We show that compensation measures aimed at improving the fairness of a crisis policy response can unintendedly nudge compliance with emergency rules. We combine information on the distribution of relief funds across Italian municipalities during the novel coronavirus pandemic with data tracking citizens’ movements through mobile devices and navigation systems. To assess the impact of transfers on compliance, we exploit a sharp kink schedule in the allocation of funds. The empirical analysis provides evidence that compliance increased with transfers, suggesting that the observance of emergency rules also depends on the fairness of the pandemic policy response. The exercise of coercive power is only one of the factors of state effectiveness. A broader view gives reciprocal obligations between institutions and citizens an essential role . EnlightThe novel coronavirus outbreak offers a convenient scenario for studying the relationship between fairness and voluntary compliance. In a pandemic, the spontaneous observance of emergency rules is crucial to public welfare. At the onset of the outbreak, citizens were required to comply with sudden limitations of their civil liberties that were not compensated with any evident public good equivalent in the short run. Confinement measures can be perceived as unbearably unfair to anyone needing social interaction to get an income, especially those who can neither work from home nor afford food delivery. Economically vulnerable individuals face the most challenging difficulties in coping with lockdown rules and have more substantial incentives to break social distancing norms . A pandeIn this paper, we show that measures mitigating the economic disruption caused by social distancing could unintendedly nudge compliance with restrictive orders. To address causality, we exploit the sharp kink design in the allocation of funds of a relief program explicitly aimed at improving the fairness of the pandemic policy response. On March 30, 2020, the Italian government announced an aid scheme to support economically vulnerable groups through the distribution of food stamps. We combine information on the allocation of resources across Italian municipalities with data tracking citizens’ movements through mobile devices and navigation systems, drawn from City Analytics by Enel X. As social distancing requires renouncing unnecessary movements, we follow the literature and use human mobility as a proxy for compliance e.g., . For eacThe kink design in the allocation of funds as a function of past income differentials generated a random treatment assignment in a neighborhood of the threshold point, which allows us to tackle endogeneity issues. Authorities partitioned the budget of the program, 400 million euros . We find robust evidence that, after the introduction of the program, the deviation of mobility from its baseline level increased substantially with the amount of transfers. In the week of the policy announcement, the transfers caused an increase in the mobility differential from the baseline of 3 percentage points. Given an average drop of 60 percentage points in the same week, additional 0.58€ additional transfers per capita caused a 5 per cent increase in compliance. Two weeks later, the impact of transfers on compliance was still positive, statistically significant, and sizable, with the increase in transfers leading to an increase in mobility differentials of roughly 3.5 percentage points.Standard and more recently developed RKD robustness checks show that our results resist irrespective of the bandwidth choice, with stronger effects holding in the proximity of the cut-off and the coefficient stabilizing with distance from the threshold. We show that municipal features that may affect mobility are smooth in a neighborhood of the threshold point. A placebo analysis in the spirit of the permutation test of The heterogeneity of the effects suggests that the impact of transfers on compliance is driven by the improvement in the fairness of the pandemic policy response. As civic-minded citizens have a stronger propensity for reciprocity in their relationship with the state , we testOur work relates to several strands of literature. First, we connect to studies explaining that compliance results from reciprocal obligations tying citizens to institutions . We provWe also contribute to the growing body of research analyzing the drivers of social distancing such as civic capital , social Finally, we relate to the COVID economics literature by analyzing the outcomes of policies intended to mitigate the pandemic economic disruption. Previous research addresses the impact of fiscal support for payroll and fixed costs  and tracThe remainder of the paper is organized as follows. 2In this section, we first provide some background . We then2.1On March 9, 2020, Italy was the first Western democracy to impose a national lockdown, requiring the confinement of the population at home. Authorities closed schools, restaurants, and non-essential shops and banned any outdoor activity, including walking far from home. Citizens could only leave their houses for a handful of reasons— for example, to go to the supermarket or the pharmacy—and needed to carry a document stating the reason they were outside.de facto the most substantial suppression of constitutional rights in the history of the Republic, undermined the incumbent government’s popularity  increased by about 2,953% with respect to April 2019. According to the Italian National Institute for Social Security , 51% of Italian firms, accounting for 40% of the private sector employment, adopted short-time work schemes in March and April 2020. Their employees reduced the hours worked by about 90% and experienced a 27% loss in their gross monthly wage  with the aim of preserving employment and income levels. The Decree temporarily banned layoffs, extended unemployment benefits for employees in every productive sector independently of business size, introduced a lump sum transfer targeted at self-employed and seasonal workers, and provided wage compensation for workers facing an involuntary reduction in working hours . In late May, after lifting most of the restrictive measures, the government passed a new 155 billion-euros stimulus package (Relaunch Decree on May 15), which reinforced and extended many of the Cura Italia measures, and introduced new transfers schemes to support families and businesses.To soften the economic consequences of restrictive measures, the government initially launched a 25-billion-euros package  was distributed to municipalities proportionally to their population. The remaining amount (Quota B) was allocated as a function of the difference between the municipality and the national per capita income in 2017, weighted by the population share.4Social distancing orders resulted in a dramatic increase in the demand for food and financial aid from the most disadvantaged groups. Towards the end of March 2020, tension mounted in more impoverished areas, with police patrolling supermarkets following a series of thefts. To cope with the mounting discontent, the government announced new relief measures lending € 4.3 billion  provided the general guidelines for the distribution of funds across municipalities.6For example, the municipality of Rome delivered the financial support to disadvantaged households that could not afford their basic needs and were not entitled to other kinds of transfer. Households with (strictly) less than three members were entitled to food stamps for an overall value of 300€, those between three and four members received food stamps for 400€, and families larger than five received 500€.7The municipality of Milan adopted similar criteria and delivered a 150€ voucher to households with up to three members and a 350€ voucher to families with more than three members. Potential beneficiaries were then ranked based on the criteria we show in The municipality of Naples allocated food stamps weekly. Each voucher amounted to 100€, for a total amount of 300€ over three weeks. Beneficiaries had to spend the 100€ voucher in a single shot to avoid repeated visits to supermarkets and limit social contacts.In principle, municipalities above the threshold, receiving higher resources, could allocate the extra funds to increase the scheme coverage or the voucher value, or both. However, the available evidence suggests that the municipalities in the neighborhood of the cut-off adopted similar allocation criteria. To give an example, we show in The criteria were similar, with a one-member household receiving food stamps for 150€, a two-member household receiving 250€, and a three-member family receiving 300€ in the municipality above the threshold and 325€ in the one below the threshold. Overall, the aid scheme succeeded in giving financial support to the families in need. Municipalities only slightly differentiated the value of vouchers and the population coverage. Eligibility was subject to income testing, and food stamps requests were subject to random ex post controls. Anecdotal evidence suggests that all the assigned funds were effectively distributed by local administrations and spent by beneficiaries. After its termination, the program was refunded twice in December 2020 and February 2021.82.3In this section, we describe the kink schedule in the distribution of funds. To reconstruct the allocation mechanism, we combine information about the amount received by each municipality under the two quotas, provided by the Civil Protection Department, with data on 2017 income taxes aggregated at the municipality level, provided by the Department of Finance.9A and B:We compute the municipal per capita income, Putting the two quotas together, the per capita amount of transfers received by municipality The above formula describes the kinked policy schedule. Below the cut-off, We compute the parameters of the kink design Having defined the parameter In As expected, the kink schedule identified by Importantly, since the national-municipal income gap is expressed in € -thousands, the slope coefficient . A further decline occurred after March 21, when the government tightened confinement measures by shutting down all non-necessary businesses and industries. The lockdown formally ended on May 4, but pre-crisis levels were reached only towards the end of May. The series also follows clear weekly patterns, with working days showing higher mobility and downward peaks representing the substantially smaller movements on the weekends and Easter holidays.3In this section, we first describe our regression kink design for assessing the impact of the aid program on mobility across the Italian municipalities (3.1). Then, we describe our estimation sample and the covariates we control for in the empirical analysis (3.2).3.1As described in the previous section, the per capita amount of transfers above the cut-off point is a deterministic linear function of the difference between the national and the municipal income.We exploit the exogenous change in slope at the cut-off point (kink) to identify the causal effect of transfers on compliance with stay-at-home orders, as measured by the mobility index described in Given the linear dependence of the per capita amount of transfers and municipal income above the cut-off point, an OLS estimate of the relationship between mobility and transfers would likely be biased, because municipal income may be correlated with unobservable determinants of mobility.Regression Kink Design (RKD) firstly introduced by To solve this potential endogeneity issue, we adopt the standard Define as In our case, the quantity at the denominator of We estimate It is important to stress that, by assumption, our RKD setup identifies the treatment effect of the transfers on mobility only in a neighborhood of the cut-off. Differently from a standard Regression Discontinuity Design (RDD) setting, the treatment in the RKD is inherently continuous. This implies that above the the cut-off, it is not the probability of being treated that changes. Instead, what changes is the intensity