Sensors for monitoring electrical parameters over an entire electricity network infrastructure play a fundamental role in protecting smart grids and improving the network’s energy efficiency. When a short circuit takes place in a smart grid it has to be sensed as soon as possible to reduce its fault duration along the network and to reduce damage to the electricity infrastructure as well as personal injuries. Existing protection devices, which are used to sense the fault, range from classic analog electro-mechanics relays to modern intelligent electronic devices (IEDs). However, both types of devices have fixed adjustment settings (offline stage) and do not provide any coordination among them under real-time operation. In this paper, a new smart sensor is developed that offers the capability to update its adjustment settings during real-time operation, in coordination with the rest of the smart sensors spread over the network. The proposed sensor and the coordinated protection scheme were tested in a standard smart grid (IEEE 34-bus test system) under different short circuit scenarios and renewable energy penetration. Results suggest that the short-circuit fault sensed by the smart sensor is improved up to 80% and up to 64% compared with analog electromechanics relays and IEDs, respectively.  In recent decades, power grids have been undergoing great changes led both by the adoption of new information and communication technologies (ICTs) and also by a massive integration of renewable energy sources. These modernized grids are commonly referred to as smart grids. The Smart Grids European Technology Platform defines a smart grid as “an electricity network that can intelligently integrate the actions of all users connected to it  in order to efficiently deliver sustainable, economic, and secure electricity supply” . Smart gProtection systems play an essential role in maintaining the promised power quality and reliability of smart grids. Grid reliability can be defined as the ability of a power network to perform its intended function of providing an adequate supply of electrical energy to customers efficiently with a reasonable assurance of continuity and quality . TraditiThe main objective of a protection system is to quickly detect an abnormal operation condition and decide on the most appropriate action to ensure that the faulted zone is isolated and the rest of the network works in a stable state. To detect a fault, such as a short-circuit, current monitoring devices are used to measure the current flow through the network. This current measurement is compared with a threshold current value or pick-up current of the protection devices to discriminate if the current is due to a fault situation or not. The protection unit calculates the operation time (tripping time) of the network actuators (breakers) according to their setting parameters. However, any malfunction in protection devices can result in significant damage to the electricity network infrastructure, a loss of electricity supply, and even endangerment of field crew.Protection devices employed in distribution networks have evolved over time, from analog electromechanical relays, with reduced detection capabilities, to intelligent electronic devices (IEDs) that are able to transform the analog data gathered by current and voltage transducers into digital data and to provide adaptive protection functionalities remotely . It mustDistributed generators (DGs) such as photovoltaic installations and wind turbines are considered key actors for enabling the implementation of smart grids . HoweverSome works in the literature have proposed the use of protection schemes intended for dealing with the distinctive features of smart grids. In  and 19]19], dataThey have to offer the ability to measure, detect, and automatically adapt their protection settings for each fault situation.These protection devices should be able to communicate both between one another and also with the actuators (network breakers) to share optimal settings as well as control actions in a decentralized architecture.Moreover, the design of new relay-based smart sensors, in which the coordination schemes could run inside each smart sensor, will help to speed up the fault detection and isolation process.The protection schemes of smart grids must deal with all the changes in the distribution networks (such as topology and DG variability); therefore, maintaining fixed protection settings of protection devices is no longer valid . To imprThis paper presents a new relay-based smart sensor that is able to locally measure, detect, and isolate a short circuit (fault) in the minimum time possible. Furthermore, the smart sensor is able to update, locally, its setting parameters in real-time operation. Once a short circuit is detected, an adaptive protection scheme (APS) running inside each smart sensor optimizes its setting parameters in communication with the rest of the coordinated sensors that detect the fault. The optimal setting parameters are selected to minimize the opening duration time of the network breaker closest to the fault.The smart sensors calculate the opening duration time of the network breakers, according to the fault measurements and their optimal settings, and they send those breakers the opening activation order. The information sharing among the coordinated smart sensors and the network breakers is based on the IEC 61850 Standard  using GOA smart sensor is proposed that is able to locally calculate and update its parameters by means of an extended current-time search-space for each fault situation. Firstly, it should be noted that traditional protection devices use only fixed time-current curves according to  and secoA peer-to-peer communication is performed between coordinated sensors, based on the IEC 61850  to optimThe main contributions of this paper are twofold: It must be pointed out that, to the authors’ knowledge, none of these aspects have been addressed in the scientific literature.The primary purpose of an electrical network is to efficiently deliver reliable electricity to consumers. Protection systems are of utmost importance in the reliability of electrical networks, since they are directly linked to interruptions in the power supply affecting the grid reliability . During network disturbances, such as short circuits or faults, protective devices used for the protection of the electrical network must detect the fault and activate the opening of the networks’ breakers in order to isolate the faulted zone. The correct intervention of the protective devices minimizes the outage time of the grid and reduces the effect of the fault currents on the network equipment. The fault-clearing process is based on the selectivity protection property , which mAnalog electromechanical relays are characterized by inverse time-current curves defined by the IEC 60255-151 . ElectroTo obtain a correct actuation of the protection equipment, power networks are subdivided into protection zones. Protection devices (relays) are responsible for detecting any fault that occurs in an assigned area, known as the primary protection zone. Moreover, they may properly provide backup protection to an area outside their primary zone (downstream). This means that each zone is protected by two relays: a primary relay (PR) and a backup relay (BR). The PR operates under short circuits inside its primary protection, and the breaker closest to the fault is the one that opens first, whereas the BR operates only if the PR fails to isolate the fault after a time delay. Each zone is overlapped by its adjacent zone to avoid unprotected (blind) areas. This overlapping is accomplished according to the location of the protection equipment electromechanical relays and network breakers.Electrical distribution networks typically consist of a secondary substation and a main feeder with lateral branches. In Smart grids are characterized by a high penetration of renewable energy sources, known as DGs, spread over a network. DG units are characterized by a bidirectional power flow from the DG to the grid. Depending on both the fault and the DG location, the operation of the protection devices can be affected. Assume a radial distribution network with two feeders connected to the secondary substation (bus 1), similar to the one depicted in PV inverters are equipped with overcurrent protection that limits the inverter output current up to 1.3 of the rated current . DependiIf there are clouds or an absence of sunlight, then the net power injected by the PV generators into the grid is zero a. In thiIn the case of large PV generators and diurnal conditions b, if a fIn this case, if a fault occurs in Zone 3, two different situations can unfold:Given the previous issue, DG connection to smart grids causes a reverse power flow from the DG that could lead to the untimely action of the protection device, which is a selectivity problem. Therefore, traditional protection coordination schemes, with fixed setting parameters, become ineffective in smart grids with DGs. It is thus necessary to develop new protection schemes that are able to adapt the setting parameters of the protective devices in relation to the intermittent share of distributed generation ,33.Several approaches exist in the scientific literature for addressing the protection coordination issue in distribution networks with DGs. The authors in  proposedThe previously mentioned protection schemes have one main limitation: the protection coordination problem considers a static network; that is, the adjustment of protective devices is achieved considering the amount of DG installed capacity in a predetermined network with a fixed demand. Therefore, for real-time variation in load demand or generation, the proposed schemes will only be valid for the conditions of generation, demand, and network topology for which the protective devices have been adjusted . The evoIn smart grids, several parameters must be measured, such as voltage, current, temperature, and phase, to be able to detect any parameter fluctuation in near real time and manage the