% confidence ellipse, respectively. The geometrical complexity of COP trajectory increases as the two-dimensional FD passes from 0 to 2.where MPF AP and MPF ML: represents the mean frequency contained within a power spectrum, and was determined for AP and ML directions as follow:f represents frequencies in the signal, and P is the amplitude of Power Spectral Density (PSD) at each frequency. The PSD was computed from unfiltered AP and ML time series using the multitaper estimation methodwhere All the computations were performed using a customized MatLab code .Preliminary tests for normality (Shapiro-Wilk test) and for equality of sample variances (Levene’s test) were performed to provide the basis for using parametric statistics on a small sample.For each condition, each parameter was quantified computing mean, standard deviation, standard error and range over all the five participants. Since the small sample, range was used as measure of variability in the analytic summary of descriptive statistics, whereas, for clarity of illustration, standard error was used as error bars in the plots.For repeated measures ANOVA (see Results section), the critical value of F was adjusted applying Greenhouse-Geisser correction, that produces a P-value more conservative. This procedure corrects the repeated measures ANOVA with respect to a possible violation of the sphericity assumption, that is, the variance of the differences among all combinations of independent variables must be equal.The level of significance was set at P < 0.05 for all the statistical tests. Multiple post hoc pairwise comparison was performed by two-tailed paired t-test with Bonferroni correction.2p). The η2p describes the percentage of variance of the dependent variable attributed to the independent variables of interest. For the correlated samples in the post hoc paired test, the effect sizes were determined by using Hedges’ gav, which standardized mean differences based on the average standard deviation of both repeated measures. The Hedges’ g represents a correction of the more common Cohen’s d index, since the latter provides a biased estimate of the population effect size. This correction is particularly crucial when small samples are compared. The effect size computations were based on the recommendation suggested by LakenTo assess the magnitude of the ANOVA outcomes, the effect sizes were estimated by using partial eta squared values .How to cite this article: Valle, M. S. et al. Quantitative analysis of upright standing in adults with late-onset Pompe disease. Sci. Rep.6, 37040; doi: 10.1038/srep37040 (2016).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


The problem of data association for target tracking in a cluttered environment is discussed. In order to improve the real-time processing and accuracy of target tracking, based on a probabilistic data association algorithm, a novel data association algorithm using distance weighting was proposed, which can enhance the association probability of measurement originated from target, and then using a Kalman filter to estimate the target state more accurately. Thus, the tracking performance of the proposed algorithm when tracking non-maneuvering targets in a densely cluttered environment has improved, and also does better when two targets are parallel to each other, or at a small-angle crossing in a densely cluttered environment. As for maneuvering target issues, usually with an interactive multi-model framework, combined with the improved probabilistic data association method, we propose an improved algorithm using a combined interactive multiple model probabilistic data association algorithm to track a maneuvering target in a densely cluttered environment. Through Monte Carlo simulation, the results show that the proposed algorithm can be more effective and reliable for different scenarios of target tracking in a densely cluttered environment. As an important part of information fusion theory, target tracking has obtained more and more attention in wide applications. The main purpose of target tracking is to prevent false tracking or lost tracking, and ensure that the tracking is effective and accurate. Ship target tracking on the surface of the sea has been widely used in both military and civil fields. The performance of using radar to track surface ships are usually affected by sea clutter . Due to Even though the JPDA has gained more and more attention in the field of target tracking, it tends to coalescence when two targets are in parallel or at a small-angle crossing. The exact nearest-neighbor probabilistic data association (ENNPDA)  algorithWhen dealing with the problem of maneuvering target tracking in the densely cluttered environment, due to the uncertainty of the target motion, the multiple model algorithm assumes that there are many possible target movement models, different movement patterns with different motion models, realizing the mutual switch between different modes. Then the maneuvering target state estimation problem is converted into a target motion pattern recognition problem. In order to achieve multiple-target motion multiple-model tracking, the interactive multiple-model (IMM) algorithm, originally developed by Blom and Bar-Shalom , and theIn this paper, a novel probabilistic data association algorithm is proposed based on the distance weighting method. This algorithm not only improves the performance of single-target tracking in densely cluttered environments, but can also avoid coalescence when the targets are in parallel or in small-angle crossing scenarios. Based on the frame of C-IMM-PDA, and using the improved PDA filter, the algorithm also does well when tracking maneuvering targets in densely cluttered environments. The target tracking system is described in In a target tracking dynamic system, the major purpose is to estimate the parameters of the target that evolve sequentially with time. As measurement data become available, the unknown parameters forming a state vector are estimated sequentially using measurement data. Tracking in time with the problem of parameter estimation can be readily formalized in the following framework. In most surface ship tracking applications, the noise terms are additive, so the expression of the state equation and the measurement equation are defined as follows:The state equation (Equation (1)) describes the evolution or transition of The measurement Equation (2) relates function As for PDA, there are two assumptions: (1) a measurement can only have one source; (2) no more than one measurement can originate from a target. Suppose the set of validated measurements at time Here, we use a Kalman filter to estimate the state of the target. The prediciton of the state and the measurement at time Denote association events as As we know, the definition of events are mutually exclusive and limited: If there is no measurement that falls into the validation region, namely The error covariance associated with the updated state estimation can be expressed as follows:The association probability is the likelihood of tric PDA , the assterature  has certThe association probability expression with the distance weighting is show below:The normalized association probability expression is show as Equation (10):Here, with the new association probability, we use a Kalman filter to estimate the target state. The calculation is shown in Equations (5) and (6).The traditional algorithm is just a combination of the interactive multiple model and the probabilistic data association together. On the one hand, each model uses an independent validation region to obtain the validated measurement. However, for the entire system, the validation region may not be optimal, which can increase the target estimation error, and finally lead to a lost target or tracking the wrong target. On the other hand, with the increase in the number of targets and the number of target motion modes, the computational cost will also increase. Thus, the literature  proposes1. Interaction Mixed with the Estimate from the Previous TimeStarting with 2. Submodel Filter and PredictionWith the mixed initial state Here, we use the comprehensive prediction of the measurement and the comprehensive prediction covariance matrix tectonic tracking region. Its definitions are as follows:Here, using definitions from Equations (13) and (14), the parameters of the comprehensive validation region can be given as:Set Suppose Using Equation (16) to update each filter will lead to the estimation covariance being large; here we use Equation (17) to correct its covariance:3. Model Probability UpdateThe model probability is updated by Here, considering model probabilities update as an independent part of IMM, 4. Interaction Ouput Estimation ResultsFinally, the model-conditioned estimates are calculate using Equation (19).Assume the target state is In the constant velocity model (CV model), the movement characteristic is the velocity of the target, which remains the same, and the model parameters are as follows: where The turning motion of the target is usually referred to as a coordinated turn (CT model). With a known target turning rate In this section, the performance of the improved PDA algorithm are evaluated and compared with the existing method of PDA. Assume detection probability The initial state is (1)Two parallel-target tracking. The initial states are (2)Two small-angle crossing target tracking. The initial states are In this section, the performance of the proposed algorithm is evaluated and compared with the existing method of C-IMM-PDA. The initial states In this paper, we proposed a novel probabilistic data association algorithm based on distance weighting for target tracking. Due to clutter distribution being random, and the measurement originating from the target is more likely closer to the predicted measurement, this important prior information is introduced as a distance weight to optimize the association probability, which can enhance the association probability of the measurement originating from the target. When the improved algorithm is applied to non-maneuvering target tracking, the algorithm can be more accurate to realize the single non-maneuvering target tracking in a densely cluttered environment. For two-target tracking, it can avoid tracking coalescence whatever two targets are in parallel or at a small-angle crossing in a densely cluttered environment. For maneuvering target tracking in densely cluttered environments, based on the frame of C-IMM-PDA, we use the improved PDA to realize the data association and a Kalman filter to estimate the target state. Simulation results show the performance of the improved C-IMM-PDA algorithm is better than the C-IMM-PDA when tracking maneuvering targets in densely cluttered environments. Above all, with the increase of clutter density, the performance of the improved algorithm did not degrade significantly, which can ensure the real-time processing and accuracy of target tracking in densely cluttered environments.