of the treatment. This difference has implications for the interpretation of the coefficient of interest, The In 3.2We start with 7257 municipalities in the 17 (out of 20) Italian regions for which it was possible to match the data on the aid program transfers with municipality tax records.We aggregate daily mobility data for each municipality at the weekly level. We keep only municipality-week observations for which the daily mobility index is non-missing for the entire week. We also drop provinces where all municipalities are either all above or all below the cut-off of the kink design. After putting together the municipality-week panel, the final sample consists of 47997 municipality-week observations for 5333 municipalities observed between the 10th week (March 9–15) and the 18th week 18 (May 4–18).Finally, we complement our dataset with a set of municipality-level covariates that could affect mobility but have no relationship with the kink, as confirmed by the results of the balancing test.We use ISTAT 2011 Census data to control for municipalities’ population and degree of urbanization, as people living in small towns may have to travel higher distances to reach the workplace or satisfy basic needs.Since the essential activities that remained open during the lockdown are a source of mobility, we also control for the number of active firms and the number of workers in 3-digits NACE categories using data from the 2018 ISTAT register of Active Enterprises (ASIA - Enterprises). Specifically, we compute an indicator of firm density as the number of firms divided by the municipality’s surface. We also build an indicator of the share of essential workers over the population. We define the essential NACE categories following the classification proposed by Recent economic studies suggest that compliance with confinement measures also is a matter of social capital . Healthy14Finally, we control for the change in mobility during the first week of the lockdown, which provides the baseline level of compliance observed in each municipality.3.3As suggested by The second testable condition requires the conditional distribution of the pre-determined covariates to be smooth around the cut-off point. To test for the smoothness of the first derivative of covariates’ conditional expectation functions, we estimate separate kink regressions for each municipality-level covariate we use in our preferred specifications, using both a linear and a quadratic polynomial. The results in 4We first present our results about the impact of the relief program on compliance across Italian municipalities 4.1We start by providing a graphical representation of the cross-sectional relationship between mobility and the running variable of the kink design, i.e., the gap between the national and the municipal per capita income. While, as described in the previous section, the kink parameter The first thing to notice in More importantly, a change in slope is visually evident at the cut-off. The negative change in slope suggests that the treatment negatively affects mobility across municipalities.We now turn to the estimates of the treatment effects. The two lockdown weeks before the program announcement (week 11 and week 12) serve as a placebo test in the spirit of According to our main specification  approved on April 24 replaced the transfers scheme addressed in our empirical analysis with new relief measures following different allocation rules. As the cut-off ceased to play a role in the allocation of funds, we cannot observe the treatment effects in its neighborhood anymore. In addition, the government lifted most restrictions from May 4  of placebo estimates. Results of this procedure are shown in Finally, we conduct an exercise similar in spirit to the “Difference-in-Discontinuity” (Diff-in-Disc) approach proposed by 16Notwithstanding these differences, we adapt the “Diff-in-Disc” approach to the RKD setting to capture potential unobservable confounders that may affect our estimates. For this purpose, we jointly estimate our treatment effects in a pooled regression considering all weeks 10–18, i.e., the entire observation period. In this specification we exploit the availability of repeated observations for each municipality by including municipality fixed-effects and the interactions between the covariates used in the main specification and week indicators. Week 12 is used as baseline. In order to include just observations close to the cut-off point, the bandwidth used is the CCT optimal bandwidth for week 13.4.3Quota B received 11 percent additional resources for any given 1,000€ deviation from the threshold point. Our empirical analysis shows that these extra funds translated into an increase in compliance – i.e., an increase in the mobility differential relative to the baseline – of roughly 3 percentage points, so that the increase in transfers led to a 5 percent reduction in mobility.Municipalities entitled to the program’s Although the program was not intended to nudge compliance with shelter-in-place orders, improving the fairness of the COVID-19 policy response may have strengthened its overall legitimacy, helping citizens to internalize the societal benefits of restrictive measures. In this section, we delve deeper into the transmission mechanism of the effect and provide evidence suggesting that the fairness channel is empirically relevant.Many authors connect the willingness to comply with rules with the belief that policy actions are appropriate and fair, as if a “social contract” binds citizens to obey their polity’s law e.g., . EspeciaHowever, citizens are not necessarily all alike in their approach to reciprocity and compliance. Following this line of reasoning, we expect civic culture to catalyze the impact of relief policies, with more civic municipalities manifesting a stronger reaction to transfers and, therefore, a higher compliance. We test for this mechanism by exploiting several sources of municipality-level information to build a battery of civic capital indicators.In line with the abundant literature on civic capital, we first use census data to construct a municipality-level indicator of the density of voluntary associations e.g., . In thei5Emergency rules enacted to tackle extraordinary threats to public welfare can cause severe welfare losses for specific strata of the population, thereby undermining the overall fairness of the crisis policy response.Since the beginning of the coronavirus crisis, confinement orders and mobility restrictions cause tremendous economic losses, worsen poverty and inequality, and threaten the social contract between citizens and the state. The economic hardship and the suppression of civil liberties can be unbearably unfair to impoverished individuals who cannot work from home and need to carry on income-generating activities.In this paper, we exploited a sharp kink design in the allocation of aid funds across Italian municipalities to study the impact of relief policies on compliance with confinement measures. We provided robust evidence that, after the introduction of the program, compliance increased with the resources allocated to each municipality. The effect is economically sizeable and resists typical and more recently developed RKD robustness checks, such as bandwidth changes, with stronger effects holding in the proximity of the cut-off and the coefficient stabilizing with distance from the threshold.Overall, the evidence on the relationship between poverty and social distancing in the coronavirus crisis points out the importance of tuning relief programs also in light of their potential impact on compliance. Programs targeted at individuals with lower incentives to comply may play a significant role in ensuring the observance of emergency rules. On a more general note, our evidence is consistent with the public economics literature that investigates the moral and social dynamics of tax compliance, suggesting that the perception of the political process as fair results in a stronger willingness to contribute to the welfare of the community .Our results put forward actionable insights for policymakers. The finding that compliance was lower in poorer municipalities suggests that low-income agents face the most challenging difficulties in coping with stay-at-home orders. However, improving the fairness of the crisis policy response and alleviating the essential needs of economically disadvantaged groups can nudge social distancing substantially. This result suggests that relief programs must also be designed in light of their potential impact on compliance with emergency measures. Targeting relief measures at economically disadvantaged groups could more effectively support compliance than indiscriminate fiscal stimuli. More in general, compensation programs can improve the perceived fairness of the crisis policy response, thereby nudging people to internalize restrictive measures’ objectives and making them more willing to voluntarily bear sacrifices for the common good.The authors declare no conflict of interest.


In the complex and variable marine environment, the navigation and localization of autonomous underwater vehicles (AUVs) are very important and challenging. When the conventional Kalman filter (KF) is applied to the cooperative localization of leader–follower AUVs, the outliers in the sensor observations will have a substantial adverse effect on the localization accuracy of the AUVs. Meanwhile, inaccurate noise covariance matrices may result in significant estimation errors. In this paper, we proposed an improved Sage–Husa adaptive extended Kalman filter (improved SHAEKF) for the cooperative localization of multi-AUVs. Firstly, the measurement anomalies were evaluated by calculating the Chi-square test statistics based on the innovation. The detection threshold was determined according to the confidence level of the Chi-square test, and the Chi-square test statistics exceeding the threshold were regarded as measurement abnormalities. When measurement anomalies occurred, the Sage–Husa adaptive extended Kalman filter algorithm was improved by suboptimal maximum a posterior estimation using weighted exponential fading memory, and the measurement noise covariance matrix was adjusted online. The numerical simulation of leader–follower multi-AUV cooperative localization verified the effectiveness of the improved SHAEKF and demonstrated that the average root mean square and the average standard deviation of the localization errors based on the improved SHAEKF were significantly reduced in the case of the presence of measurement abnormalities. The Global Navigation Satellite System (GNSS) is often unavailable in deep water environments, and inertial/dead reckoning (DR) navigation technology is usually considered. The Doppler velocity log (DVL) can measure the velocity of autonomous underwater vehicle (AUVs) and it can carry out autonomous navigation and localization without installing additional sensors and external reference information when the DVL is combined with the Inertial Navigation System (INS). In a multi-AUV formation, there will be localization error growth over time for the AUVs, which are only equipped with inertial/DR equipment. We can improve the localization accuracy of the whole system by improving the localization accuracy of each AUV, but there is a great sacrifice in cost. Therefore, researchers have proposed leader–follower multi-AUV cooperative localization methods ,2,3. AUVlth leader AUV) and a follower AUV (the jth follower AUV) are analyzed by a simplified level equation under reasonable assumptions, and the non-rotating east, north, and up (ENU) geographic reference system The navigation motion of AUV formation in a GNSS-denied environment is a complex three-dimensional process. If the formation adopts the leader–follower multi-AUV structure, the system includes multiple leader AUVs and follower AUVs; a leader AUV and a follower AUV exchange and share information through underwater acoustic communication equipment . After tx, y respectively represent the coordinates of the