corrective actions to assure grid reliability under fault conditions. Furthermore, the measured data must be readable by intelligent devices and contain a timestamp as well as the sensor location to facilitate decision support in smart grid operation .Data acquisition module. This module is in charge of monitoring and measuring the analogue signal in real time by means of the electricity transducers installed in the network.Data conditioning. In this module, the analogue electrical signal is conditioned and converted into a digital signal. After the sampling stage, the root mean square (RMS) value of the sampled signal is calculated and used to obtain the fundamental component of the measured signal.Microprocessor unit (MPU). This module is responsible for processing the digital signal in order to detect and activate the network breaker to isolate the faulted zone. This is the core of the sensor in which the smart-sensor settings are updated depending on the network conditions and fault situation. Inside the MPU, the optimization algorithm (the APS) is responsible for selecting the optimal setting parameters that minimize the operation time of the PR and BR of the faulted zone. When a fault occurs, only the PR of the faulted zone executes the APS in the MPU to determine the optimal setting parameters of the primary and backup smart sensors. Moreover, the MPU algorithms are able to transform a physical measurement in an electric signal that could be processed, stored, and communicated to other devices through a bidirectional communication channel [ channel ,37. FinaSynchronization module. An internal clock allows for the synchronization of the acquired digital data with an external time reference that could be shared with other devices, such as global positioning systems (GPS). Using measurement synchronization helps to improve the quality and accuracy of the measurement data. In smart grids, measurement synchronization is of great importance for operational and protection issues.Communication module. The communication module is responsible for the peer-to-peer communication between the smart sensors. For communication issues, smart sensors use the IEC 61850 standard [standard . When a Additional module for metadata sensor storage. This module allows the device to perform supplementary tasks related to the following: smart-sensor description and identification capability (self-description and self-identification); quality control of the work achieved by the smart sensor; and operation error reporting .The relay-based smart sensor proposed in this paper is a single device composed of several modules : Data acThe operation carried out by the sensor is the following: th” measures the current seen by the sensor and calculates its RMS value. This RMS value is processed into the “ith”smart sensor’s MPU where it is compared with the Ipickup threshold value of the “ith” smart sensor. If the measured current value is higher than its Ipickup value it means that a fault has been sensed by the smart sensor “ith”. Consequently, the communication module of the smart sensor “ith” sends a GOOSE message to the downstream smart sensor “ith+1” which has to discriminate, itself, if the current seen by the sensor “ith+1” corresponds to a fault or not. If the sensor “ith+1” detects a fault it sends a goose message to the upstream sensor “ith” and to the downstream sensor “ith+2”. The peer-to-peer communication between consecutives sensors continues until it reaches the last smart sensor that does not sense any fault so that the faulted zone is identified. A smart sensor “iOnce the faulted zone has been identified, the last two smart sensors that sensed the fault are identified as primary and backup sensors, respectively. The MPU of the primary smart sensor determines the optimal setting parameters of both smart sensors responsible for protecting the faulted zone, and the optimal setting parameters for the backup smart sensor are sent via GOOSE messages through the communication module. Afterwards, the primary sensor sends the opening order to the corresponding breaker via GOOSE messages by means of the communication module. If the primary sensor fails, the backup relay sends the opening order to the breaker according to its activation time value.The smart sensor proposed in this paper offers added value to utilities, because of the telemetry functionality as well as remote operation and corrective action or predictive decision-making process, thereby improving grid efficiency and integrating new sensor technologies. The novelty of the smart sensor lies in the peer-to-peer communication capacity between the smart sensors of a faulted zone (the PR and BR) to isolate the fault and to establish a stable operation condition. The smart-sensor APS takes into account different smart grid operation conditions regarding DG integration and network topology. The APS also optimizes the primary and backup protection setting parameters to minimize the tripping time of the actuators (breakers) and isolate the faulted zone as quickly as possible. For that purpose, the APS employs three setting parameters  that extend the operation area of the smart sensor beyond the standard curves defined by the IEC 60255-151 standard .In the smart sensors, the IEC 61850 standard has been implemented so that the primary smart sensor (the PR) is able to communicate the adaptive protection setting parameters to the backup smart sensor (the BR) via GOOSE messages. The incorporation of these smart sensors into smart grid protection schemes allows for the enhancement of the network operation thanks to the real-time actions. It has to be highlighted that the smart sensor can be combined with other measurement devices such as phase measurement units (PMUs). PMUs have been used to monitor long transmission lines since 1970 to improve the network observability or to provide synchronized measurements to transmission line protection devices  ,39. PMUsIf PMUs were deployed in distribution networks as detailed in this paper, the proposed smart sensor can use, directly, the measurements provided by the installed PMUs. In this case, the PMU’s measurements will enter directly to the MPU where all the acquired measurements, provided by the conventional transducers and PMUs, will be processed to detect and activate the network breaker to isolate the faulted zone.The objective of the smart-sensor protection scheme is to minimize the operating time of the coordinated smart sensors (the PR and BR) while maintaining selectivity and enabling the isolation of the faulted zone. As previously mentioned, classical analog electromechanical relays have proven to be inefficient when applied in networks with DGs . To solvsults in  obtainedariables . A limitariables .The proposed smart-sensor coordination approach is formulated as a nonlinear multivariable mixed-integer nonlinear programming (MINLP) optimization problem. Relay-based smart-sensor parameters α, n, and rding to .The advantage of optimizing three variables instead of two ,46 is thNote that for real-time operation, where only two relay-based smart sensors must be coordinated for each zone, the optimization of three degrees of freedom for each smart sensor does not require a relevant computational burden.A crucial aspect in smart grids is the communication between devices connected to the network. Several standards have emerged as alternatives to create the backbone and communications network for smart grids. The most highlighted outcome of this standardization initiative is the IEC 61850 standard because of its ability to provide standard object-oriented modeling that could be mapped to various protocols. The IEC 61850  is an inGOOSE messages entail a fast communication channel to share events-related information between multiple smart grid devices mapped by the IEC 61850, mainly those related to the critical information of smart grids. Furthermore, GOOSE messaging allows for the exchange of both digital and analogue data between peer-to-peer devices with an average processing rate of 12 ms. Peer-to-peer communication in the IEC 61850 environment introduces the concept of publisher and subscriber devices regarding the information exchange. When a device publishes a GOOSE message, only subscriber devices receive it and react according to their functionality in the distribution network. In this paper, IEC 61850 and GOOSE messaging are used with the aim of sharing the optimal protection setting parameters between the PR and BR of a faulted zone and sharing the tripping signal to the network breaker to isolate the fault. For that purpose, the primary smart sensor runs the APS and publishes the optimal protection setting parameters to the BR of the faulted zone and the associated tripping time of the network breaker to the primary smart relay. Although the GOOSE messaging information is published for all devices connected to the distribution network, only subscriber devices (backup smart sensor and primary network breaker) receive it. α and n using Equation (2). These parameters are updated according to each situation of grid topology :The proposed optimization problem is subjected to the following constraints:The protection coordination criterion establishes the minimum time elapsed between the operation of the primary and the backup protection, known as the coordination time interval (CTI). To ensure the correct coordination between the primary and backup smart sensors, the coordination time must be greater than the minimum established time (7):n.The time that a smart sensor takes to detect a fault produced in its zone of influence and activate the opening of the breaker must be bounded. Equation (8) determines the operating time limits of the relay-based smart sensor:r, respectively.The operating time of the smart sensor is directly proportional to the r, respectively.The plug setting multiplier (PSM) is the ratio of the fault current , and until the stop criteria are met, a loop begins whose objective is to generate a new population, Once the objective function has been evaluated (F (y), Step 4), and as long