In upright stance, light touch of a space-stationary touch reference reduces spontaneous sway. Moving the reference evokes sway responses which exhibit non-linear behavior that has been attributed to sensory reweighting. Reweighting refers to a change in the relative contribution of sensory cues signaling body sway in space and light touch cues signaling finger position with respect to the body. Here we test the hypothesis that the sensory fusion process involves a transformation of light touch signals into the same reference frame as other sensory inputs encoding body sway in space, or vice versa. Eight subjects lightly gripped a robotic manipulandum which moved in a circular arc around the ankle joint. A pseudo-randomized motion sequence with broad spectral characteristics was applied at three amplitudes. The stimulus was presented at two different heights and therefore different radial distances, which were matched in terms of angular motion. However, the higher stimulus evoked a significantly larger sway response, indicating that the response was not matched to stimulus angular motion. Instead, the body sway response was strongly related to the horizontal translation of the manipulandum. The results suggest that light touch is integrated as the horizontal distance between body COM and the finger. The data were well explained by a model with one feedback loop minimizing changes in horizontal COM-finger distance. The model further includes a second feedback loop estimating the horizontal finger motion and correcting the first loop when the touch reference is moving. The second loop includes the predicted transformation of sensory signals into the same reference frame and a non-linear threshold element that reproduces the non-linear sway responses, thus providing a mechanism that can explain reweighting. Spontaneous sway in human upright stance is reduced when touching a space-stationary reference with a finger ,2. The aWhen moving the touch reference, light touch cues signal a superposition of body and touch reference motion. Since humans use light touch cues to control balance, moving the touch reference evokes body sway ,6. This To identify whether a change in finger position relative to the body is due to self or touch reference motion, the nervous system needs to compare light-touch cues to other cues signaling body sway. When closing the eyes, the main additional sensory contributions are the proprioceptive reference to the floor and the vestibular reference to gravito-inertial space . In upriThe experimental setup to test the hypothesis evolved from a consideration of the change in the relative positions of the finger and body that results from angular body sway around the ankle joints. During anterior-posterior sway, the finger moves along an arc, where the absolute motion largely depends on the radius given by the distance between the ankle joints (the center of rotation) and the finger. To test our hypothesis, we assumed that light touch is integrated as a variable encoding angular movement around the ankle joints. Assuming this assumption holds, the sway responses should depend only upon angular stimulus motion, and should be independent of the radial distance of the touch reference from the ankle joint. Thus, the prediction is that a moving tactile stimulus will evoke the same amplitude of sway when it is presented at two different heights, when the stimulus amplitudes are matched for angular motion around the ankle joints.To maintain balance during light touch, the CNS must distinguish between stimulus and self-motion. Otherwise, large stimulus amplitudes could endanger postural stability. Therefore, some mechanism is required to down-weight the contribution of light touch cues in such situations. Such a mechanism has been discussed in earlier studies describing non-linearities in sway responses to light touch stimuli –10, but To test the above predictions, system identification methods can be applied to test different model structures. In this approach, small stimuli that mechanically perturb balance or evoke a conflict between sensory signals are used to probe the dynamics of the human balance control mechanism ,14. In aTo investigate the sensory integration of light touch cues, a similar approach can be used. Since touch reference motion evokes sway responses, it can be used to probe the dynamics of the control mechanism. Using a similar stimulus to that proposed by Peterka , at seveTo test our hypotheses, we used a combination of experiments and model simulations. The experiments used touch reference motion stimuli of different amplitudes, applied at two different heights while the evoked body sway was measured. In contrast to our first prediction, the results suggest that humans primarily stabilize body-finger distance during light touch, without transforming the touch signal to an angular variable. Furthermore, our results suggest a mechanism that transforms other sensory cues (e.g. proprioception & vestibular information) from angular ankle-based coordinates into expected body-finger translation. This is in full agreement with the hypothesized transformation of sensory cues to comparable physical variables. The model simulations suggest that the expected body-finger distance is then compared to the actual body-finger distance encoded by light touch cues to generate reweighting. As such, the identified mechanism is reminiscent of the ‘Disturbance Estimation and Compensation’ concept –18.Eight subjects  with average height 175 +/- 11 cm, mass 70.5 +/- 13.7 kg and aged 27 +/- 2.5 years participated in the study. The study was approved by the University of Birmingham Ethics Committee, with subjects giving their written informed consent prior to the experiments.Subjects stood barefoot with feet together on a force plate . With the right thumb and index finger, they lightly gripped a force sensor  attached to the end-point of a robotic device . The force sensor allowed for the measurement of grip force. The robotic device was movable in 3 dimensions, and was placed such that the zero position of the touch reference was 35 cm in front of the ankle joints and 35 cm to the right from the middle of both feet. Two electromagnetic motion sensors  were placed at hip and shoulder level to record body sway. Stimulus, actual touch reference motion, touch force, body sway, and ground reaction forces were recorded at 50 Hz using a PC with an AD converter .The robotic device was programmed to move in a small circular arc in the sagittal plane, with the center of the circle at the ankle joints  movement without feet. The COM was derived from the motion of the hip and trunk sensors, by initially calibrating their motion against the center of pressure (COP) as recorded by the force plate. During very slow movement, the COP can be used as a projection of the COM . SubjectMarkers were attached to a corselet (shoulder marker) and at the approximate height of the greater trochanter (hip marker). After performing the calibration routine as described above, six experimental trials were run in random order, with a brief break in between trials. Before each trial subjects were instructed to close their eyes, stand comfortably upright and hold the robotic device lightly between their index finger and thumb without evoking large forces. Measured grip force was below 1N with Mean ± SD across trials 0.54 ± 0.38 N. To distract subjects from the balance task, and to reduce auditory orientation cues, subjects listened to non-musical audio  via headphones.TSang) and angular COM motion (BSang); 2) horizontal translation of the stimulus (TStrans), along with horizontal translation of the COM (BStrans). The first cycle of each trial was discarded to avoid transient effects. For body sway, the mean was subtracted from each cycle to avoid an influence of drifts on the data. Across the remaining 11 cycles of each subject, the arithmetic mean was calculated for each point in time. Since the stimulus is identical for each cycle repetition, the arithmetic mean provides an estimate of the body sway response to the stimulus reducing the effect of random sway components. To test the angular integration hypothesis, the root-mean square (RMS) of the angular sway response was calculated for each subject and compared between the two heights. For equal angular stimuli, identical RMS values would indicate similar sway response amplitudes and therefore an independence between the two heights. The analysis was repeated comparing body sway (COM) and stimulus as horizontal translation, instead of angular movement.All analysis and model simulations were performed