longitude and latitude position of the AUV converted into the geographical coordinate system, and V, Assuming that the depth of an AUV can be measured directly and accurately by depth gauge, the discrete-time nonlinear kinematics equations of an AUV are as follows:jth follower AUV at time k are defined as follows:T” represents the transpose mode of the vector matrix.The state vector The observed values of the control input are as follows:jth follower AUV can be expressed as follows:When lth leader AUV and the jth follower AUV. It was assumed that the forward movement direction of the follower AUV was consistent with the positive direction of the lth leader AUV at time k is k are as follows:jth follower AUV and the lth leader AUV are as follows:jth follower AUV and the lth leader AUV. It is assumed that In this study, the cooperative localization information mainly included the relative distance and relative direction angle between AUVs and the position coordinates of the leader AUV. The follower AUV established the measurement equation by obtaining the cooperative localization information shared by the leader AUV. jth follower AUV to obtain the following [The observed value ollowing :(7)r⌢k,xIf  is substjth follower AUV is established as follows:jth follower AUV as follows:From  and 9),,9), we oThe EKF algorithm is used for state estimation. The steps in a single filtering cycle are as follows.Step 1 (state prior estimation):Step 2 (the innovation sequence update):f with respect to f with respect to Step 3 (error covariance updating of state a priori estimation):h with respect to Step 4 (filter gain update):Step 5 (state a posteriori estimation update):Step 6 (error covariance of state a posteriori estimation):Ref.  analyzesRefs. ,14 studiAll the above studies were under the steady state of the system. We know that the noise error of an AUV sensor is related to the process noise error and measurement noise error in the cooperative localization algorithm based on an EKF, but there are differences between process noise error and measurement noise error. Through error uncertainty propagation analysis ,13,14, iThe Sage–Husa adaptive filtering algorithm is an improvement based on the classical Kalman filtering algorithm. The Sage–Husa filter adaptively estimates system process noise and measurement noise online, including the mean vector  follows ,15:(17)qSince the innovation vector affects the calculation of We focused on finding a method to detect an anomaly and re-estimate the statistical characteristics of the measurement noise when the measurement noise was abnormal, which is discussed next in this paper.This innovation can reflect the relationship between the observed value and the estimated value of a measurement model, so it is often used to measure the filtering performance of a Kalman filter ,17. Accom is the degree of freedom, and The probability density function of the innovation can be written in the following form:If there are some observed outliers in the measurement model, or the measurement noise is affected by other noises and no longer conforms to the Gaussian distribution,  and 19)19) will m if the assumption holds. The significance level is set as It is generally believed that we should pay attention to the position of recent measurements in the current filtering in order to prevent filtering divergence; hence, we need to pay special attention to the innovation sequence ,19,20,21In the filtering process of the improved SHAEKF, we used  to judgeThere is a negative sign in the above formula. In order to prevent the measurement noise estimation from losing its positive definiteness, the measurement noise covariance matrix Replace If  is substIt is easy to verify that the mean value of The suboptimal MAP estimates of the measurement noise covariance matrix are obtained from  and 26)26):(27)RConsidering that b is the fading memory factor, b was larger, From , the estIn addition, considering that the state posterior estimation In order to verify the feasibility of the improved SHAEKF algorithm, a leader AUV and a follower AUV were simulated in this study. Monte Carlo method was used in the simulation, and the simulation parameters were set as shown in We designed the AUVs to move along a straight line or a curve at a uniform constant speed, the actual trajectory and the DR calculation results of each AUV in a simulation test of the whole simulation are shown in As can be seen from It can be seen from In order to evaluate the performance of the improved algorithm more effectively, we introduced the average root mean square of localization error (ARMSE) and the average standard deviation of localization error (ASDE). ARMSE and ASDE can be defined as follows:As can be seen from The conventional EKF was only the best estimator when some preconditions were true, for example, when the Gaussian distribution measurement noise had a completely known mean and covariance. However, in the practical application of multi-AUV cooperative localization, the actual observation might be vulnerable to outliers. Therefore, a leader–follower multi-AUV adaptive cooperative localization filtering method based on innovation was proposed in this paper. Simulations showed that the improved SHAEKF could effectively resist the influence of measurement anomalies. Although the improved SHAEKF could ensure the filtering fault tolerance and localization accuracy of a leader AUV and a follower AUV in the case of abnormal measurement, we did not further study the influence of abnormal process noise on cooperative localization. In the future, we will further study the cooperative navigation and localization of multiple leader AUVs and multiple follower AUVs and expand from a two-dimensional plane to a three-dimensional space. All AUVs in the group were regarded as a unified system to improve the navigation and localization system model. AUVs exchanged their information, including measured and estimated position data, we then proposed an interactive multi-model fusion estimation method for future work to correctly estimate some parameters that could not be accurately obtained in the AUV dynamic model, including multi-observation information and multi-motion model information, so as to increase the robustness of collaborative navigation and localization.


In this paper, the design of low probability of intercept (LPI) radar waveforms considers not only the performance of passive interception systems (PISs), but also radar detection and resolution performance. Waveform design is an important considerations for the LPI ability of radar. Since information theory has a powerful performance-bound description ability from the perspective of information flow, LPI waveforms are designed in this paper within the constraints of the detection performance metrics of radar and PISs, both of which are measured by the Kullback–Leibler divergence, and the resolution performance metric, which is measured by joint entropy. The designed optimization model of LPI waveforms can be solved using the sequential quadratic programming (SQP) method. Simulation results verify that the designed LPI waveforms not only have satisfactory target-detecting and resolution performance, but also have a superior low interception performance against PISs. Low probability of intercept (LPI) radar waveforms have been developed to combat passive interception systems (PISs) for several decades ,2,3. ComIn frequency amplitude adjustment modeling, it is crucial to establish the performance metrics of both the radar and the PIS. For radar detection performance, besides metrics such as output signal-to-noise ratio (SNR), relative entropy, and mean square error, the method of maximizing mutual information has been widely used in optimal radar waveform design  and the entropy of a Gaussian random variable, the terms in Equation (1) can be calculated asThus, the KLD between In the design of LPI radar waveforms, the resolution performance should also be considered, which is another quite important performance measure for radar. In this paper, we use autocorrelation to describe radar resolution performance, which is a more concise way of representing the ambiguity function. For time, the worse the autocorrelation is, the better the range resolution is. Correspondingly, for frequency, the worse the autocorrelation is, the better the velocity resolution is. Next, we will utilize joint entropy to describe the autocorrelation.Suppose the samplings of the transmitted waveform Since the joint probability density function of these samples is If the designed waveform has a perfect resolution performance, then the samples are independent. It means that the joint entropy is equal to the sum of the entropy of each sample, that is: From Equation (7), we find that the smaller the value of the metric, the better the resolution performance of the transmitted waveform, and when the transmitted waveform is white Gaussian noise, the value of the metric For frequency, resolution performance has the same computational procedure. We only need to substitute It is a common view that white noise is the best LPI waveform. The closer the distance between intercept signal ce, etc. ,16,17. TThe KLD between When Since the KLDs LPI radar waveform design is a trade-off between the performance of radar and of PISs, which is to maximize the detection and resolution performance of radar and minimize the interception performance of PISs. In fact, the primary task of the emitted waveform is to accomplish target detection and resolution. The designed radar waveform should be considered for its LPI capability under the condition of meeting radar performance. Therefore, we minimize the KLD In order to achieve the optimal solution of Equation (11), the discrete form of the optimization problem first needs to be obtained, which can be written asWhen An efficient method for solving nonlinear constrained optimization problems is the combination of the interior point and sequential quadratic programming (SQP) methods. Here, we use the algorithm proposed by Byrd  to solveIn this section, several simulation experiments are provided. The simulation parameters are: In order to verify the superiority of our proposed LPI radar waveform design method, SNR loss is treated as a performance degradation metric for radar and the PIS, which can be defined as u et al. , which jThe baby-blue dotted lines (only one-sided PSDs are shown) in For experiment 1, since For experiment 2, since Since the PIS has no prior information about the transmitted waveform, a reduction in peak power may have a serious effect on its output SNR. In contrast, radar can reduce the effect significantly using the matched filtering technique. As shown in experiment 2 of Since the LPI waveforms (which are designed to minimize the interception performance of a PIS with a certain loss of radar detection performance) do not have good range and velocity resolution, we also need to further design LPI radar waveforms to satisfy a given requirement of radar resolution performance. In this subsection, we further optimize the LPI radar waveforms, which are designed in The one-dimensional zero-delay and zero-Doppler cuts of the ambiguity function of these optimized LPI radar waveforms are shown in γ=0.0001  and γ=0.γ=0.0005 , and difIn order to verify the superiority of LPI performance of the designed radar waveforms, we calculate the performance degradations In response to the LPI requirements of modern military radar, waveforms with a fixed average power constraint have been designed from the perspective of information flow to minimize the interception performance of a PIS (which is measured by the KLD in this paper) under the condition that both the detection performance and resolution performance of the radar make some concessions. In this paper, we presented a simple information theoretic metric to measure the resolution performance of radar by utilizing the joint entropy theory. Simulations verify the superiority of the designed radar waveforms in radar detection, resolution performance, and the LPI performance.