as the stop criteria are not met, the genetic operators are applied to create the next study population by first selecting (Step 5) the individuals that will constitute the parents in the reproductive process. The GA uses the roulette selection method to prioritize solutions that yield better aptitude values over those obtaining worse aptitude values. This method allows the best search areas to be exploited.After the population of parents is obtained, the crossing is carried out (Step 6). Among all the techniques related to this process, the one chosen here is the single point crossing technique, since the size of the chromosomes used is small. Moreover, the utilization of other techniques could break the chain of the population considerably, leading to a loss of relevant information about the improved search areas. For the crossing probability, a value of 0.8 has been established .The next step in the generation process of a new population is the application of the mutation operator (Step 7). The objective of this operator is to introduce diversity in the population or rescue information that may have been lost in the selection and crossing processes. Since the probability of crossover is high, a mutation probability  of the parents with the children has been chosen, based on the theory of evolution, according to which the children inherit the best properties of the parents in terms of adaptation to the environment.From the intermediate population, composed of children resulting from the crossing and mutation processes and along with the population of the current generation, a new population corresponding to the next generation, −6.Tolerance of solutions: of the suitable values obtained by the best solution of two consecutive generations, the minimum tolerance value considered is 10Maximum number of generations: a maximum number of 100 generations has been chosen.Two stop criteria have been defined:s = 2) for each fault situation . The genetic algorithm is in charge of optimizing the tripping time of two consecutive relays (PR and BR) once the fault has been detected. Consequently, it can be easily scaled up to large network because, independently of the network size, the genetic algorithm optimizes only the parameters for the primary and backup relay where the fault has been detected.In this paper, the number of smart sensors to coordinate simultaneously is two (Na secondary substation (69 kV/24.9 kV);a main feeder and five laterals;two photovoltaic PV farms at Nodes 20 (DG20) and 22 (DG22) with a rated power of 12 MW;nineteen customers with a nominal load demand of 12 MW; andseven relay-based smart sensors (S_1 to S_7) at Nodes 1, 4, 8, 12, 14, and 16 of the main feeder and at Node 26 of Lateral 5.The proposed smart-sensor coordination scheme was implemented in a smart grid based on the topology of the IEEE 34-Node Test Feeder , as illuThe smart sensors’ location sectionalizes the main feeder of the studied smart grid into seven protection zones . The lenSeven fault scenarios were considered to test the accuracy of the proposed smart-sensor coordination see . ScenariScenario B was chosen to demonstrate the application of the protective smart protection scheme. In this scenario , a threeOnce the fault is detected, the PR-based smart sensor (S_2) runs the APS hosted in its MPU in order to determine the optimal setting parameters of both S_2 and S_1 for the optimal isolation of the faulted zone (Z2). The APS employs the extended area of the relay-based smart sensors to be coordinated, delimited by the imposed limits in (11) and (12) and the pick-up current values given by . The optAfter calculation of the optimal setting parameters of the relay-based smart sensors by the APS, the smart sensors compute the activation time of the actuator in charge of opening and clearing this faulted zone. According to S_1 and S_2′s setting parameters in The operation of the smart-sensor coordination is explained as follows: To demonstrate the network reliability improvement by the smart sensors, the tripping times of three protection methods are compared: the classic coordination, a linear programming coordination, and the proposed optimal smart-sensor approach. The protective devices are electromechanical relays (ERs) when the classical protection schemes are implemented, IEDs in case of the linear programming function, and relay-based smart sensors (S_1 and S_2) for the proposed optimal approach. In all cases, fault Scenario B is considered (three-phase fault in Z2).the red dots indicate the tripping times of ER1 and ER2 when the classical tripping function is considered according to IEC standard 60255-151 ,24;the green dots indicate the tripping times for IED1 and IED2 when the linear programming technique is implemented ; andthe blue dots indicate the optimal tripping time established by the smart-sensor optimal APS coordination (S_1 and S_2).As illustrated in ® [The genetic algorithm was programmed in Matlab®  on a 2.7® .IEC 61850-5 states that the transfer time of GOOSE messaging for a Trip command shall be such that the command should arrive at the destination device within 3 ms ; consequ-Fault type: a three-phase fault (Scenarios A and C) and a single-phase-to-ground fault (Scenarios D and E). -Fault location: a fault in Zone 2 of the main feeder (Scenario E) and a fault in Zone 7 corresponding to Lateral 5 (Scenario F). -Operation conditions: one or two DG units in operation in the smart grid. In both cases, the DG penetration level is 50%.The proposed smart-sensor optimal protection coordination is now examined for different fault conditions: The results of the operating times obtained by the three compared coordination methods  for the main feeder faults as well as the lateral fault  are presented in To validate the smart-sensor protection coordination proposed in this paper under different network situations, two important situations are studied: (i) the influence of DG penetration levels and (ii) the influence of the impedance fault values. High impedance faults in distribution networks produce low-magnitude fault currents that could be considered as normal current values corresponding to normal operations. A study to ascertain the impact of the PV penetration level as well as fault impedance on the protection coordination was performed for Scenario E , correspIt must be highlighted that when the fault resistance and the DG penetration level increase, the classical  and linear schemes (IEDs) fail to isolate the fault. Furthermore, for the 50% DG penetration level and single-phase-to-ground fault with a fault resistance greater than zero, the smart-sensor protection coordination is the only scheme capable of protecting the network—by adapting the protection setting parameters to obtain a fast response—and maintaining the selectivity, as can be seen in The integration of distributed generation into smart grids could cause malfunctioning of the protection schemes, mainly because of the bidirectional power flows and their contribution to fault currents. With the aim of improving the reliability of smart grids, new protective devices and protection schemes must be developed to deal with the renewable energy impact on fault currents. The ability of smart sensors to acquire, monitor, and process measured data, as well as to execute optimization algorithms in their MPU, plays a vital role in smart grid protection. Incorporating smart sensors into the protection schemes reduces the activation time of network breakers and thus improves smart grid reliability.In this paper, a relay-based smart sensor is proposed that offers the capability of updating its adjustment settings in real time in coordination with the BR. The protection scheme is able to optimize the setting parameters of the smart sensors for different network operation conditions. It employs three setting parameters  in the optimization process, so that the operating area of the relay-based smart sensor is expanded, compared with the time-current curves defined by IEC 60255-151. The communication of the proposed smart-sensor protection coordination scheme can be implemented in a smart grid by using the communication standard IEC61850, so that smart sensors’ protection setting parameters as well as network breaker opening signals are exchanged via GOOSE messages.The proposed relay-based smart sensor and the protection scheme were applied to a smart grid with DGs. The performance of the smart-sensor protection scheme was tested for different DG penetration levels, fault types (single-phase-to-ground and three-phase faults), and faulted zones . In all cases, the APS hosted in the smart sensors’ MPU was capable of adapting, in real time, the performance parameters of the smart sensors responsible for protecting the faulted zone according to the operating conditions of the smart grid at the time of the fault measured by the smart sensors. Moreover, the adaptive smart-sensor protection coordination scheme proposed in this paper reduced the activation time of the network breakers by more than 80% and 64% compared with analogue electromechanical relays  and IEDs (linear programming), respectively. This ultimately translates into a more reliable network operation in the presence of DGs. Furthermore, it has been demonstrated that the relay-based smart sensor proposed in this paper is the only option that is able to clear the faulted zone of a smart grid with DGs when subjected to high impedance fault conditions. In this paper, it has been shown that information and communication technologies (ICT) play a vital role in smart grids where the IEC 61850 standard has started to be used for smart grid protection. One of the more important challenges is to integrate wireless communication into smart grid devices interconnecting an increasing number of smart grid sensors in the IoT world. In the future, the proposed smart sensor will be based on IoT-IEC 61850 communication offering wireless peer-to-peer communication between relay-based sensors  by means of GOOSE messages improving the communication among all the smart sensors spread over the grid.