using Matlab and Simulink . Two different stimulus-response combinations were used during the analysis: 1) angular stimulus  was used to statistically test effects of height and angular stimulus amplitude on angular body sway. A one-way repeated measures ANOVA was used to test the effect of horizontal stimulus amplitude on horizontal body sway responses, where a statistical test of height was not possible. The reason is that horizontal displacement multiplied by height provides pairwise identical samples and therefore a pairwise linear dependence between the stimuli at the low and high height.For a more detailed characterization of the sway responses and for model-based interpretations, the spectral characteristics of the translational sway responses were analyzed. To this end, the spectra of individual translational body sway and recorded stimulus cycles were calculated using the Fast-Fourier-Transform implemented in the function ‘fft’ in Matlab. The arithmetic mean of the spectra was calculated across cycles and subjects. Averaging across subjects introduces inter-individual variability in the data. However, it also reduces overall variability, which was required given the low signal power at higher frequencies. Frequency response functions were calculated for each experimental condition as the ratio between averaged translational sway response spectra and averaged translational stimulus spectra . These cTStrans) and horizontal COM displacement of body sway  refer to the proprioceptive cues that encode the horizontal distance between touch reference and body COM and its velocity  refer to the vestibular-derived angular body orientation in space AND the proprioceptive orientation with respect to the floor. Since the floor was space-stationary in our experimental setup, both these sensory systems signal the same physical quantity and are lumped together as one signal in the model. Sensors BSang also encode position and velocity cues and are assumed to have ideal dynamics.Our model assumes that horizontal body-finger distance, as well as the body angle relative to the space vertical are available to the brain through sensory cues. Sensors in the model refer to complex sensory systems with a neural integration of multiple transducer signals and across multiple joints. The underlying assumption is a reconstruction of the body kinematics that have evoked the transducer signals. While neural correlates of kinematic variables have been found in the spinal cord and cerebellum of cats and rats ,23, usinBSang are fed back and amplified by a neural PD controller to generate the torque driving the body [The sensory cues of Sensors the body ,18. The the body . The outexp and FRFsim are the complex valued frequency response functions from the experiments and the model simulations, respectively. The objective function contained a sum across all frequencies f and conditions c, such that one set of parameters was obtained for all six experimental conditions. The objective function was minimized using the ‘trust-region-reflective’ algorithm as implemented in the function ‘lsqnonlin’ of the Matlab Optimization Toolbox . The function was run several times manually changing starting parameters to avoid local minima. Several parameters were fixed during the optimization procedure. These parameters were the biomechanical parameters , which were derived from subjects’ anthropometrics and using anthropometric tables [hTP), which was given by the experimental setup, and the low-pass filter constant Flp of the torque feedback. The latter was fixed to a value obtained from the literature [Kp and Kd, the lumped time delay dt, the force feedback loop gain Glp, the light touch loop gain LT, and the estimator gain and threshold Ge, and Te, were subject to the optimization procedure.The structure and parameters of the neural control model for the integration of light-touch cues were subject to the analysis in the current study. The structure was inspired by the Disturbance Estimation and Compensation (DEC) concept ,17,26 anc tables , the heiterature , since te(t) and the simulation output s(t) in the time domain. For both sequences e(t) and s(t), the mean was subtracted before calculating VAF usingVariance accounted for (VAF) was calculated for each experimental condition to assess the quality of the model quantitatively. VAF was calculated from the squared difference between experimental sway responses across cycles and subjects As an additional source of information, also random sway, defined as the sway component not correlated with the stimulus, was analyzed. An estimate of random sway in the time domain can be assessed by calculating the standard deviation across cycles for each point in time. The RMS of the standard deviation was calculated for each subject and the same statistical analysis was performed as for the body sway responses.The ratio of COM response RMS and stimulus RMS  was reduAfter discovering an effect of touch reference height on angular COM responses for identical angular stimulus amplitudes , a seconThe analysis of the translational components was conducted in the post-hoc analysis after rejecting the main hypothesis. The stimulus design did not allow a statistical analysis of the effect of height on the translation data. The reason is that translation stimulus amplitudes are pairwise linearly related through the touch reference height. However, translational response RMS values showed a gradual increase with translational stimulus amplitudes. No systematic difference, where sway responses of the low and high height are systematically shifted to each other were visible, indicating that sway responses were independent from the height of the touch reference.Plant’, ‘Sensors’, and ‘Balance control without light touch’ were formulated based on earlier studies . After the transformation, the signal is identical to the change in body-finger distance, when the touch-pad is stationary. In other words, the transformed signal represents the change in body-to-touch reference distance as expected from body sway velocity BSang. This expected BTtrans). The difference between these two signals provides a reconstruction of the horizontal finger velocity and therefore the light touch stimulus velocity The model that was identified to best describe the data shown in dies see . The idegration’  consists concept ,17. The T˙^trans  sensed bity TS˙^ .The estimate is based on noisy sensory cues and not ideal with 1) limited sensitivity and 2) an undershooting where the estimated motion is only partly compensated. In agreement with the DEC concept , these iAn optimization approach was used to identify the set of parameters that best reproduced the experimental frequency response functions. Kp, Kd, and Glp were similar to parameters reported in the literature, despite using a different perturbation  was 25% of the feedback gain without light touch (Kp). The estimator parameters were also in a feasible range, with the gain factor Ge smaller than one and the velocity threshold Te in the range of the stimulus velocities. compare ,27). The0.2 s in ). ParameThe random sway component of horizontal body sway is plotted against stimulus magnitude in Three angular stimulus amplitudes were applied at two heights of the touch reference, and the evoked sway responses were compared. Identical angular stimulus amplitudes evoked sway responses which were significantly larger in the high height conditions as compared to the low height conditions . This fiThe experimental results and the model-based interpretation provide consistent evidence for the idea that light touch cues are integrated as horizontal body-finger distance. However, other solutions might also be possible if they encode a geometric variable that is similar to the horizontal. For example, the absolute hip-finger distance or the horizontal shoulder-finger distance would only slightly differ from the horizontal body COM-finger distance. Such differences cannot be separated based on the presented experimental setup, which was designed to test whether humans integrate light touch cues as an angular variable.Different touch heights might have also led to geometric differences in the arm configuration. Although arm kinematics were not measured, a theoretical analysis of the geometric changes showed that subjects had larger changes in shoulder angle at the high position, as compared to the low position. Since our results suggest that the touch height has no effect on sway responses, the integration of light touch cues seems to be independent from the joint angular configuration.In summary, the presented approach