Existing detection methods face a huge challenge in identifying insulators with minor defects when targeting transmission line images with complex backgrounds. To ensure the safe operation of transmission lines, an improved YOLOv7 model is proposed to improve detection results. Firstly, the target boxes of the insulator dataset are clustered based on K-means++ to generate more suitable anchor boxes for detecting insulator-defect targets. Secondly, the Coordinate Attention (CoordAtt) module and HorBlock module are added to the network. Then, in the channel and spatial domains, the network can enhance the effective features of the feature-extraction process and weaken the ineffective features. Finally, the SCYLLA-IoU (SIoU) and focal loss functions are used to accelerate the convergence of the model and solve the imbalance of positive and negative samples. Furthermore, to optimize the overall performance of the model, the method of non-maximum suppression (NMS) is improved to reduce accidental deletion and false detection of defect targets. The experimental results show that the mean average precision of our model is 93.8%, higher than the Faster R-CNN model, the YOLOv7 model, and YOLOv5s model by 7.6%, 3.7%, and 4%, respectively. The proposed YOLOv7 model can effectively realize the accurate detection of small objects in complex backgrounds. An insulator is a special kind of insulation control and is essential electrical equipment in overhead transmission lines. In early years, insulators were mainly used for power poles and gradually developed into disc insulators, usually made of glass or ceramics, hung on one end of the connection tower of high-voltage power lines. They fill the role of electrical insulation and mechanical fixation in transmission lines . In addiAmong these defects, the most common faults are insulator damage and surface defects caused by pollution flashovers. The damage is mainly caused by insulator manufacturing defects, the combined action of various stresses, and other reasons. Surface defects are mainly caused by partial discharge in pollution flashovers. Pollution flashover means that pollutants are attached to the insulation surface, and soluble substances gradually dissolve in water under wet conditions, forming a conductive film on the insulation surface that reduces the insulation strength and increases the leakage current, resulting in partial discharge . AccordiThe traditional insulator-defect detection method mainly uses helicopter-manned inspection, field inspection, or traditional detection algorithms to analyze pictures taken by robots or drones . HoweverIn recent years, with the development of deep-learning theory and the improvement of computer performance, target detection algorithms based on deep learning have been widely studied because of their good generalization ability and cross-scene ability . Zheng eThe current research is mainly divided into two categories: the first is a two-stage object detection model represented by Region-based Convolutional Neural Networks (R-CNNs) , Fast ReCompared with the above algorithm, the YOLOv7 model proposed by Wang et al.  in 2022 Aiming at the above problems, this paper proposes an improved insulator-defect detection method based on the YOLOv7 algorithm. Firstly, to improve the accuracy and efficiency of detection, this paper uses the anchor box size obtained from the K-means++ clustering insulator dataset to replace the default anchor box size of YOLOv7. Secondly, the coverage of overhead transmission lines is vast and the background of the collected image data is relatively complex. The deep-learning object-detection algorithm must be able to eliminate the interference of the complex background. In view of the complex background of image data, the CoordAtt attention mechanism and HorBlock module are integrated into the original backbone network to enhance the network’s ability to extract image features and increase the network’s detection accuracy for small insulator defect targets. The SIoU regression loss function and focal loss classification function are introduced to improve the network convergence speed and detection efficiency and solve the dataset’s sample imbalance problem. Finally, SIoU-NMS is used to implement a new non-maximum suppression process to reduce the problem of false detection of insulators and insulator defects. Experimental results show that the improved network has a better detection effect on insulator defects in complex environments.There are few insulator-defect datasets published for overhead transmission lines, or even in the whole electric power field. In total, 1600 original images were captured from Baidu and Google or collated from public datasets . The resIn a deep-learning model, numerous data samples are needed for model training to reduce the over-fitting problem. In the model-training stage, the more sufficient and comprehensive the data collected are, the more significant the model recognition effect. Therefore, the number of samples is expanded by data augmentation. The data augmentation strategy adopted in this paper includes morphological operations such as angle rotation, saturation adjustment, image up and down flipping, and translation. At the same time, the model uses the Mosaic data enhancement method at the input end. The four defect images are spliced by random scaling, random clipping, and random layout, which can improve the model classification performance. The mixup data enhancement method is also adopted and the two images are interpolated proportionally to mix the samples. Even color space conversion is carried out, and the pictures’ hue, saturation, and exposure are changed, in order to minimize the over-fitting of the network and improve the generalization ability of the training model. The input to the model after a series of operations is shown in In addition to the above regularization techniques, this paper also adopts standard methods such as early stop, weight regularization, dropout, and batch normalization in the training phase to prevent overfitting of the model.At the same time, the Labelme tool is used to label the ground-truth box of the image, and the label category is divided into pollution flashover, damage, and insulator. Finally, the labeled insulator dataset is divided into training, verification, and test sets. There are 1600 picture samples in this experiment and the dataset was divided at a ratio of 7:2:1. The number and distribution of tags in the dataset were counted; the results are shown in In The detection framework of the proposed method in this article is shown in YOLOv7 uses the K-means algorithm to cluster the anchor boxes obtained from the COCO dataset by default and uses the genetic algorithm to adjust the anchor boxes during the training process. However, the K-means clustering algorithm’s convergence depends heavily on the cluster center’s initialization . TherefoThe traditional K-means algorithm selects multiple clustering centers at once, while the K-Means++ algorithm selects only one cluster center at a time. The improved method allows the random center point chosen to not just tend to the optimal local solution, but to come as close as possible to the optimal global solution.(1)x is the sub-target mark sample box, and c represents the center of the cluster;Randomly select a sample target box from the dataset as the initial cluster center and calculate the minimum intersection ratio distance (2)X is the total sample of the target marker frame;Calculate the probability (3)Repeat Steps 1 and 2 until all clustering centers are selected.(4)K is the number of anchor boxes with different sizes, and its value is determined by the number of anchor boxes of the detection model. Since the detection model in this paper contains three detection feature maps, and each feature map corresponds to three anchor boxes, Calculate the distance from each sample in the dataset to the cluster centers, divide the sample into the class corresponding to the cluster center with the smallest distance, and recalculate the cluster center of each category Specific steps are as follows:The small-sized anchor box corresponds to the final output of the 80 × 80 feature map, which is responsible for detecting small-sized objects. The medium-sized anchor box corresponds to a feature map with a size of 40 × 40, which is responsible for detecting medium-sized objects. The large-sized anchor box corresponds to a feature map with a size of 20 × 20, which is responsible for detecting large objects in the image.The inspection model for insulator defects in this paper is shown in First, the input side performs data enhancement operations such as Mosaic, random cropping, and scaling on the image to avoid overfitting. The backbone part comprises CBS, MP, and ELAN modules. The MP module consists of maxpooling and CBS modules. The CBS module consists of regular convolution, batch normalization, and activation functions. The difference between the CBS module and a traditional CNN network is that the Leaky ReLU function replaces the activation function with the SiLU function. The ELAN module can control the shortest and longest gradient paths, and deeper networks can learn and converge efficiently. The ELAN module is also composed of several CBS modules. The input feature map does not change the size of the feature map after passing through the ELAN module, but only changes the number of output channels at the end.The improved network adds the HorBlock module between the third and fourth CBS modules in the backbone section. It adds the CoordAtt attention mechanism between the original backbone and neck sections. The improved network can make the model pay more attention to valuable content and locations in the input image samples. Feature information can be effectively extracted for small targets and targets with complex backgrounds to improve detection accuracy.The neck consists of a path aggregation network PAN (path aggregation network) and a feature pyramid network FPN (feature pyramid network). After the 32-fold downsampling feature map output by the backbone passes through the SPPCSP module, the number of channels changes from 1024 to 512. Then, the feature map performs feature fusion according to the top-down strategy and the bottom-up method. The structure of PA-FPN efficiently fuses feature maps at different levels. Compared with YOLOv5, YOLOv7 replaces the CSP module with the ELANC module, and the downsampling becomes the MP2 layer. After the PAFPN network, the network’s output is three layers of feature maps of different sizes. Finally, the network outputs the prediction results through the RepC and Conv modules in the head part.After the network passes through the third CBS module of the backbone, the size of the feature map is further reduced by half and the feature information is greatly reduced. To retain the nonlinear ability, establish long-range attention, reduce the phenomenon of gradient dispersion, and improve the detection of insulator defects. HorBlock blocks consisting of gnConv  recursivThe gnConv module is built using standard convolution, linear mapping, and element multiplication, but with input adaptive spatial blending capabilities similar to self-attention. Layer norm calculates the mean and variance of all parameters in all channels and then normalizes them. The main structure of gated convolution is not very different from a standard CNN, but the gating mechanism is introduced in the convolutional layer. First, the number of feature channels is adjusted by two convolutional layers. Next, the output feature map with separable convolution is divided into multiple parts, and each part is multiplied element by element to obtain the output feature map. Recursion here is the constant multiplication of elements, through which higher-order information can be saved.Due to the complex and changeable environment in which the insulators are located, to improve the characteristic expression ability of the model on insulators and defective parts, an attention mechanism module is added to the end of the YOLOv7 backbone network.Attention mechanisms can generally be divided into channel attention mechanisms, spatial attention mechanisms, and a combination of the two attention mechanisms. Traditional attention mechanism modules such as Squeeze-and-Excitation attention (SE)  and ConvThe Coordinate Attention mechanism  capturesThe CoordAtt attention mechanism framework diagram is shown in The input is pooled horizontally and vertically to preserve the long-distance dependencies of both directions. The information in both directions is then stitched. Next, the feature map is split and convoluted to focus on both horizontal and vertical directions. The two-part feature map output by the module can be pinpointed to the row and column of the target object that we are interested in.The loss function of the YOLOv7 model consists of three parts: localization loss Set the confidence threshold and SIoU threshold;(2)Calculate the confidence level of all preliminary prediction boxes output by the network model, put the preliminary prediction boxes whose confidence level is higher than the confidence threshold in the candidate list, and sort the preliminary prediction boxes in descending order of confidence from high to low in the candidate list;(3)Take the initial prediction box with the highest confidence from the candidate list, save it to the output list, and delete the initial prediction box from the candidate list;(4)Calculate the cross-merger loss of the initial prediction box with the highest confidence obtained in the previous step and all the other preliminary prediction boxes in the candidate list, and delete the initial prediction box whose cross-merger loss is higher than the set SIoU threshold from the candidate list;(5)Repeat Steps 3 and 4 until the candidate list is empty;(6)Use the preliminary prediction box in the output list as the final prediction box.The improved non-maximum suppression algorithm of SIoU-NMS is used to filter the preliminary prediction box of the image output to be recognized, and the final prediction box is obtained by the following steps:To verify the effectiveness of our model, we conducted neural network training and testing with the following computer-configuration parameters and super-parameter settings shown in .After training the model, we visualized the feature map of the trained model . The infFrom the visual feature map after the first convolution