To provide high-precision positioning for Internet of Things (IoT) scenarios, we optimize the indoor positioning technique based on Ultra-Wideband (UWB) Time Difference of Arrival (TDOA) equipment. This paper analyzes sources of positioning error and improves the time synchronization algorithm based on the synchronization packet. Then we use the labels of the known position to further optimize the time synchronization performance, and hence improve TDOA measurements. After time synchronization optimization, a Weighted Least Square (WLS) and Taylor coordination algorithm is derived. Experiments show that our optimization reduces the average positioning error from 54.8 cm to 12.6 cm. The number of connected devices is increasing rapidly and will soon continue to grow exponentially. Internet of things (IoT) is a hot research topic, including various application scenarios such as smart transportation, smart security, indoor positioning, etc. Therefore, research on indoor positioning and Location-Based Service (LBS) are receiving increasing attention ,2. ThankGNSS is a widely used outdoor positioning technology based on traveling time measurement of the arriving signals. It demonstrates high accuracy, good stability and global coverage. One of the key technologies of GNSS is the time synchronization of the signal transmitter and receiver. When the observation error of the arrival time of the electric signal is less than 3 nanoseconds, the positioning accuracy is better than 1 m. However, we cannot directly transplant GNSS technology to indoor positioning  because Synchronization based on a known reference label. Here, the time difference between the signals from the reference label or mobile label and the two fixed base stations is called the single-difference. The difference between the known reference label and another mobile label is defined as the double-difference, which eliminates the clock differences of both the base stations and the labels. This algorithm is inherited from the GPS double-difference observation algorithm and is very common in pseudo-satellite and Locata indoor positioning ,8. Both Synchronization based on two-way ranging. In this scheme, both base stations and labels are transceivers. The label (or base station) receives the signal sent by the base station (or label) and forwards it back. After receiving the response signal, the base station (or label) can calculate the distance to the label (or base station) by calculating the time interval between the sent and the rebound signal. Scholars have proposed a scheme to achieve wireless (UWB) clock synchronization by using two-way message exchange ,11. The Synchronization based on timestamp . In thisAmong UWB positioning techniques, time-based positioning solutions are dominant, including Time of Arrival (TOA) and Time Difference of Arrival (TDOA) methods. In time-based indoor positioning solutions, time synchronization technology is the cornerstone of high-precision positioning . In TOA-In summary, this paper tries to improve the time synchronization scheme with timestamp. The improved scheme is called clock synchronization based on synchronization packets. First, a master base station is selected from among the base stations participating in the positioning, and the other base stations are considered slave base stations ,16. ThenThe positioning equations based on TDOA measurements have nonlinear characteristics. Therefore, we usually need to convert it into a linear system of equations before solving. Friedlander et al. , Schsu eThis article focuses on UWB indoor positioning technology based on time difference of arrival (TDOA). First, the clock synchronization problem is solved, then the residual error is calibrated, and finally the positioning algorithm is optimized.TOA measures the propagation time of the signal from the label to the base station. The one-way observation equation can be expressed as:The time difference of arrival (TDOA) between two base stations (A1 and A2) to the same label can be expressed as:Assuming hardware . It is uIn summary,  is 1 ns , then thC(t) denote the base station clock time. For a perfect clock, In general, the base station uses a hardware oscillator to generate the time label. Let the en found  that alt(1)The master base station sends a synchronization packet (2)The label sends a positioning packet (3)The master base station sends a synchronization packet In this paper, we first select a master base station among the base stations participating in positioning, and the other base stations are called the slave base stations. Then, the master base station periodically sends synchronization packets to the slave base stations to achieve clock synchronization between the base stations. In this algorithm, the TOA value recorded by the base station clock is converted into the corresponding TOA value of the master base station clock. Among them, the TOA value measured by the master base station does not need to be converted. Finally, the converted TOA value of the slave base station minus the TOA value of the master base station can get the TDOA value after clock synchronization. The process of obtaining the label TDOA value is:Both According to Equation (4), the clock of the master base station The TOA value recorded by the base station clock is converted into the corresponding TOA value of the master base station clock; the calculation method is as shown in Equation (6):Because both In addition to clock synchronization, there are multipath effects, hardware delays, media delays, and other errors in the positioning process. Therefore, this paper proposes an error processing scheme based on the calibration method, which uses the labels at known locations to determine the error value and stores it in the local server. Then in the following positioning steps, the error value is used to compensate the TDOA value to reduce the positioning error.In the calibration method, first, a label The time difference In summary, Based on the error calibration, this paper proposes a Weighted Least Square (WLS) and Taylor collaborative positioning algorithm based on error calibration, which uses WLS to estimate the initial value of the label and uses the Taylor algorithm to determine the label coordinates. The error calibration value is used to compensate the TDOA value of WLS equations and Taylor algorithm.As shown in Equation (11), the distance between the base station Set the base station Let In conclusion, we getTo reduce the impact of TDOA measurement errors on the positioning results, Equation (15) adds a covariance matrix. After matrix transformation, we get:Equation (16) is a system of equations based on WLS, with small calculation amount and fast speed. When the positioning is in a complex environment such as NLOS, the measurement accuracy of the label TDOA value will be reduced. However, after the error calibration of the TDOA value, the calculation result of Equation (16) can still roughly reflect the true position of the label. Therefore, the solution based on the WLS equation system can meet the requirements of the initial coordinates of the Taylor algorithm. The Taylor algorithm adjusts the label coordinates through the local WLS solution. It has high precision and good stability, but it has a strong dependence on the selection of the label initial coordinates. In summary, this paper proposes a WLS and Taylor collaborative positioning algorithm based on error calibration.The standard Taylor algorithm is expressed as Equation (17) .(17)h=GLet, After compensating the TDOA value with error calibration, To illustrate the effectiveness of the error-calibrated WLS and Taylor collaborative algorithm (WLS-Taylor) in real indoor scenarios, experiments were needed. The experimental equipment came from Jiangsu Tangen Technology Co., Ltd. The experimental area was approximately 7 m long and 6 m wide, and was located on the fourth floor of a building of the East China Normal University, being a typical meeting-room environment including one table, chairs, one projector, cabinets, pendent lamps, etc. The experimental environment is shown in We used TDOA in the UWB positioning system for the experiment. The system included a hardware and a software component that supported clock synchronization and multiple label access. As shown in In the experiment, we preliminarily selected some test points, and sequentially placed the bracket that was used to hold the label at those points. Then, we collected approximately 3000 sets of data without interruption, where the signal of the label was sent at a frequency of 32 Hz. Finally, different algorithms were used to calculate the estimated coordinates of the labels to achieve a controlled experiment. The actual position of the label is measured by an infrared rangefinder, the estimated coordinates were calculated by different algorithms. Afterwards, we calculated the root mean square error between the actual position and the estimated coordinates and the mean of the RMSE (root mean square error) for 3000 data sets which recorded as the positioning error at that point.The average root mean square error between the actual position and the estimated position is used to measure the positioning error of the algorithm.To verify the validity of the WLS-Taylor algorithm, we compared it with the Chan and Taylor (Chan–Taylor) algorithm  using TDIn the Chan–Taylor algorithm, the output of the Chan algorithm is the initial input of the Taylor algorithm. Then, the