is not able to determine which exact reference is encoded by light touch cues. However, our result strongly suggest that it is a horizontal kinematic variable and that it is independent from the geometric configuration of the arm.Sway response amplitudes increased with the horizontal translational stimulus amplitudes . In agreLight touch feedback’). Second, a mechanism that automatically reduces the influence of the light touch feedback, when the touch reference is sensed as moving in space (Touch motion estimator’).The experimental results provide a broad characterization of human sway responses across frequency, six stimulus amplitudes, and two heights . The modLT. The consistent pattern of sway responses when considering the stimulus as horizontal motion  is multiplied by the estimated gain factor BTtrans) and cues signaling body-sway in space (BSang). To fuse these signals, the brain needs to transform the cues signaling body sway—here the proprioceptive reference to the floor and the vestibular gravito-inertial reference—into an expected horizontal body-finger distance. Using the transformation allows for subtraction of the actual change from the expected change in body-finger distance, where the difference is a reconstruction of the horizontal finger movement in space ’ using the small angle approximation).The negative feedback alone would lead to a linear increase in sway response amplitude with increasing stimulus amplitude. Since a linear increase is not in agreement with human behavior, our results support the existence of a reweighting mechanism that reduces the effect of light touch cues with increasing stimulus amplitude. Earlier studies suggest that humans use a reconstruction of external disturbances in the control of upright stance –18,26. FhTP means a change in the loop gain of the velocity signal from Sensors BTtrans. This aspect might be related to the results of the random sway analysis as discussed below.The conversion from angular lean to horizontal distance is a step that needs to be actively implemented by the brain and has some interesting consequences. First, it requires that the brain knows the actual height of the touch reference and is able to use it to amplify a sensory signal. Second, extracting the height and using a horizontal kinematic variable in the control mechanism also requires the knowledge of vertical and horizontal body orientation. The role of the subjective vertical and horizontal in human perception and postural control is well founded . The preIn addition to analyzing the evoked sway response, we also analyzed the random sway component unrelated to the stimulus. All neural processes, sensory cues and muscle contractions contain noise and inaccuracies . It was Our results showed a significant effect of height but not of amplitude for random sway, where random sway was larger in the high conditions . The finBTtrans) contain less noise as compared to the other sensory systems (BSang). As described above, a change in height of the touch reference changes the loop gain of the velocity signal of Sensors BSang (gain factor hTP in the Touch motion estimator). This change in loop gain also amplifies noise present in this signal, and would lead to an increase in random sway with stimulus height, as observed in our results. However, it should be noted that the noise only becomes effective when stimulus and superimposed noise cross the threshold. This would also predict that the noise shows a dependency on the stimulus amplitude, if the stimulus is so small that stimulus and noise only partly cross the threshold. Such an effect can neither be confirmed nor rejected by our results, but requires further experiments. In the absence of a stimulus, i.e. with a stationary touch pad the threshold blocks most of the noise and random sway would further decrease.To model the effect of different noise sources quantitatively in a non-linear model largely increases the complexity and is not covered in this study. However, the model and the results allow some qualitative considerations. Given the observed reduction of spontaneous sway ,2, lightTouch motion estimator  and is not expected in spontaneous sway.In summary, changing the height of the touch reference leads to a change in loop gain when calculating the expected touch reference motion. The change in loop gain would then amplify the noise stemming from the proprioceptive reference to the floor and vestibular cues, thus leading to a change in random sway in dependence on touch reference height. Notably, this change in random sway depends on the activity of the The study tested whether humans integrate light touch stimuli as angular body rotation around the ankle joints using rotational stimuli. The results clearly rejected the hypothesis and a second analysis step was added to further investigate our findings. The interpretation that humans use the horizontal movement of the stimulus when integrating light touch cues is therefore explorative and needs to be verified in future studies. Also the model-based interpretation of our results rests on the assumption that light touch is integrated as horizontal body-finger distance. However, the ability of the model to accurately reproduce the experimental data supports the hypothetical interpretation that horizontal body-finger distance is the variable encoded by light touch.h in Plant/Physics to hTP) provide only slightly worse simulation results. Thus, more experimental data is required to further refine the model.The model was inspired by earlier quantitative models of perturbed upright stance and provides a consistent explanation of our experimental findings. An underlying assumption of our model (and others) is that the central nervous system integrates different sensory inputs into a single reference frame for controlling balance. While this seems like the most parsimonious control principle, we cannot rule out multiple sensorimotor control processes operating in parallel. An obvious limitation of the model is that it does not contain noise, leaving the observed random sway unexplained. Importantly, noise, stimulus characteristics and the overall dynamics of the system interact with the non-linear threshold that explains the changes in sway response amplitudes dedicated to reweighting. Future approaches should aim to include noise in the simulations to provide an explanation of sway responses to the stimulus and random sway. Finally, the model structure as presented in Light touch requires an additional task for the arm and possibly also the upper body to maintain the low touch forces at the contact point. The reason is that with just a passive connection to the touch reference the connection would maintain a stiffness from the stabilization of the arm. When body sway changes the distance between finger and touch reference, the stiffness would generate a force and the force limit of 1 N is quickly exceeded. As a consequence, the instruction to subjects to maintain a low force at the contact point results in an active tracking of the touch reference. This tracking is partly visible in the stabilization of the body with respect to the touch reference. However, additional corrections of the arm likely exist due to the much smaller inertia of the arm as compared to the large inertia of the body.Some studies suggest that the forces exerted at the touch reference are major contributors in the integration of the light touch cues . From ouPrevious research on visually-evoked postural responses suggests a connection between conscious motion perception and the strength of the evoked sway response . In our The study shows that sway responses to a moving reference are independent from touch height, while random sway not related to the stimulus appears to become larger with increasing height. Additional analysis steps suggest that light touch cues are integrated as horizontal body COM movement with respect to the finger (i.e. the touch reference). A quantitative model for the integration of light touch cues was presented. The model simulations suggest that the central nervous system converts sensory cues to comparable variables prior to the fusion process. The model further provides a potential explanation for reweighting of light touch cues through a non-linear threshold mechanism in the sensory reconstruction of the stimulus.S1 DatasetEach file provides the time traces of the whole body center of mass or the stimulus for one individual experimental trial of one subject. Each row contains one of the eleven cycle repetitions recorded within each trial and used for analysis.(ZIP)Click here for additional data file.