layer, we can see that the features extracted from the model have particular emphasis; some focus on edge features and some on overall features. Of course, this is only the feature map after the first convolution layer. Compared with the deeper features, the shallow features are mostly complete, while the deeper network features will be fewer. From the feature map output after the backbone, we can see that adding an attention mechanism will play a good role in strengthening the feature map and suppressing some unnecessary features. The feature maps corresponding to the last three layers are used to detect large, medium, and small targets, which significantly improves the multi-scale detection capability of the model.After the target is detected, the model also needs to carry out classification tasks. To comprehensively and objectively evaluate the performance of our model in this paper, we used a confusion matrix Shown in  for compTP represents correct detection—the prediction of the model is positive and the actual value is also positive. FN represents detection error—the prediction of the model is negative and the actual value is positive. FP represents detection error—the prediction of the model is positive but the actual value is negative. TN represents correct detection—the model prediction is negative and the actual value is also negative.The expressions of precision and recall are as follows:Mean average precision (mAP), which depends on precision and recall, is used to measure the accuracy of the model.To verify the effectiveness of the improved method proposed in this paper, we performed comparative experiments on the setting of super-parameters of the anchor box, the selection of the loss function, and the selection of attention mechanisms. The baseline of each experiment is the YOLOv7 model. Because this paper’s primary goal is to improve detection accuracy, our experiment here mainly uses recall, precision, and mAP to evaluate the effect.First, we determined the nine parameter values of the anchor box. For the generation of the anchor box, we used the K-means algorithm to cluster the anchor box of the COCO dataset and K-means++ clustering to compare the parameters. It can be seen from the results shown in  that allThen, we made a comparison of different loss functions. YOLOv7 uses CIoU as its loss function. We compared the performances of three methods: GIoU, CIoU, and SIoU (ours); the results are shown in As seen from In order to add appropriate attention mechanisms to the network, this paper added SE, CBAM, and CoordAtt attention mechanisms to the backbone layer and feature fusion layer of the model for training and comparison. The results are shown in The effect on model detection caused by different attention mechanisms added to the backbone is different. Not every kind of attention will improve the model’s performance after joining the network. Although SE attention ignores location information, it also considers channel attention. From the results, the performance effect of the model is reduced after SE attention is added to the backbone. CBAM tries to use location information by reducing the channel dimensions of the input tensor and then calculating spatial attention by convolution. However, convolution can only capture local relationships; it cannot model long-term dependencies crucial to visual tasks. After CBAM attention is added to the backbone, the performance effect of the model is improved, but it is not apparent. The CoordAtt attention mechanism embeds location information into channel attention, capturing remote dependencies in one spatial direction and keeping accurate location information in another. According to the results, the mAP increased by 1% after adding CoordAtt to the backbone. This proves that using the CoordAtt attention mechanism can make the network model notice the target in a broader range and improve the detection ability of the network.Ablation experiments were carried out to verify the positive impact on the network of the improved strategy proposed in this paper. The improved strategy proposed in this paper was trained on the insulator dataset. The experimental ablation results are shown in The first row in the table is the detection result of the original YOLOv7 network. It can be seen from the above table that when the HorBlock module and CoordAtt module are added to the original network, mAP@0.5 and accuracy are increased by 1.3% and 1.1%, respectively, compared with the original YOLOv7 without any improvement strategy. When YOLOv7 uses the K-means++ algorithm to cluster anchor boxes generated by insulator datasets, the positioning accuracy is improved to 3.6% higher than the original YOLOv7 algorithm. In addition, because the K-means++ algorithm does not increase the number of layers and parameters of the network, it will not reduce the model’s speed. Moreover, K-means++ does not have the problem of significantly affecting the initial value selection, which can improve the speed of model border regression. Using the improved strategy of SIoU+NMS, precision increased by 2.4% and mAP@0.5 increased by 1%.Combining the above three groups of improved methods, it can be found that the combined improved algorithm has the best effect; the detection accuracy can reach 94.9% and mAP@0.5 can reach 93.8%, which can meet the requirements for detection accuracy on insulator images.Precision and recall cannot be used as the only indicators to measure the model’s performance, as they may lead us to misunderstand the model’s performance. Therefore, we further use a PR curve to measure the model’s performance. The PR curve comprehensively considers the precision and recall rate of each category detected by the model.The PR curve of this model is shown in The ablation experiments can only prove that the improved strategy in this paper is effective compared with the original algorithm, but whether it can reach an advanced level needs to be proved. Therefore, under the same experimental conditions, a series of comparative experiments were carried out on insulator datasets between the improved method and the current mainstream target detection method.The comparison of the training results of different models is shown in Compare the loss function curves during model training; Finally, Based on the comparison and analysis of the above series of experiments, it can be concluded that the improved YOLOv7 algorithm proposed in this paper has obvious advantages in detection accuracy. Although the speed is decreased to a certain extent, it can still meet the real-time requirements of insulator-defect detection in practical engineering.To better verify the generalization ability and robustness of the model in this paper, we specifically selected small targets and targets in complex environments in the test set for testing. In the contrast-detection experiment, to verify that the model in this paper is more suitable for insulator-defect detection, we also purposely add the comparison of detection results of the YOLOX model. The detection results are shown in In conclusion, the results of ablation and comparison tests show that the strategy in this paper has significantly improved the accuracy of insulator-defect detection.Dian et al.  previousThe improved strategy proposed in this paper provides more possibilities for small-target detection such as insulator defects. In the future, this model can also be applied to various small-target detection scenarios in agriculture and industry. Finally, the improvement of this paper is mainly in the backbone of the network. The detection head is also important for model fusion features. We plan to expand our research in the future to understand the network model more fully.This paper proposes an improved YOLOv7 insulator-defect detection method, which can accurately identify insulators and their defects in transmission line images with complex backgrounds. The experimental analysis proves that the anchor box generated by clustering the target box of the insulator dataset with K-means++ can improve the detection accuracy and effect. Combining the CoordAtt attention mechanism and HorBlock module in the network can increase the expression ability of the feature graph, optimize the feature representation of the insulator-defect target, and improve the detection effect of the insulator-defect target. Finally, SIoU, the loss function, introduces the concept of the angle between the real box and the predicted box to help calculate the distance between the two boxes, accelerating the network’s convergence. By adding the above strategies, the improved model increases recall and mAP@0.5 by 2.5% and 2.7%, respectively, compared with the original network. In addition, the detection speed of the model is still 91 fps, which can meet the needs of real-time high accuracy. Compared with other models, this method has obvious advantages.There are still some improvements to be made. At present, the insulator defects in the dataset are external contour damage, and there is no image dataset of internal crack defects of insulating materials. Suppose that an internal crack defect in the insulating material shows some characteristics on the outer surface of the insulator. We will further improve the dataset to detect insulator defects in that case.


The use of the tension band technique for patellar fracture fixation has been associated with a loss of the rigidity of the construct after cyclic loading. Biomechanical studies have shown the biomechanical superiority of the crossed pin configuration relative to the traditional parallel one. Here, we describe a modified tension band technique that involves the use of crossed pins and a figure-of-eight passed as close to the bone as possible through a lateral parapatellar approach. The basic surgical technique and our case series are reviewed. The tension band technique relies on the principle that applying an implant, such as a wire or a plate, on the tension side of the bone results in the conversion of the tensile forces into compression forces, provided that the compression cortex is sufficient . TensionThe patellofemoral joint is a highly complex structure. First, the contact area between the patella and the femoral condyles increases and moves proximally during flexion . Second,Here, we describe a modified tension band technique for the management of patellar fractures. The technique involves a crossed pin configuration and a lateral parapatellar approach.Surgical techniquePreoperative anteroposterior and lateral radiographs are obtained, as well as a CT scan if needed. The procedure is performed under fluoroscopy. The patient is placed in a supine position and a tourniquet is applied to the proximal thigh (surgeon’s preference). A lateral parapatellar approach is performed, in particular, an anterolateral approach is made Figure , followeSmall vertical incisions are made through the quadriceps and patellar tendons on the medial side to identify the k-wires. When identified, the k-wires are backed out to allow just enough length to allow the passage of a secure tension band wire. Tension band wire is then placed in the standard way but has to go through the tendons to minimize the potential of the tension band wire cutting through the tendon on tensioning. The author’s preferred method is to put the wire first on the proximal fragment from medial to lateral, followed by the distal fragment from lateral to medial. Appropriate management of the tension band wire is required to prevent unnecessary repetitions of the task. Tension band wire is tensioned using a standard tensioning method. When it is confirmed that the tension wire is in the appropriate place behind both k-wires on the medial side of the patella, both k-wires are bent, rotated into the correct position, and backed out to get the loop of the k-wires as close to the patella as possible. The same is repeated on the lateral side, with the main caveat that the k-wires should be cut at the appropriate length and bent directly into the most appropriate position, and that twisting of the wires will affect the position of loops on the medial side. Incisions in the tendons are closed with a reabsorable suture. The final reduction is confirmed by palpating the joint from inside through the lateral arthrotomy if the joint laxity allows. Finally, the position of the k-wires and the figure-of-8 are checked with the image intensified and the wound is closed in layers.Full weight-bearing is typically initiated immediately post-surgery. Patients have a hinged knee brace locked in extension for two weeks. The brace is opened in progressively increasing flexion two weeks post-surgery.Case seriesSix patients with patellar fractures were treated operatively with this technique. Four of the patients were male, and two of them were female. The mean age of the patients was 41.17 years (a range of 20-60). Five of the patients had comminuted fractures, and one of them had a transverse fracture pattern. There were no intraoperative complications. The average follow-up of the patients was 7.83 months (range 2-22). Radiographic union was achieved in all patients, and there were no infections. None of the patients complained of stiffness, anterior knee pain, or symptomatic hardware. One of the patients had an implant removed. This patient, however, had concomitant lower limb fractures and multiple operations in the following months. Representative X-rays of patients treated with the crossed pins tension band technique are shown in Figures The tension band technique has been associated with high complication rates and an early mobilization may require a more rigid construct. Several studies have shown a displacement in the fracture site after cyclic loading ,3, and tA biomechanical study by Baran et al. showed that for optimal stabilization, the tension force transfer should be done directly on the bone and that interposed tendinous tissue reduces stability . AccordiIn conclusion, the tension band technique for the management of patella fractures has been associated with many complications. In this study, we present a modified tension band method with a crossed pin configuration and through a lateral parapatellar approach. Although only a limited number of patients were treated with this technique, the short-term clinical and radiological outcomes are very promising. The crossed pin tension band technique follows sound biomechanical principles, is reproducible, and yields satisfactory outcomes.