Taylor algorithm is sequentially iterted to adjust the coordinates of the label until the sum of the absolute values of the label coordinate change is less than the threshold, outputting the final estimated coordinates of the label.In the Chan–Taylor algorithm, an extra weighted least squares operation is added to further decrease the perturbation errors of Initial coordinates. In the WLS-Taylor algorithm, we directly used the initial coordinates as the initial value of the Taylor algorithm. The reason for this change is that for the Chan–Taylor algorithm, the primary purpose of the Chan algorithm also meets this requirement, and the calculation amount is smaller than the Chan algorithm because one WLS operation is removed.The WLS-Taylor algorithm with error calibration uses a pre-calibrated value of error to compensate for the measured TDOA values in the WLS-based equation set and the Taylor algorithm. The results of the WLS-based set of equations were used as the initial values for Taylor and the same calculation of C-T algorithm, allowing us to find the coordinates of the label.We calculated the difference  between the 3000 sets of labeled TDOA measurements and the true value to evaluate the performance of the clock synchronization method based on the synchronization package. The TDOA measurement value was obtained by Equation (6). The real TDOA value acquisition is divided into three steps. At first, we calculated the actual distance between the label coordinates and the coordinates of each base station. Second, the distance from the slave base station to the label minus the distance from the master base station to the label was calculated. Third, by dividing by the speed of light, we finally obtained the real TDOA value. Because it is the same system, the base station has the same hardware construction. The clock deviation  between one slave base station and the master base station is listed here, and the results are shown in As shown in As shown in In experiments to verify the validity of the WLS-Taylor algorithm, neither the Chan–Taylor algorithm nor the WLS-Taylor algorithm compensated for TDOA values using error scales. The experiment used nine test points to evaluate algorithm performance, except for one error calibration point. The Cumulative Distribution Function (CDF) curves, which are able to completely describe the probability distribution of a real random variable for the positioning results, are shown in It can be seen from As shown in To confirm the effectiveness of the error calibration, the TDOA error with error calibration between one slave base station and the master base station was compared with that without error calibration, as shown in The experiment was based on clock synchronization, as shown in The green curve in It can be seen from As shown in Focusing on the problem that indoor positioning is difficult to achieve high-precision positioning, this paper studied the UWB indoor positioning scheme based on TDOA. The core part was clock synchronization, error calibration and collaborative positioning. With respect to clock deviation between the base stations of UWB positioning system, this paper first proposed a clock synchronization algorithm based on synchronization packets. Then this paper analyzed the principle and error source of TDOA positioning algorithm, and the use of labels with known positions to pre-calibrate errors such as hardware delay and multipath. The error calibration value is stored in the local server to compensate the TDOA measurement value in the actual positioning. Finally, this paper proposed a WLS and Taylor collaborative positioning algorithm based on error calibration. First, the error calibration value is used to compensate the TDOA value, then WLS is used to estimate the initial coordinates of the label and the Taylor algorithm is used to determine the label coordinates.To obtain a more accurate TDOA value, the clock synchronization method in this paper sends a synchronization packet with a small period. In the next step, algorithms such as Kalman filtering can be introduced to track the clock deviation to reduce the frequency of synchronization packets. This method reduces the calculation load, production cost and volume of the mobile terminal (label), without laying a large number of additional hardware equipment, and without changing the existing hardware equipment, completely relying on software for implementation, strong operability, and easy for popular applications. It has great advantages and business prospects in the indoor positioning application environment where the manager application is the main management for multiple users. In addition, the calibration algorithm has a weakening effect on the multipath effect, but it still has a greater impact on the positioning accuracy and needs further study.


Mining massive prescriptions in Traditional Chinese Medicine (TCM) accumulated in the lengthy period of several thousand years to discover essential herbal groups for distinct efficacies is of significance for TCM modernization, thus starting to draw attentions recently. However, most existing methods for the task treat herbs with different surface forms orthogonally and determine efficacy-specific herbal groups based on the raw frequencies an herbal group occur in a collection of prescriptions. Such methods entirely overlook the fact that prescriptions in TCM are formed empirically by different people at different historical stages, and thus full of herbs with different surface forms expressing the same material, or even noisy and redundant herbs.We propose a two-stage approach for efficacy-specific herbal group detection from prescriptions in TCM. For the first stage we devise a hierarchical attentive neural network model to capture essential herbs in a prescription for its efficacy, where herbs are encoded with dense real-valued vectors learned automatically to identify their differences on the semantical level. For the second stage, frequent patterns are mined to discover essential herbal groups for an efficacy from distilled prescriptions obtained in the first stage.We verify the effectiveness of our proposed approach from two aspects, the first one is the ability of the hierarchical attentive neural network model to distill a prescription, and the second one is the accuracy in discovering efficacy-specific herbal groups.The experimental results demonstrate that the hierarchical attentive neural network model is capable to capture herbs in a prescription essential to its efficacy, and the distilled prescriptions significantly could improve the performance of efficacy-specific herbal group detection. Traditional Chinese Medicine (TCM) has a long history of several thousand years, and during such long period massive prescriptions are accumulated. These prescriptions were providing effective protection for ancestors of Chinese people from different diseases for thousands of years, and are applied widely even nowadays . HoweverRhizoma Rhei are heat-clearing and detoxicating, removing accumulation with purgation, and so on. When combined with Coptis chinensis and Radix Scutellariae, Rhizoma Rhei can deliver the efficacy of heat-clearing and detoxicating. On the other hand, Rhizoma Rhei plays the efficacy of removing accumulation with purgation when combined with mirabilite . Hence, TCM doctors not only know the efficacy of herbs but also master the efficacy of herbal groups when making prescriptions.The efficacy of a prescription is not simply the addition of all herbs. On the contrary, they interact with each other and show better curative efficacy and fewer side effects than a single one. Besides, the efficacy of a single herb generally is diverse, and practitioners need to control single herbs with multi-efficacy to play an expected efficacy during diagnosing disease and making prescriptions. For example, the efficacies of Therefore, TCM researchers draw more and more attentions recently in herbal group mining, and gain some promising results –13. HoweIn order to overcome the difficulties mentioned above, in this paper we devise a two-stage approach to detect efficacy-specific herbal groups (ESHGs) from prescriptions in TCM. The first stage is performing recognition of essential herbs in a prescription for its efficacy, and the second stage collects all prescriptions of an efficacy with their respective essential herbs to discover ESHGs. For the first stage a hierarchical attentive neural network model is employed, and by means of its attention mechanism, essential herbs in a prescription for its efficacy are recognized. For the second stage frequent pattern mining is incorporated to discover the ESHGs of an efficacy from its distilled prescriptions obtained in the first stage. We conduct a series of experiments to verify the effectiveness of our two-stage approach from two angles. The first one is the ability of the attention mechanism to capture essential herbs for a prescription efficacy and thus distill the prescription for subsequent frequent-pattern-based ESHGs detection, and the second one is the quality of the ESHGs discovered with our two-stage approach. The experimental results demonstrate that the hierarchical attentive neural network model is capable to capture herbs in a prescription essential to its efficacy, and the distilled prescriptions significantly improve the effect of ESHGs detection.The major contributions of this work are three-fold: (1) a deep learning model is