Micro-electro-mechanical-systems (MEMS) inertial measurement unit (IMU) outputs are corrupted by significant sensor errors. The navigation errors of a MEMS-based inertial navigation system will therefore accumulate very quickly over time. This requires aiding from other sensors such as Global Navigation Satellite Systems (GNSS). However, it will still remain a significant challenge in the presence of GNSS outages, which are typically in urban canopies. This paper proposed a rotary inertial navigation system (INS) to mitigate navigation errors caused by MEMS inertial sensor errors when external aiding information is not available. A rotary INS is an inertial navigator in which the IMU is installed on a rotation platform. Application of proper rotation schemes can effectively cancel and reduce sensor errors. A rotary INS has the potential to significantly increase the time period that INS can bridge GNSS outages and make MEMS IMU possible to maintain longer autonomous navigation performance when there is no external aiding. In this research, several IMU rotation schemes  are analyzed to mitigate the navigation errors caused by MEMS IMU sensor errors. As the IMU rotation induces additional sensor errors, a calibration process is proposed to remove the induced errors. Tests are further conducted with two MEMS IMUs installed on a tri-axial rotation table to verify the error mitigation by IMU rotations. Tens of years ago, to maintain long term autonomous navigation performance, the inertial navigation system (INS) was designed based on high end inertial sensors such as ring laser gyro (RLG) and fiber optical gyro (FOG). However, the large size  and high cost have limited their use to various applications. With the development of micro-electro-mechanical system (MEMS) technology, the MEMS-based inertial sensors became available to the commercial market in 1990s and they quickly found applications for indoor pedestrian and robotic navigation because of their low-cost, small-size, light-weight and low-power consumption . MEMS IMThis paper investigates a different approach to limit the accumulation of navigation errors in MEMS-based INS. Instead of focusing on the use of external aiding information by existing methods, it uses a rotary INS to reduce the navigation error growth by rotating the IMU. A rotary INS is an inertial navigator in which the IMU is installed on a rotation platform. By rotating the IMU in certain pre-defined schemes, it can change the characteristics of the inertial sensor errors and consequently reduce the accumulation of navigation errors. For example, the rotation of IMU with a constant angular rate can modulate the constant inertial bias into periodic signals and an integration of the modulated inertial data over a complete rotation cycle can eliminate the bias impact on the navigation solutions. Rotary INS technique has been widely applied in marine navigation for submarines and warships ,15,16. HAlthough the requirement for a rotational platform would increase the complexity and cost of the use of the rotation modulation technique, it will be advantageous to attach the MEMS IMU to a rotating platform that is already built in the vehicle, such as the wheel for land vehicle, the airscrew for the helicopter, and the propeller for the boat, just to mention a few. In a recent research, gyros are attached to the wheel of a ground vehicle and the results have demonstrated that a low-cost MEMS IMU can provide a very accurate navigation solution using the rotation modulation technique . In the (1)Error analysis for IMU rotation about X- and Y-axes: As previous research indicated that the IMU rotation about the Z-axis cannot modulate the errors in the Z-axis, which results in accumulated azimuth and velocity errors, this research conducts error analysis with IMU rotations about the X- and Y-axes, and compares three different rotation schemes for navigation applications.(2)The calibration of gyro scale factor and installation errors: As the gyro scale factor and installation errors induce additional sensor errors when IMU rotates, which will deteriorate the error migration performance, a process to calibrate gyro scale factor and installation errors is proposed for the MEMS-based inertial system.(3)Experiments and tests with real rotated data: As MEMS IMU outputs contain significant bias instability error, the sensor biases will vary randomly over time, not behave as constants. Tests with real rotated data are necessary in order to study the feasibility of MEMS-based rotary inertial system in real scenario.Comparing to the low-cost MEMS IMU, FOG and RLG errors are orders of magnitude smaller, and thus the application of the rotation modulation technique to FOG and RLG based IMU can effectively mitigate the error accumulations. However for MEMS IMU, due to their significant bias instability, scale factor, installation errors, as well as noise, how can the application of the rotation modulation technique help reduce the navigation errors is not clear so far which requires investigation. Although the idea of MEMS-based rotary INS had already been proposed, it was verified only by simulations in previous research . Real roThe remainder of this paper is organized as follows. The concept of rotary INS was initially proposed for the gimbaled inertial system by . AfterwaAs the IMU is rotating in the rotary INS, a new frame in which the inertial readings are collected is introduced, in addition to the traditional coordinate frames in conventional INS. This new coordinate frame can be referred as inertial sensor frame or IMU frame, and its axis are aligned with the sensitive axis of inertial sensors with the origin defined as the origin of IMU.Generally speaking, the mechanization algorithm of rotary INS is very similar to the one of conventional INS. As the inertial readings are collected in sensor frame, a transformation process is required, as shown in Equations (1) and (2).With the transformed specific force and angular rate in body frame, the mechanization of the conventional INS can be used to derive position, velocity and attitude solutions as shown in The inertial sensor errors are firstly introduced and the mitigation of navigation errors is then investigated using three different IMU rotation schemes, each rotating about X-, Y- and Z-axes, respectively. All analyses are conducted in static mode and the body frame is assumed to be aligned with the navigation frame to simplify the analysis.The specific forces and angular rates collected by the accelerometer and gyro triads contain different types of errors, such as noise, turn on biases, scale factor errors and installation errors. The sensor errors are the major error source that causes navigation errors. Usually, the sensor error model for gyros and accelerometers can be described by Equations (3) and (4), respectively .(3)ω˜=ωThe gyro and accelerometer biases normally contain two parts, namely, deterministic part and random part. The deterministic part is constant but it differs each time when the sensor is turned on, known as turn on bias in some literatures. The random part varies with time and it is quantified by the bias instability ,13,22. TThe scale factors of gyro and accelerometer cause sensor errors from the true value. Usually the scale factors for gyros and accelerometers are represented by the diagonal matrices in Equations (5) and (6), respectively, and they are quantified in unit of part per million (ppm). Normally the scale factor for MEMS IMU varies as a function of surrounding environments (such as temperature) ,23.