The combination of advanced radar sensor technology and smart grid has broad prospects. It is meaningful to monitor the respiration and heartbeat of grid employees under resting state through radar sensors to ensure that they are in a healthy working state. Ultra-wideband (UWB) radar sensor is suitable for this application because of its strong penetration ability, high range resolution and low average power consumption. However, due to weak heartbeat amplitude and measurement noise, the accurate measurement of the target heart rate is a challenge. In this paper, singular spectrum analysis (SSA) is proposed to reconstruct the eigenvalues of noisy vital signs to eliminate noise peaks around the heartbeat rate; combined with the variational modal decomposition (VMD), the target vital signs can be extracted with high accuracy. The experiment confirmed that the target vital sign information can be extracted with high accuracy from ten subjects at different distances, which can play an important role in short distance human detection and vital sign monitoring. The combination of radar technology and the smart grid system has broad application prospects. The traditional inspection of the artificial power grid will threaten the life and health of inspectors in extreme weather such as thunderstorms. In today’s smart grid system, the airborne laser radar has been used for power patrol, and the relevant information of power lines is automatically extracted through the laser point cloud data , which nWith the development of wireless communication technology, the extraction of human respiration and heartbeat has entered the wireless era. Compared with the traditional contact vital sign monitoring technology, it can measure the target vital signs without knowing and comfort. Reference  proposedThe original vital signs signal cannot be directly obtained from the radar echo. Because there are direct waves reflected by static targets and they may have DC components in the radar echo, data preprocessing is required for the radar echo first. For the original vital sign signal, reference  proposedIn this paper, SSA is innovatively applied to reduce the noise of vital signs and eliminate noise interference, combined with the VMD algorithm to achieve high accuracy of target vital sign detection based on a UWB radar sensor. The main contributions are as follows: (1) Singular value decomposition (SVD) is proposed to adaptively implement UWB radar echo to eliminate static clutter and reduce echo noise. (2) Singular spectrum analysis (SSA) is proposed to eliminate noise peaks around the heartbeat rate. The experiment confirmed that the target vital sign information can be extracted with high accuracy from ten subjects at different distances, which can play an important role in human detection and vital sign monitoring.It is common knowledge that when the human body breathes, the chest cavity will continuously fluctuate periodically. However, the beating of the heart can also make the chest rise and fall slightly. By transmitting electromagnetic waves, the radar can detect the ups and downs on the chest caused by the breathing and heartbeat. It is mainly reflected in the changing distance between the antenna of the radar receiver and the chest cavity. The periodic change of this distance reflects the frequency of respiration and heartbeat. Therefore, non-contact vital signs can be extracted through the radar, as shown in The echo signal after data preprocessing can be expressed as:With the two-dimensional Fourier transform for radar fast-time In summary, fundamental and harmonics of respiration and heartbeat exist in the radar slow-time signal spectrum: For Equation (5), we discretize radar fast-time and slow-time, In the actual detection environment, the radar echo is more complex. In addition to the static clutter and vital signs mentioned above, it may contain a direct-current (DC) component. The appearance of the DC component is related to the base drift of the working temperature of the radar receiver hardware. Because both DC component and static clutter are constant, they can be removed by the same method. In order to extract the one-dimensional time domain vital signs, the preprocessing of radar echo is essential. Singular Value Decomposition (SVD) is an algorithm widely used in the field of machine learning. It is often used for matrix data compression, that is, to express the original matrix by factorization. Because the radar echo can be regarded as a two-dimensional matrix based on distance and time, SVD can be used to reduce its dimensionality—that is, to eliminate static clutter and reduce echo noise—and retain the original vital sign signals captured in the radar echo. The radar echo is decomposed by SVD:The singular values obtained by SVD correspond to the components in the radar echo matrix. Singular values have the following characteristics:Static clutter and DC correspond to a large singular value, usually only one, which is The singular value corresponding to the matrix noise is small, but the number is large, and is distributed in the lower right corner of the diagonal matrix.The size of the singular value corresponding to the vital signs signal is obviously separate from the static clutter and matrix noise, and it is distributed several times after the static clutter.Generally, the second singular value Zero the singular values in the diagonal matrix After filtering out static clutter and preliminary noise reduction in the matrix by SVD, the human vital signs signal can be considered to be the most energetic in the radar echo. The distance from the thorax to the radar antenna fluctuates around The analysis object of this algorithm is a one-dimensional time series, and the trajectory matrix is first constructed by lagging the original series and performing SVD on it. Then, the additive components of the signal are separated and divided into reconstructed original sequences according to the singular value size selection. The whole process is summarized in four parts: embedding, SVD decomposition, grouping and reconstruction.EmbeddingAssuming that the object of analysis is a one-dimensional finite time series: [Set SVD decompositionSingular value decomposition of the trajectory matrix GroupingThe grouping is the representation of the trajectory matrix ReconstructionFirst calculate the projection of the hysteresis sequence The window length Variational modal decomposition can decompose the original signal into a set of intrinsic mode functions (IMF) components with sparse characteristics by searching for the optimal solution of the constrained variational model. VMD is written as a constrained variational problem :(22)minuIn this chapter, we used radar to real test, and simulate that employees are in a sitting position and monitor their vital signs. We also analyzed the method and effect of radar echo preprocessing based on SVD proposed in this paper. The SSA-VMD method proposed in this paper is used to compare the extraction results of the vital sign signals extracted from the echoes with VMD ,16,17,18The Xethru X4M03 UWB radar module from Novelda was used to acquire human vital sign signals, and the subject sat quietly at about 0.6 m in front of the radar to simulate the employee’s attitude in a resting state and wore a contact finger clip measuring device with Chinese medical certification to acquire vital sign data as the reference standard value. The X4M03 module and the experimental scenario are shown in Import the original radar echo collected by the upper computer software Xethru Explorer into Matlab2018 and draw the energy map; static clutter exists at close proximity and significant undulating movements at a distance of 0.6 m, as shown in In this test, the contact finger clip measuring instrument synchronously detected that the human respiration was 16 times/min (about 0.267 Hz) and the heart rate was 90 times/min (about 1.5 Hz). In the spectrum of the sign signal, there were obvious peaks at 0.2652, 0.5304, 1.014 and 1.513 Hz, which were known as respiratory fundamental frequency, respiratory second harmonic frequency, respiratory fourth harmonic frequency and heartbeat frequency, respectively. It can be seen that there was a large amount of noise around the peak heartbeat rate, which seriously interferes with the accurate extraction of the heartbeat.VMD decomposition of the original vital sign signal is performed to extract the sign information. Ideally, the signals to be extracted are respiratory and heartbeat signals, and the modal number In addition to parameter As shown in Next, perform the SSA-VMD proposed in this paper to the original vital sign. According to the radar parameter sampling duration and sampling rate, as well as the SSA window length Therefore, the first 40 singular values are selected for vital sign reconstruction. The time-frequency domain of the reconstructed signal is shown in In order not to lose generality, this chapter conducts a comparison experiment on the accuracy of heartbeat frequency extraction based on the SSA-VMD method and the VMD method at different distances. The experimental subjects were ten healthy young people, all aged 22–24 years old. The distances were set to 0.6 m and 1.2 m, and five subjects were tested at each distance. The subjects sat quietly in front of the radar and wore finger clip detectors to obtain standard physical sign information for comparison with the radar data.The results of the experiment are shown in (1)The experimental analysis of the actual detected signals shows that the heartbeat frequencies extracted based on SSA-VMD benefit from the noise reduction of the original sign signals, and their spectral components are single and far less affected by noise.(2)The experimental data of multiple people under different distances of actual detection show that the accuracy of the heartbeat frequency extracted based on SSA-VMD is higher than that of the single VMD method, contributing to a more accurate heartbeat frequency extraction.In this paper, based on the detection of human vital signs by ultra-wideband radar, the SSA-VMD vital sign detection method is proposed for the existence of noise in the original vital sign signal, which seriously affects the accurate extraction of faint heartbeat frequency. The results are verified by actual detection findings as follows:


Wilson assumed that the ventricular gradient (VG) is independent of the ventricular activation order. This paradigm has often been refuted and was never convincingly corroborated. We sought to validate Wilson’s concept by intra-individual comparison of the VG of sinus beats and ectopic beats, thus assessing the effects of both altered ventricular conduction (caused by the ectopic focus) and restitution (caused by ectopic prematurity). We studied standard diagnostic ECGs of 118 patients with accidental extrasystoles: normally conducted supraventricular ectopic beats  and aberrantly conducted supraventricular ectopic beats  or ventricular ectopic beats . In each patient, we computed the VG vectors of the predominant beat,  The ventricular gradient (VG), defined as the integral of the ECG amplitude over the QT interval, has intrigued many investigators since it was introduced by Wilson et al. in 1931 —when vecOur here-described work aims to further contribute to verifying the paradigm of an activation-independent VG. The following introduction discusses the concept of the VG and defines the electrophysiological mechanisms that play a key role in experiment design and in interpreting the observations made by both others and ourselves in order to test the concept of an activation-independent VG.In 1957, Burger mathematically derived a formula for the VG in 3D vectorcardiographic space. He showed that VG, computed as the 3D integral of the heart vector over the QT interval, is proportional to the volume integral of the 3D action potential duration gradients over the heart . This caIn the same publication, Burger pointed out that the ventricular gradient  equals the sum of the areas covered by the course of the heart vector during the QRS complex and during the T wave, briefly called the QRS integral and the T integral, respectively.Like the QT integral, the QRS and T integrals are vectors, of which the spatial directions identify the QRS and T axes, respectively. The angle between the QRS and T integrals is the QRS-T angle. The relations between the QRS and T integrals, the QRS-T angle, and the ventricular gradient can be associated with specific ECG phenomena like concordance/discordance; this is extensively discussed and illustrated in several papers, including those by Draisma et al. , Man et Our current study focuses on the 3D QT integral/spatial VG, leaving the QRS integral, the T integral, and the spatial QRS-T angle out of consideration.Burger assumed that In 1983, Geselowitz theoretically showed that the QRST integral is determined by spatial heterogeneity in the area under the action potential, rather than by heterogeneity in action potential duration alone [Notably, the term “ventricular gradient” is somewhat confusing because the VG is computed from the ECG as the spatial integral of the course of the heart vector. According to Burger’s relationship, this spatial QT integral equals the volume integral of action potential gradients in the heart, which is also not a gradient in the true sense of the word. However, because “ventricular gradient” has become a generally accepted term, it is not practical to change it, though it is essential to realize its physiological and mathematical background.The mathematical concepts formulated by Burger  and GeseThe presumed independence of the ventricular activation order potentially renders the spatial VG useful in ECG diagnostics. When, in a patient, the QRST morphology changes while the VG remains the same, these changes should have been caused by differences in the depolarization order, not by changes in the intrinsic electrophysiological properties of the cardiac myocytes. However, when both the ECG and the VG change, the electrophysiological properties of the myocardium must have changed too. This property of the VG could be helpful in, for example, detecting acute ischemia in patients with a new left bundle branch block (BBB). If the acute ischemia causes the new BBB, not only the ECG but also the VG of this patient should have changed due to ischemia-based action potential changes. If the new BBB is caused by a local defect in the conduction system but unrelated to acute ischemia, the VG is expected to remain unchanged.However, for decades the concept of VG conduction independence has met with criticism. Simonson et al.  did not According to the formulae of the ventricular gradient developed by Burger  and GeseAfter it became possible to reliably measure myocardial action potentials ,18, the Electrical restitution is an electrophysiological mechanism that plays a role in experiments or observations intended to provide evidence in favor or against the concept of an activation-independent VG. Experiments intending to study abnormal activation sequences often need premature stimulation to ensure pacemaker capture. The same holds for ectopic beats that might serve as an “experiment of nature” to alter the cardiac activation order: in most cases, ectopic foci must fire prematurely to become manifest ectopic beats. Hence, an abnormal ventricular activation sequence generally requires premature stimulation or a premature extrasystole. However, prematurity alters the action potential morphology.The electrophysiological effects of premature stimulation of the heart are commonly described by the electrical restitution curve, originally defined by Bass in 1975 . In expeVG changes due to S1S2 restitution are caused by restitution heterogeneity in the heart: regional differences in the APD change in response to the premature stimulus. The study by Srinivasan and colleagues , set up When the restitution curves measured at various sites in the heart run parallel, changes in action potential duration due to a premature stimulus will be the same, and the VG will not be affected. When the restitution curves are not parallel, the regional action potential changes are not the same, which implies restitution heterogeneity and, as a consequence, changes in the VG.From the data published by Srinivasan and colleagues, it is difficult to predict what will happen in a specific case, characterized by a certain degree of prematurity and a specific stimulus site or the site of origin of a ventricular extrasystole. Restitution curves were only measured, and pacing was only performed at a limited number of sites. However, a general conclusion can be that there may be situations with given prematurity and a stimulus site in which all APDs exhibit a similar change and the VG will not or barely change, while there may also be situations in which this is not the case. Particularly in situations involving stimuli with higher prematurity  the curves are sometimes less parallel, while left-ventricular endocardial pacing seems to induce the most heterogeneous restitution curves.Another more complex manifestation of electrical restitution is the dependence of APD on stimulation cycle length. Franz et al.  showed tLaboratory experiments in preparations from dog hearts have shown that, after adaptation to a step decrease in CL, epicardial action potentials shorten more than endocardial action potentials . This heCardiac cells are electrically connected; electrotonic currents flow through gap junctions between cells as a consequence of differences in intracellular potential . This imTo investigate the presumed independence of the VG on the ventricular activation order, Lux and colleagues made body surface potential maps in dogs with various pacing modalities, measured QRST integrals at all 192 electrode sites  and constructed QRST iso-area maps ,31. TheyIn our view, these observations, in which electrotonic effects are used to explain the possible dependence of the VG on ventricular activation order, are not essentially different from the S1S2 restitution curve measurements by Srinivasan and colleagues .In intact hearts, S1S2 restitution curves cannot be measured for isolated areas: they necessarily include the electrotonic effects of the activation-recovery pattern associated with the site of stimulation/origin of the extrasystole.As well as including ventricular extrasystoles as per Cosma et al.’s study, we included patients with supraventricular extrasystoles;Instead of comparing the ventricular gradient vector magnitude of the sinus beat and extrasystole, we compared the ventricular gradient vectors, thus considering any differences in magnitude, direction, and combinations as a change;We included the prematurity of the extrasystoles in our analysis.In conclusion, we consider the S1S2 restitution curves as measured by Srinivasan and colleagues  as a valAnonymous, retrospective, observational.The ECG shows a normal sinus rhythm;The ECG shows at least one spontaneous supraventricular or ventricular ectopic beat;The predominant supraventricular beat has a well-identifiable J point, allowing for reliable determination of the QRS duration;The predominant beat does not fulfill the criteria for a strict left bundle branch block (LBBB) configuration .ECGs were drawn from the ECG database of the Leiden University Medical Center (LUMC) in which, since 1986, the ECGs recorded in the LUMC have been stored. Within an arbitrarily chosen 10-month period, we collected all technically sound digital standard 10-s 12-lead ECGs of patients > 18 years old that satisfied the following criteria:Of note: the wording “predominant beat” refers to the most frequently occurring beat in a particular ECG recording; it may have a normal or pathological QRST waveshape, depending on the patient.The ECG facilitated a reliable baseline assessment throughout the entire recording, including the ectopic beat of interest;A context of at least four predominant supraventricular beats preceding the ectopic beat, as well as at least one predominant supraventricular beat immediately following the ectopic beat with a compensatory pause, was required;To ascertain stable cellular electrophysiology, the minimum four predominant supraventricular beats preceding the ectopic beat had to pass a check for rhythmic regularity: ECGs with intervals between predominant beats that differed more than 10% from the average interval were excluded;In ECGs that contained multiple ectopic beats that satisfied the selection criteria, only the first ectopic beat was analyzed;In patients with multiple ECG recordings that satisfied the selection criteria, only the first recording was analyzed (to prevent double inclusion of patients).For this study, we applied an ECG selection strategy to ascertain several conditions that were technically needed for reliable ECG analysis. ECGs were excluded if they did not comply with one or more of the following conditions:The ECGs were analyzed and generally characterized by the Glasgow Royal Infirmary (GRI) software , thus laThe ECGs were additionally analyzed by the Leiden ECG Analysis and Decomposition Software (LEADS) . BrieflyFor the purpose of this study, ectopic beats also had to be analyzed. Given ectopic beats usually miss an isoelectric segment preceding their onset, they do not contribute to baseline estimation. To facilitate the analysis of a separate ectopic beat, a special experimental version of the LEADS program was developed, in which the ectopic beats were baseline-corrected, with the baseline as calculated from the surrounding predominant beats in the ECG recording.The magnitude of the difference vector between the VGs of the ectopic and predominant beats: The magnitude of the difference between the VG magnitudes of the ectopic and predominant beats: The angle α between the VGs of these two beats.From the variables produced by LEADS, we calculated the prematurity of the ectopic beat . From the VG vectors of the predominant and ectopic beats, We divided the ectopic beats into three categories: supposed supraventricular origin and normal conduction , supposed supraventricular origin and aberrant conduction , and supposed ventricular origin (V).Comparisons of the initial 20 ms in the predominant and ectopic beats have been made by careful inspection of the ECGs in a multi-channel display of all ECG leads over 10 s by four of the authors  jointly, thus removing subjectivity as much as possible. The decision about the similarity of the initial 20 ms of the ectopic and predominant QRS complex was taken on the basis