incorporated into the ESHGs detection task, where a dense real embedding is learned for every herb to capture semantical correlations among herbs, thus overcoming enormous differences in herbal name usages in the long period of TCM history; (2) a hierarchical attentive mechanism is proposed to capture essential herbs in a prescription for its efficacy to distill the prescription for the purpose of improving ESHGs detection; (3) a series of experiments is conducted to investigate the performance of our model for identifying herbs in a prescription essential to its efficacy and detecting ESHGs for a particular efficacy, and the experimental results verify the effectiveness of our two-stage approach.In recent years, many disciplines witness rapid growth in employing data-intensive approaches based on machine learning and data mining technologies to discover patterns hidden in a massive volume of data. Likewise, some efforts have emerged in TCM recently which utilize machine learning and data mining technologies for discovering knowledge from TCM literature –18, clinWith regard to types of knowledge to be discovered from prescriptions in TCM, herbal groups having a particular efficacy are of great significance for TCM theory as well as for its practice, thus becoming a primary focus in recent works on TCM prescription data mining and knowledge discovery. The efficacy of herb has been identified and summarized through serval thousand years of clinical practices, but there are many herbal groups for disease/symptom/efficacy still needed to be further mined. Current approaches to perform such task proposed by now are mostly utilizing co-occurrence frequency of herbs in a prescription collection to measure their strengths in forming a herbal group with a particular efficacy or toward a particular disease/symptom. While initially the Apriori algorithm or its some accelerated variations are employed in these frequency-based approaches , 18, 27 jun-chen-zuo-shi) in a prescription, thus a group of herbs for a set of symptoms can be inferred by the model.In order to overcome the difficulties faced by raw-frequency-based approaches, Wang et al.  incorporAlthough the recent studies such  and 21]21] have To tackle the issues mentioned above, a two-stage approach to detect essential groups for a particular efficacy from TCM prescriptions is proposed in this paper. In the first stage, we devise a neural network model to distill prescriptions in TCM, in which herbs are embedded into dense real vectors learned automatically to capture the semantical correlations, and a hierarchical attentive mechanism is proposed to recognize essential herbs in a prescription for its efficacy, filtering out insignificant herbs. For the second stage, ESHGs are mined from the distilled prescriptions acquired in the first stage. Finally, we collect a set of efficacies labeled with their known herbal groups by TCM experts as the gold-standard test data to verify the effectiveness of our approach in discovering ESHGs.As discussed above, our solution to ESHGs detection consists in a two-stage approach, in which the first stage is to capture essential herbs in a prescription for its efficacy thus resulting in a cleaned collection of prescriptions, and the second stage is to discover ESHGs from the distilled prescriptions. The architectural diagram is given in Fig. sigmoid output, denoting the probability of a prescription to a given efficacy, and the corresponding attentive weights of the herbs in the prescription expressing their correlations to the efficacy. For a given efficacy, we collect prescriptions with the efficacy as positive samples and prescriptions without the efficacy as negative samples, and train our hierarchical attentive neural network with these samples. Afterwards, the trained model is used to distill the positive samples with the following strategy: the herbs with attentive weights below a prespecified threshold in a positive sample prescription are treated as being unrelated to the efficacy and thus filtered out from the prescription, and the remaining herbs are thought as essential in the prescription for its efficacy. The distilling process in the first stage is then followed by the second stage, as shown in Fig. In order to capture essential herbs in a prescription for its efficacy, we devise a hierarchical attentive neural network with its The hierarchical attentive neural network devised to identify essential herbs in a prescription for its efficacy is shown in Fig. N rows corresponding to distinct herbs of TCM, which are expressed in H with real-valued vectors of dimensionality k distinct herbs H, the herb embedding layer of our model first extract those row vectors indexed with H (i.e. the embeddings of those herbs in H),and stacks them into a matrix P for our model. Afterwards, the matrix  P and enrich every herb’s embedding in P for its efficacy which are verified by the last layer, i.e. the output layer. The two attention layers together transform the initial representation Let P and its initial representation P to form a weight distribution vector of the dimensionality k, and all such vectors of the k distinct herbs are collected into the matrix P according to the weight distribution vector of an herb over all the herbs of P, resulting in an updated representation for the herb. Formula”. For the second type of data, we extract the prescriptions having the efficacies in the gold standard dataset from the prescription databaseEmpirical evaluation of our method requires two types of data. The first one is the efficacies with their known corresponding ESHGs as the gold standard data, and the second one is the prescriptions accompanying with their efficacies as the data to be mined for detecting ESHGs. Due to the lack of gold standard data widely accepted for our task, we intentionally collect efficacies having known reliable ESHGs from Internet , and invite a TCM expert to evaluate these collected ESHGs, finally obtain a data set of 14 efficacies with their corresponding ESGHs for our evaluation. For instance, the efficacy For a specific efficacy, we treat prescriptions with the efficacy as positive samples and prescriptions without the efficacy as negative samples. Because of the data skew for positive and negative samples, we utilize an under-sampling method to obtain a balanced dataset in a ratio of positive to negative samples of 1:1 for each efficacy. And the numbers of prescriptions extracted for each of the 14 efficacies are listed in Table recall metric.The purpose of our work is to capture the essential herbs in a prescription for a given efficacy by a classification process and then discover ESHGs from the essential herbs in prescriptions. Hence, the evaluation metrics are the accuracies of the discovered ESHGs instead of the classification. Due to the lack of gold-standard data widely accepted for our task, we could not find out all possible ESHGs for calculating the e is an efficacy with its gold standard ESHGs e, and the Dice coefficient on e ishg and hg| and For a given efficacy, there are multiple gold standard ESHGs, as shown in Table  formula .10\docume, when it identifies Based on formula , the ide formula  to formu formula .11\docum“heat-clearing and detoxifying” with its gold standard ESHGs and the corresponding prescriptions out of the data as our development dataset, and based on the development, we set the hyperparameters of our model as shown Table H is initialized randomly, and the attentive weights in 10 runs of the training process are averaged as the final attentive weights of herbs in a prescription to discover essential herbs in the prescription for its efficacy.In order to determine the optimal hyperparameters in our model, we leave the efficacy N herbs are chosen to form the corresponding distilled prescription. In order to improve the quality of the distilled prescriptions, the positive and negative samples are fed into the hierarchical attentive neural network 10 times with its different random initializations of the parameters, thus resulting in 10 groups of the attentive weights. Afterwards, all the 10 attentive weights for an herb in a positive prescription are summed, and the herbs in a positive prescription are ranked in descending order of their summed attentive weights, and the top N herbs are retained as the elements of the corresponding distilled prescription.For a given efficacy, its positive and negative samples first pass through the hierarchical attentive neural network and with the model all herbs in these samples obtain their corresponding attentive weights relative to the sample prescription they belong to. After that, all herbs in a positive prescription are ranked in descending order of their attentive weights, and the top N, and also for K, the size of an itemset in the Apriori algorithm, and the support threshold min_sup in the Apriori algorithm. Furthermore, we also run the Apriori algorithm with the same parameter settings (i.e. the K and min_sup) on all the positive prescriptions without the distilling process, and compare the results to the corresponding results obtained with the distilling process. Furthermore, in order to verify the stability of our two-stage approach, we perform the two-stage processing 10 times on the same positive and negative samples, and the 10 experimental results in terms of 95% confidence interval are reported hereafter to represent the effectiveness of the approach for an efficacy.The resultant