(5)Si-axis and j-axis .Due to the imperfection of inertial sensor assembling and installation, the three sensitive axes of the sensor triad are not perfectly orthogonal with each other, which cause the sensed inertial value of one axis to project into the two other axes. The installation error for gyros and accelerometers can be described by Equations (7) and (8), respectively, and they are quantified using the unit of angle. Similarly, the installation errors are also temperature-dependent .(7)Ng=[Although the sensor biases, scale factors and installation errors vary in nature, they are considered to be constants in a short time period under stable temperature, e.g., during a complete rotation cycle, to simplify the analysis.As the IMU rotates about its X-axis with a rate of ω, the transformation matrix between the body frame and the sensor frame can be described by Equation (9).By applying the above transformation matrix, the gyro and accelerometer biases in the navigation frame can be described by Equations (10) and (11), respectively ,25. ThesAlthough IMU rotation can modulate the sensor constant biases, it also induces additional gyro biases proportional to the rotation rate due to the gyro scale factor of the X-axis as shown in Equation (14). After a complete rotation cycle, the rotation-induced gyro bias results in the accumulated attitude errors as shown in Equation (15). Similarly, the IMU rotation rate will be projected to the Y- and Z-axes due to gyro installation errors, and leads to additional gyro biases as shown in Equation (16). Although the rotation-induced gyro biases can be modulated, and the resulted attitude errors are removed after a complete rotation cycle as shown in Equation 17), it still degrades the navigation solutions within the rotation cycle , it stil.(14)δωSWhen IMU rotates about the Y-axis, both gyro and accelerometer biases in X- and Z-axes are modulated, so the attitude and velocity errors caused by those errors are automatically removed in east and vertical directions after a complete rotation cycle, while the errors in north direction propagate in the same way as in conventional INS, as shown in Equations (18) and (19). Similarly, the IMU rotation also induces the errors in the Y-axis due to the scale factor of the rotation axis, and the errors in the X- and Z-axes due to the gyro installation errors, as shown in Equations (20) and (21), respectively .(18)dn=The gyro and accelerometer biases in X- and Y-axes are modulated when IMU rotates about Z-axis, therefore the attitude and velocity errors caused by such errors are self-eliminated in the east-north plane after a complete rotation cycle, though the errors in vertical direction still propagate in the same way as in conventional INS, as shown in Equations (22) and (23). Because of the gyro scale factor in the Z-axis and the installation errors, the IMU rotation also induces gyro biases, which can be described by Equations (24) and (25) ,26.(22)For the IMU rotation about the X-axis, the unmodulated accelerometer bias causes the linear velocity errors and quadratic position errors over time in the east direction, as shown in Equation 26). The unmodulated gyro bias in the X-axis results in accumulated attitude error in the east direction, which causes projection error of the local gravity on the north direction. Eventually, it leads to quadratic velocity errors and cubic position errors over time as shown in Equation (27) ,6. Altho. The unmSimilar to the IMU rotation about the X-axis, the unmodulated accelerometer bias in the Y-axis leads to the linear velocity errors and quadratic position errors in the north direction, while the unmodulated gyro bias and scale factor in the rotation axis result in the quadratic velocity errors and cubic position errors in the east direction, for the IMU rotation about the Y-axis.For the IMU rotation about the Z-axis, the unmodulated accelerometer bias causes the linear velocity and quadratic position errors in the vertical direction, while the unmodulated gyro bias and scale factor of the rotation axis results in the azimuth errors, which lead to the horizontal velocity and position errors. For the IMU rotation about the X or Y-axis, as the velocity and position errors in the east or north directions accumulate quadratically and cubically over time, they are mostly much greater than the ones for the IMU rotation about the Z-axis, which is related to the coupling of the azimuth errors and the vehicle dynamics . Therefore, the IMU rotation about the Z-axis is more suitable than other two rotation schemes for navigation applications. The rest of the paper will concentrate on the use of this rotation scheme.(1)The IMU rotation modulates the constant biases of inertial sensors that perpendicular to the rotation axis, and the attitude and velocity errors caused by such biases are self-eliminated after a complete rotation cycle;(2)The constant biases of inertial sensors in the rotation axis cannot be modulated, and the attitude and velocity errors caused by such errors propagate in the same way as in conventional INS;(3)The IMU rotation induces an extra error in the gyro of the rotation axis due to gyro scale factor, and this error results in accumulated attitude errors in the direction of the corresponding rotation axis;(4)The IMU rotation also induces extra errors in the gyros that are perpendicular to the rotation axis due to gyro installation errors, resulting in attitude and velocity errors.(5)As the rotation-induced errors are proportional to the rotation rate, which is usually much more significant than earth rotation rate, a calibration process is required to remove the rotation induced errors.Other conclusions are summarized as follows:As the IMU rotation induces additional gyro biases, which eventually leads to navigation errors ,26, a caAs the IMU rotation does not introduce any linear motion of IMU, the theoretical gyro outputs in body frame can be described by Equation (28), when body frame is static relative to local level frame.The theoretical and actual gyro outputs in the sensor frame can be described by Equations (29) and (30), respectively, and the gyro errors are given in Equation (31).The earth rotation rate can be ignored in the above error model because: (1) the earth rotation rate cannot be sensed in most MEMS IMU due to their significant gyro bias instability and noise; and (2) the IMU rotation rate is much more significant than earth rotation rate. By ignoring the earth rotation rate, the above gyro error model can be simplified as shown in Equation (32).With different IMU rotation rates, the least square algorithm is applied to estimate the gyro scale factor, The calibration process can be described as two steps: (1) the tested IMU remains still on the rotation platform for 60 s; and (2) the IMU rotates along with the rotation platform at a designated rotation rate about Z-axis for 60 s. The total calibration time is 2 min. According to the error model in Equation (32), the gyro biases can be estimated from the inertial data collected in static period, while the gyro scale factor, y errors ,28, so tARW is the angular random