of similar polarity and rate of rise/fall ,39,40,41The separation into ectopic beats of supposed supraventricular origin with and without aberrant conduction, and ectopic beats of supposed ventricular origin, was made to contrast the influence of solely restitution on the VG (by comparing ectopic beats of supposed supraventricular origin and sinus beats) and the combined influences of restitution and activation order differences on the VG (by comparing sinus beats on one hand and aberrantly conducted ectopic beats of supraventricular origin and ectopic beats of ventricular origin on the other hand).To compare After querying the ECG database, 375 ECGs matched the inclusion criteria, of which 257 ECGs were excluded due to the reasons listed in 2; 72.8% of patients had a BMI > 25.0 kg/m2; 25.4% of patients were obese (BMI > 30.0 kg/m2). p < 0.001), slopes close to 1, and, for the linear regression forced through the origin, an R-squared value that explains nearly all variance in the dependent variable.p = 0.04) and in patients with ventricular ectopic beats (p < 0.001). No other statistically significant differences emerged, although the impression arises that the VG magnitudes of the predominant beats of patients with aberrantly conducted supraventricular ectopic beats and of patients with ventricular ectopic beats are smaller than those of patients with normally conducted supraventricular ectopic beats. The limited number of patients with normally conducted supraventricular ectopic beats (N = 6) and the unpaired statistical testing precluded further conclusions regarding this observation.We investigated the dependence of the VG on activation order and restitution by analyzing standard diagnostic ECGs with a spontaneous ectopic beat, measuring intra-individual differences between the VGs of predominant and ectopic beats in 118 patients  with varEctopic VG vector magnitudes were significantly larger than predominant VG magnitudes for SA and V, but not for SN ectopic beats . VG diffIf we would interpret the VG magnitude as measuring the heterogeneity of ventricular action potential (AP) morphologies, the conclusion would be that ectopic beats bring about an increase in AP heterogeneity. We must realize, however, that the VG is—like many other ECG phenomena—subject to cancellation. Hence, when including cancellation in the VG interpretation, it may be more correct to interpret the VG as the net resulting AP heterogeneity. Depending on the net resulting AP heterogeneity of an individual patient’s predominant beat  with the VG of a QRST complex with a different ventricular activation order, we should take into account that several physiological mechanisms can alter the APD distribution in the heart, and thus affect the QRST integral in Burger’s formula. Only when the APDs remain the same, or lengthen or shorten homogeneously, is the VG unaffected because the spatial differential (nabla) in the Burger formula remains unaffected. Examples can be seen in Our current study suggests that restitution effects cause heterogeneous APD changes throughout the heart, thus affecting the cell-to-cell APD gradients (the nabla in Burger’s formula). This would mean that intra-individual VG comparisons should be made either at equal heart rates . Alternatively, comparisons should be made between the VGs derived from the predominant QRST complex and derived from a non-premature extrasystole or from an incidental QRST complex with an intraventricular block.Because the effects of autonomic nervous system (ANS) activity are non-homogenously distributed over the heart, e.g., with different APD responses in the epicardium and endocardium, ANS activity should preferably be the same during the time of occurrence of the reference QRST pattern and that of a deviating QRST pattern. Constant ANS activity is likely the case when a single extrasystole interrupts a regular supraventricular rhythm. The extrasystole will usually have a lower stroke volume, hence the systolic pressure of the pulse wave in the aorta and carotid arteries will be lower (or even absent) for the extrasystolic beat. This has, via the arterial baroreflex, consequences for the parasympathetic and sympathetic ANS outflow . This causes an increase in heart rate and in cardiac contractility. However, such reflex responses occur only after a delay of one or more seconds, not during the extrasystole itself. Hence, the VG of a single non-premature extrasystole or the VG of an interrupting sinus beat with an intermittent bundle branch block can be compared with the VG of the predominant beat.Beats with a different electrical ventricular activation order than the reference beat, e.g., a heartbeat with an incidental intraventricular block, a ventricular extrasystole, or a paced beat, necessarily cause different electrotonic currents. As already discussed in the introduction, due to electrotonic currents, action potentials of a certain myocardial region are influenced by action potentials of neighboring regions within the space constant (1–2 mm). The net result is that action potentials of a specific myocardial region will be influenced by action potentials from different neighboring regions if the trajectories of the depolarization or repolarization wavefronts change. To our knowledge, the influence of electrotonic effects in VG validation studies cannot be controlled. It is also difficult to assess. If differences are measured between the VGs computed from the predominant supraventricular QRST complex and computed from a non-premature extrasystole, it is likely to attribute this to electrotonic effects rather than to restitution effects.A final mechanism that may methodologically complicate a VG validation study is mechanoelectrical coupling. When measuring the VG in a QRST complex that differs from the predominant QRST complex because of a deviating ventricular activation pattern, the mechanical forces that develop as a function of time in the ventricles are different from the forces in the predominant QRST complex. Due to mechanoelectrical coupling , action potential morphology changes occur, and the VG will change. Again, this is difficult to measure in an epiphenomenon such as the ECG. Electrocardiographic imaging could possibly be helpful in assessing APD changes due to electrotonic effects or mechanoelectrical coupling.Our observations were made in humans, whereas several elementary studies on the VG were performed in dogs ,31,32,33In contrast to previous studies, which all had a limited amount of cases, we studied a larger number of subjects, allowing for statistical analysis.The relatively large amount of subjects allowed for the observation of a rich variation of prematurity, which permitted the study of prematurity as a possible relevant factor in VG variability.Our computations were the first in which the differences between ventricular gradients were expressed as VG difference vector magnitude rather than the VG magnitude difference. In our computations, any change in the VG, be it an increase, a decrease, or a rotation, contributes to the difference between two VG vectors.Compared to previously published research, our study is of additional interest due to a number of methodological aspects in the study design:Because our study is an “experiment of nature”, the site of the ectopic pacemaker and its prematurity could not be controlled. This left us with an analysis of the pooled data of a patient group in which the individually different ectopic pacemaker sites and prematurities between patients have to replace experimentally controlled variations in ectopic pacemaker site and prematurity within subjects.Another limitation is the uncertainty in the baseline estimation of the ectopic beats. Because the VG is an ECG-amplitude integral, it is sensitive to baseline errors. Due to the prematurity of ectopic beats, it is not possible to accept the voltage immediately preceding that beat as an isoelectric reference (as we routinely do in sinus beats). Instead, we had to construct an interpolated baseline that was assessed with the aid of the isoelectric reference amplitudes associated with the sinus beats immediately preceding and following the ectopic beat.The VG of the predominant beat could be computed in an averaged beat, whereas the VG of the ectopic beat was necessarily computed in a single beat, which is more susceptible to noise. However, because of careful visual checking of the baseline assessment and excluding patients with a failed baseline, the remaining errors cannot explain the sometimes-large differences between the VGs of the predominant and ectopic beats within certain patients.Another limitation is the uncertainty regarding the classification of premature beats with strict LBBB configuration. We have classified these as beats of supraventricular origin with aberrant conduction (this was the case in 10 patients). However, there is a possibility that strict LBBB beats can also be generated by right ventricular ectopy. Although such extrasystoles often impress with an LBBB-like pattern, it is not known if these beats comply with the strict LBBB criteria. However, in our view, this uncertainty is not relevant to the conclusion of our study.A final limitation is that the VCGs were not directly recorded, e.g., by a Frank VCG-recording system, but instead were mathematically synthesized by the Kors transformation . The impHowever, there are some limitations:During the period in which the VG concept was formulated, it was considered important because of its presumed independence of ventricular activation order. In this way, the VG could help to diagnose ECG changes in a given subject as a change in either ventricular conduction or in the electrophysiological properties of the ventricular myocardium. Later, additional use of the VG in risk assessment was proposed . Both aWe compared, within patients, the ventricular gradient of their sinus beat and of a supraventricular normally conducted extrasystole, a supraventricular aberrantly conducted extrasystole, or a ventricular extrasystole. Ventricular gradient differences were expressed as ventricular gradient difference vector magnitudes. The prematurity of the extrasystoles was included in our analysis and interpretation. We sometimes observed large differences between the ventricular gradients of the sinus beats and those of the extrasystoles, especially when the extrasystoles had prematurity of <0.80. We concluded that the tenet of the conduction-independent ventricular gradient does not hold in this study group but also reasoned that a methodologically correct comparison of ventricular gradients would require equal heart rates or a spontaneous or stimulated ectopic beat that is not premature.As a final remark, it should be stated that a possible invalidation of Wilson’s premise of a conduction-independent VG would not imply that the VG has no diagnostic potential in electrocardiography. Changes in the VG occurring in a clinical setting, in which the ventricular activation order is presumably not altered, may indicate pathology-associated action potential changes. An example is the VG change observed in pulmonary hypertension, caused by changes in the right-ventricular action potentials due to mechano-electrical feedback as a consequence of elevated right-ventricular pressure .