distilled prescriptions are then fed to the Apriori algorithm for mining ESHGs of the efficacy. We investigate different settings for the parameter K2, 3, 4}.Table “activating blood to resolve stasis ”, without the distilling process the number of the frequent 2-itemsets . However, when 4, the aggressive distilling process leads to an obvious decrease in the performance. As we increase N  for the herbs in a prescription. We sort all the herbs in a prescription in a descending order of their attentive weights, compare them against the annotated essential herbs and accordingly evaluate the effect of our approach for the essential herb detection.In this subsection, we further verify the effect of the hierarchical attentive neural network for capturing essential herbs in a prescription for its efficacy. For the purpose we collect some additional prescriptions with efficacies from the 14 ones in Table MAP (Mean Average Precision), which is widely used for quantitative analysis of ranking algorithms in information retrieval and search engines. Suppose a prescription p has AP) of the hierarchical attentive neural network on this prescription is defined as:position(i) is the position of the essential herb i in the ranking list returned by our hierarchical attentive neural network for the prescription p. Furthermore, if an efficacy e has MAP of the neural network for e is“tranquillization”, for which the “Rhizoma Ligustici Chuanxiong, Radix Paeoniae Alba, Radix Rehmanniae Recens, Caulis Spatholobi, Folium Mori, Flos Chrysanthem, Tribulus terrestris, Herba Mentha, Rhizoma et Radix Notopterygi, Semen Ziziphi Spinosae, Radix Ginseng ” and labeled wrongly with the auxiliary efficacy “tranquillization”, but in fact its primary efficacy should be “clearing liver heat and restraining liver yang”. The label noise results in the erroneous essential herbs identified by the hierarchical attentive neural network.As for the evaluation metric, we employ a traditional one, namely Jun-Chen-Zuo-Shi into our model is another interesting point in our further study.In summary, we utilize a neural network with two attentive layers to identify essential herbs in a prescription for its efficacy, and then discover ESHGs from TCM prescriptions. The efficacy of a prescription is very complicated which is related to herbal combination, herbal dosage, and dosage form. There are still some factors we have not considered. As a successor of this work, we intend to incorporate more herbal information such as dosage into our model to further lift the performance. Furthermore, discovering regularities in TCM prescription composition with data-driven methods and leveraging such regularities to guide the ESHGs detection are another our effort direction. Additionally, integrating the principle of In this paper we propose a two-stage approach for discovering ESHGs from TCM prescriptions. We devise a neural network with two attentive layers to capture semantical correlations among herbs in a prescription and at the same time identify essential herbs in a prescription for its efficacy. Such attentions are beneficial to overcoming the difficulties when performing data mining on the prescription data accumulated in the long period of TCM history. The detailed experiments verify the effectiveness of our two-stage approach in the whole as well as the hierarchical attentive neural network for identifying the essential herbs in a prescription for its efficacy.


Cerebral palsy is a physical impairment stemming from a brain lesion at perinatal time, most of the time resulting in gait abnormalities: the first cause of severe disability in childhood. Gait study, and instrumental gait analysis in particular, has been receiving increasing attention in the last few years, for being the complex result of the interactions between different brain motor areas and thus a proxy in the understanding of the underlying neural dynamics. Yet, and in spite of its importance, little is still known about how the brain adapts to cerebral palsy and to its impaired gait and, consequently, about the best strategies for mitigating the disability. In this contribution, we present the hitherto first analysis of joint kinematics data using permutation entropy, comparing cerebral palsy children with a set of matched control subjects. We find a significant increase in the permutation entropy for the former group, thus indicating a more complex and erratic neural control of joints and a non-trivial relationship between the permutation entropy and the gait speed. We further show how this information theory measure can be used to train a data mining model able to forecast the child’s condition. We finally discuss the relevance of these results in clinical applications and specifically in the design of personalized medicine interventions. Cerebral Palsy (CP), the most frequent cause of severe disability in childhood, is the result of a single brain lesion at perinatal time, which may affect the brain to various degrees . SubsequThese considerations have led to the development of Instrumental Gait Analysis (IGA), a set of techniques that are able to objectively quantify human gait. Its use is gaining followers in clinical practice and research. IGA assesses patient’s specific problems by measuring how the body moves as a whole and providing spatio-temporal parameters ; and by further acquiring high frequency kinematic measurements of those joints that align the lower extremity segments along the patient’s gait cycle: the period of time between two consecutive floor-heel contacts of the same foot . More imAs for any signal-dependent biological system, joint movements during gait are the sum of stochastic and deterministic influences . It thusIn this paper, we present the first (to the best of our knowledge) analysis of the joint kinematics during the gait cycle of healthy children and children with bilateral spastic CP, through the assessment of the signal’s single-scale and multi-scale Permutation Entropies (PEs) ,13. As oOur aim is to study PE as a measurement of motor control, thus being complementary to existing indexes for the assessment of motor impairment. We used traditional statistical methods and diagnostic models based on data mining algorithms to demonstrate a significant increase in the permutation entropy of CP children’s movements. The magnitude of such an increase depends in a non-trivial way on the joint analyzed and varies across the spectrum of functional disability, suggesting the existence of different adaptive mechanisms in the lesioned motor system. In addition, we found that the permutation entropy is negatively correlated with the walking speed, in both groups of children. CP children walk slower than healthy children, so that their entropy values are higher, but we demonstrate that having a CP condition increases this effect in some joint gait movements. We believe that the use of PE opens new doors towards the analysis of motor control in healthy subjects and patients, with potential clinical and therapeutic implications.We start with an analysis of the differences between our control subjects and CP patients in terms of gait single-scale permutation entropy for each movement; see In healthy subjects, single-scale PE varies according to the movement plane. Adduction-abduction and rotational movements tend to have greater values of PE than flexion-extension movements. The same applies to distal joints (ankle and forefoot) in comparison to proximal joints (knee and hip).p-values of two-sided t-tests for the null hypothesis that patients and control subjects have an identical PE average. The four disaggregated violin plots also suggest that the PE is correlated with the GMFCS scale, with Levels III and IV  showing the highest entropy values. This is further confirmed in In general, the permutation entropy of patients, averaged over their corresponding cycles, is higher than that of control subjects. This difference is further confirmed by In order to better understand the relationship between the observed PE and other gait characteristics, There are several possible explanations for these relationships of PE with walking speed, which are not mutually exclusive. Firstly, normalized walking speed is merely related to PE because both speed and PE are related to the severity of motor alteration in CP. This is supported by the relationship of PE with GMFCS. Secondly, speed has an influence on PE, and those subjects who cannot walk faster due to the motor impairment recruit neural gait strategies with lower PE values. Thirdly, CP patients recruit gait strategies that have higher PE and slow preferred walking speed without any direct relationships between these two factors.A complete explanation would require a full causality analysis and possibly a specific experiment in which the gait speed is forced to be constant, which would entail several technical and medical difficulties and is beyond the scope of this work. Nevertheless, the results presented in this section allow us to confidently conclude that, above and beyond the difference in speed, patients’ gait is less predictable (and less controlled) than that of control subjects; additionally, such lack of predictability seems to convey information about the progression of the disease not readily available in the gait speed.We also explored the relationships between single-scale PE and gait indices in children with CP see . Gait inAlthough the standard permutation entropy, as defined