walk of gyros, The error sources for the calibration error include the gyro sensor noise, the gyro bias instability (gyro biases are not constants but time-correlated variables), and the ignored earth rotation rate. The calibration errors of gyro biases caused by noise can be calculated using Equation (35), and the calibration errors of scale factor and installation errors caused by noise are given by Equation (36) . ApparenIt should be noted that the calibration method above is proposed to estimate gyro errors before each use of the rotary system. It requires the vehicle remains still during the calibration process, and this limits its use for on-line calibration of the rotary system. For on-line calibration, the external measurements are required, and an extended Kalman filter (EKF) is usually employed to estimate the sensor errors.By using a tri-axial rotation table as the rotation platform, two MEMS IMUs, namely MTi-G and NAV440 are tested. The rotation platform consists of a tri-axial rotation table and a console (computer) as shown in The MEMS IMUs are firmly installed on a piece of metal underneath the inner frame by screws as shown in h .The frame rotation angle data (IMU rotation angle between body frame and sensor frame) and inertial data are recorded by the console with data rates of 50 Hz and 100 Hz, respectively. The frame rotation angle will be used to calculate transformation matrix between body frame and sensor frame, which are necessary to solve the attitude solutions.The Allan variance method was also employed to study the random variations of the sensor biases as shown in The conventional INS static tests and the rotary INS static tests are conducted using both MEMS IMUs in a laboratory. The conventional INS static tests, in which the inertial data are collected while the MEMS IMU remains still on the rotation table for 6 min (the data from the 1st minute will be used to derive the gyro bias estimates), are conducted to investigate how fast the inertial errors accumulate with time in a non-rotary system and to provide a comparison to the rotary INS. The rotary INS static tests are conducted to study the feasibility of the MEMS-based rotary system, and to verify the inertial error mitigation performance through IMU rotations. Although higher IMU rotation rates can more effectively mitigate the navigation errors in theory ,25, the The means of the gyro data in three axes collected in the 1st minute provide the estimates of the gyro biases . Based oIn each individual test, the gyro scale factor of Z-axis, The major calibration error sources contain the gyro noises and the gyro bias random variations. Although longer calibration time reduces calibration errors caused by the noise, it also increases the effect of gyro bias variations on calibration results. Therefore, the choosing of calibration time is a compromise of the two factors. For both tested IMUs, the calibration time is chosen as 120 s (60 s in each step) and the reason is that the calibration errors caused by the gyro noise are comparable to the minimum bias variations for the cluster time of 120 s as shown in The rotary INS results are derived with two different data processing strategies, namely, partially calibrated data processing and fully calibrated data processing, to verify the effect of gyro scale factor and installation errors on navigation errors. For the partially calibrated data processing, the rotary navigation solutions are derived with only the estimates of gyro biases from the calibration results, so the gyro scale factor and installation errors remain in the rotary inertial data. For the fully calibrated data processing, the estimates of gyro installation errors, scale factor and biases are applied to derive the rotary INS solutions.By using two data processing methods, the obtained roll and pitch errors for the individual test with rotation rate of 10°/s are given in For each individual test, the RMS values of the position, velocity and attitude errors are calculated using partially and fully data processing strategies, as shown in For the fully calibrated data processing, the removal of the rotation-induced gyro errors in the X- and Y-axes further reduce the roll and pitch errors, as well as the horizontal position and velocity errors, comparing to the results in the partially calibrated case. The azimuth errors are also significantly reduced because of the estimation of the gyro scale factor in the Z-axis. The mean value of RMS for the horizontal position errors and the velocity errors for all tests are further reduced to 1057.2 m and 10.4 m/s, respectively. The roll and pitch errors are found much smaller than the azimuth errors. This is because the gyro errors in the X- and Y-axes are modulated by IMU rotation about the Z-axis, while such errors in the Z-axis cannot be modulated. Although a higher IMU rotation rate can more effectively modulate sensor biases and mitigate error accumulations for FOG or RLG-based system ,25, it cThe rotated Nav440 data are also processed using the two data processing methods, and the obtained roll and pitch errors for the individual test with rotation rate of 30°/s are given in By using two different data processing methods, the obtained RMS values of navigation errors for each individual test are given in It can be noted that the magnitude of the roll and pitch errors are nearly one order smaller than the azimuth errors due to the modulation of gyro errors in the X- and Y-axes. As the NAV440’s gyro bias instability and noise level are much lower than MTi-G, much smaller navigation errors are obtained for the rotary system based on NAV440.Based on the results from the conventional INS static tests and the rotary INS static tests with two different MEMS IMUs, we can see that IMU rotations can modulate the sensor errors, and mitigate their effect on navigation solutions. The gyro scale factor and installation errors will cause additional navigation errors by IMU rotations, and their calibration is therefore necessary for a MEMS-based rotary system in order to achieve better navigation performance. The rotation rate is not the only factor that affects the error modulation, which will also be affected by the sensor errors, such as the bias instability and the noise. The results also indicate that the sensor errors can be more efficiently modulated for the MEMS IMUs that have smaller bias instability and lower noise level.This paper investigates the mitigation of navigation errors due to significant MEMS inertial sensor errors by rotating IMU. Three IMU rotation schemes, each rotating about X-, Y- and Z-axes, respectively, are investigated. The related mathematical equations are derived and analyzed for each rotation scheme. A calibration method is proposed to remove the sensor biases, as well as gyro scale factors and installation errors for a MEMS-based rotary system. The tests with two MEMS IMUs on a tri-axial rotation table are conducted to verify the feasibility of MEMS-based rotary INS. The results indicate that with efficient data processing strategy, the IMU rotation can effectively modulate sensor errors and mitigate their effects on navigation solutions for a low-cost MEMS IMU. Kinematic field tests and other factors, such as vibration and wobble, that may affect the error mitigation in rotary INS, will be investigated in the future research.


A novel exciting method for a sandwich type piezoelectric transducer operating in longitudinal-bending hybrid vibration modes is proposed and discussed, in which the piezoelectric elements for the excitations of the longitudinal and bending vibrations share the same axial location, but correspond to different partitions. Whole-piece type piezoelectric plates with three separated partitions are used, in which the center partitions generate the first longitudinal vibration, while the upper and lower partitions produce the second bending vibration. Detailed comparisons between the proposed exciting method and the traditional one were accomplished by finite element method (FEM) calculations, which were further verified by experiments. Compared with the traditional exciting method using independent longitudinal ceramics and bending ceramics, the proposed method achieves higher electromechanical coupling factors and larger vibration amplitudes, especially for the bending vibration mode. This novel exciting method for longitudinal-bending hybrid vibrations has not changed the structural dimensions of the sandwich transducer, but markedly improves the mechanical output ability, which makes it very helpful and meaningful in designing new piezoelectric actuators operated in longitudinal-bending hybrid vibration modes. Piezoelectric ultrasonic actuators (PUAs) have been seen as an important and preferential type of element for precision driving due to their merits of simple structure, small size, quick response, high resolution and a lack of electromagnetic radiation ,2,3,4. PYun et al. proposed a novel PUA using a hybrid of the first longitudinal and second bending vibration modes of a sandwich transducer; their prototype achieved a no-load speed of 470 mm/s and a maximum force of 92 N . Shi et All these works used sandwich transducers operating in longitudinal-bending hybrid modes, which meant that these two types of vibrations were generated simultaneously under the same frequency. It should be noted that the longitudinal and bending vibrations are excited by independent piezoelectric elements, which are named as longitudinal ceramics and bending ceramics, separately. Usually, the longitudinal vibration of a sandwich transducer is generated by whole-piece type piezoelectric ceramic plates polarized in the thickness direction, whereas the bending vibration needed half-piece type piezoelectric ceramic plates with reverse polarizations. The difference between the longitudinal and bending ceramics required them to be located at different positions of the transducer, which limited their axial location; that is to say, the longitudinal and bending modes could not reach the maximum electromechanical coupling efficiency synchronously due to this spatial limitation.In this work, a novel exciting method for a sandwich transducer operating in longitudinal-bending hybrid modes is proposed and discussed. The longitudinal and bending ceramics are placed at the same axial location by dividing a whole-piece type piezoelectric ceramic plate into three independent partitions: the upper partition, the center partition and the lower partition. The center partition is the actuator for the longitudinal vibration, while the two outer partitions are used for the excitation of the bending mode. The finite element method (FEM) is used to verify the feasibility and superiority of the proposed exciting method. The electromechanical coupling factors and vibration amplitudes are calculated and compared with those of the traditional method. Two sandwich transducers using the new and traditional exciting methods respectively were fabricated and measured.As an operating principle, the longitudinal vibration can produce axial simple harmonic vibrations on the two end tips, whereas the bending vibration will generate simple harmonic vibrations along the transverse direction. When these two simple harmonic vibrations have the same resonance frequency and a temporal shift of 90 degrees, elliptical movements will finally be formed, which can be used for driving if a runner is pressed into contact: the transverse displacement will overcome the preload and the axial displacement can push the runner linearly. Thus, the key problem in the design of a longitudinal-bending hybrid sandwich transducer is the match between the two vibration modes used, which means that their resonance frequencies should be tuned as closely as possible. This requirement will bring limitations on the structural dimensions as the match of frequencies can only be satisfied under certain sizes.The aforementioned operating principle states that the longitudinal and bending vibration modes should be generated with a temporal shift of 90 degrees. The details of the traditional exciting method for the first longitudinal-second bending hybrid vibrations are illustrated in The new exciting method for a sandwich transducer operating in the first longitudinal-second bending hybrid modes proposed in this work is shown in In The exciting method shown in ρ = 8300 kg/m3, Young modulus E = 1.07 × 1011 N/m2, Poisson ratio σ = 0.37); the material of the end cap is duralumin alloy  and the material of the ceramic plate is PZT-4, whose physical parameters are:d, Ec, and Tε are the piezoelectric matrix, the stiffness matrix and the dielectric matrix, respectively.The electromechanical coupling factors and the vibration amplitudes of the transducers under the traditional and the new exciting methods were calculated by FEM (ANSYS software) to illustrate the differences. Firstly, two FEM models were built separately according to the arrangements of the piezoelectric ceramic plates shown in Modal analyses were then developed based on the two models, from which the resonance frequencies of the first longitudinal and second bending modes were gained, as shown in sf and the parallel resonance frequency pf can be obtained by recognizing the points with minimum impedances and maximum impedances, respectively. The electromechanical coupling factor k is calculated by the following equation [From equation :(4)k=fp2Finally, the vibration amplitudes of the longitudinal and bending vibrations were calculated to further verify the merit of the new exciting method, during which voltage with an amplitude of 100 V and a damping factor of 0.003 were applied. Four calculations were developed in sequence for the two modes under the two exciting methods, respectively. The axial vibration amplitude of the driving tip was extracted for the longitudinal vibration, while the transverse amplitude was identified to represent the bending vibration. The gained curves of the amplitude versus the frequency are plotted in These comparisons show that a great improvement is achieved in the bending vibration mode excitation, and a minute weakening occurs to the longitudinal mode. However, two other factors should be declared: the volumes of the piezoelectric elements used for the excitations and the optimal working frequencies, which are listed in The improvements of the electromechanical coupling factors and the vibration amplitudes by the new exciting method can be explained by two reasons: Firstly, it changes the arrangements of the longitudinal and bending ceramics by using whole-piece type piezoelectric ceramic plates with three separated partitions, which favors their sharing the same axial location; moreover, the bending ceramics are placed away from the neutral plane of the bending vibration, which can also obviously improve the electromechanical coupling efficiency since the piezoelectric elements near the neutral plane contribute little to the generation of the bending mode.Two sandwich transducers were fabricated using the traditional and the new exciting methods respectively, as shown in A new exciting method for the excitation of the longitudinal-bending hybrid vibrations of a sandwich piezoelectric transducer was proposed and simulated in this work. The structural dimensions, the total volume of piezoelectric elements and the exciting signals have not changed in comparison with the traditional exciting method. The changes concern the arrangements of the piezoelectric ceramic plates and the number of electrodes: each piezoelectric ceramic plate is divided into three separated partitions, which are linked with three individual electrodes. This method favors the piezoelectric elements for the longitudinal and bending vibrations sharing the same axial location. The electromechanical coupling factors and the vibration amplitudes were calculated and compared with those of the traditional method, which verified that the proposed exciting method obviously improved the bending vibration: the electromechanical coupling factor and the bending vibration amplitude increased by about 33 and 34%, respectively. The experiment results agreed well with those calculated by FEM. This new exciting method is not only available for the generation of first longitudinal-second bending hybrid vibration modes, but also suitable for the excitation of other combinations of longitudinal modes with odd number orders and bending modes with even number orders. Future work will focus on the practical use of this novel exciting method in designing a new linear piezoelectric ultrasonic actuator operating in longitudinal-bending hybrid modes.