in The top panels of i. As the purpose of this metric is to describe how the entropy evolves at different time scales, the specific value of required .Values of If the previous analyses have shown that there is a  difference between control subjects and CP patients in terms of gait PE, it is less clear whether this difference has just a descriptive value or can also be used in predictive tasks. The difference between the two aspects is far from trivial, as has been shown in recent works; the interested reader may refer to Section 3.1 of  for furti is here represented by a vector As a first approximation, each individual fier see , which hWe also explored whether single-scale PE could be used to differentiate between cycles from healthy subjects and cycles from patients classified by GMFCS stages. This allows testing the ability of PE to represent the severity of gait impairment in CP; and to further explore which joint movements are mostly related with motor disability. Random forests provide a good concordance  would help to gain further insights into the biological meaning of PE. Considering all these facts, we believe that PE is an interesting research tool, as it can easily be calculated using the current research protocols in human gait analysis, and it can provide additional information about motor control impairment in human diseases. In this paper, we describe its use as a new methodology to analyze motor control on the basis of kinematic parameters, and as a consequence, it opens new doors towards the future investigation and assessment of the effects of therapeutic interventions on CP gait, or the evaluation of alterations in movement complexity in other neurological diseases.A group of 27 healthy school-aged children  was useGait analysis was performed with a CodamotionWe calculated several indices that are commonly used as indicators of the “quality” of a particular gait pattern. These include the Gait Deviation Index (GDI)  and the IGA and clinical assessments were performed by different researchers. GMFCS stage was registered for CP patients.The concept of permutation entropy was initially introduced by Bandt and Pompe to provide researchers with a simple and efficient tool to characterize the complexity of the dynamics of real systems, without the need for introducing arbitrary thresholds or binning procedures: a limitation of existing measures, including entropies, fractal dimensions or Lyapunov exponents . The solFor the sake of completeness, we here review the main ideas behind permutation entropy, both for single and multiple time scales.D, such that:The first step in the calculation of the single-scale permutation entropy requires extracting ordinal information from the time series. Given a time series D is called the embedding dimension and controls the quantity of information included in each region, while s further controls the beginning of each region and here assumes all values in the range The second step involves associating an ordinal pattern to each region, defined as the permutation In other words, values are sorted in increasing order, with the ordinal pattern corresponding to the required permutation. A simple example may help clarify this concept. Assume a time series If all ordinal patterns are expected to appear with the same frequency in a completely random time series, this is seldom true in real-world data. One or several patterns may be under-represented (or completely missing) for several reasons, such as the presence of attractive or forbidden trajectories in the dynamics . The stai-th permutation. Values of PE close to zero indicate time series with a fixed dynamics, i.e., in which only one or a few ordinal patterns can appear, as in monotonously increasing or decreasing sequences. On the other hand, the closer PE is to one, the more random is the time series.Note that, in the previous equation, In the previous definition of the permutation entropy, the values used to calculate each permutation where sampled from the time series in a sequential way. This presents the advantage of not discarding any information and thus of including all high-frequency data in the analysis. At the same time, such an approach entails several drawbacks: it is not able to account for the multiple time scales present in the dynamics of physiological systems and is more sensitive to high-frequency noise.Y is derived as:In a way similar to how multi-scale entropies are usually defined , we hereY thus represents the average of X, drawn sequentially from non-overlapping windows. The permutation entropy is then calculated on Y, yielding a result defined as a function of the scale factor Each value of In order to fully assess the relationship between PE, CP severity and gait speed, we constructed and evaluated three types of linear mixed models.p-values for the fixed slope by means of t-values’ contrasts and calculated the The first was developed to compare PE values between gait cycles according to the GMFCS level; see The second model type was designed to assess the effect of CP and normalized walking speed on PE; see The third model type was designed to assess the relationship of gait indices and PE. The dependent variable was either GDI or GPS, while a fixed intercept and fixed slope (beta coefficient) was adjusted for each single-scale PE using a random intercept for each subject. We calculated the Random Forests (RFs) are a well-known ensemble learning method for classification, which is based on constructing an ensemble of decision trees and on choosing as output class the one selected by the majority of them ,32. RFs Classification models for CP have been constructed using the random forest algorithm, as implemented in the scikit-learn Python library . ClassifN separate times (with N representing the number of instances), each time on all the data except for one instance, and on calculating the prediction for that point. Finally, the average error and the area under the ROC (AUC) were computed for the RF, which explores differences between healthy and CP children and the weighted Cohen’s kappa in the RF, which classifies between GMFCS stages.In order to estimate the generalization accuracy of all models, a Leave-One-Out Cross-Validation (LOO CV) strategy has been implemented . It is b


In a smoke environment, suspended particles can scatter and absorb laser photons, making target echo signals extremely weak and difficult to extract and identify, which causes obvious difficulty in fixed-distance of laser fuze. In this paper, the multiple scattering model of frequency-modulated-continuous-wave (FMCW) laser fuze in a smoke environment was established. This model simulates multi-path propagation and multiple scattering of photons. At the same time, we use the correntropy spectral density (CSD) algorithm for accurate fixed-distance of FMCW laser fuze. The absolute error of distance does not exceed 0.15 m in smoke interference environment. Fixed-distance fuze is a device that measures the distance to the target by radio, laser, ultra-wideband, millimeter wave, and detonates the warhead at the best explosive point. Pulse laser fuze has been widely used for its characteristics of excellent anti-electromagnetic interference capability, simple structure, and low cost. However, pulse laser fuze is susceptible to interference from suspended particles such as smoke and clouds, which makes it difficult to extract and identify target signals ,2. CompaResearch has been done on the target echo characteristics of laser in the interference environment of suspended particles. Grabner et al. studied the effect of extinction coefficients of different concentrations of fog and haze on laser transmission . Lundin Corretropy is used to compare the degree of similarity between the two sets of signals. It was first proposed by Jose C. Principe, a professor of electrical and computer engineering at the University of Florida, and analyzed in detail ,12. GardIn this paper, we established a laser multipath propagation model in smoke interference environment in c is speed of light, T is modulation period and B is modulation bandwidth.The FMCW laser ranging system modulates the light intensity of transmitted laser signal by a signal in which instantaneous frequency varies linearly with time and uses the modulation signal as a local oscillator signal. Due to the time delay of laser transmission in the atmosphere, the instantaneous frequency of the echo signal changes. The echo signal is mixed with the local oscillator signal to obtain the intermediate frequency (IF) signal. When there is no interference, the IF signal should be a cosine signal with a certain frequency. The frequency is related to the target distance and relative speed. Symmetric triangular wave FMCW modulation is widely used because it can directly calculate the distance and speed of the target from the IF signal. The detection principle is shown in For the convenience of research, this model only analyzes the up-sweep period. At this time, the up-sweep modulation period R need to be calculated by The target distance Existing simulations of FMCW laser fuzes in smoke interference environment assume that both the fuze and target are in a stable smoke environment, assuming that the smoke scattering coefficient and extinction coefficient are fixed values. In fact, as fuze gradually approaches the target covered by smoke, the occurrence of smoke interference is a random dynamic process from scratch. In our earlier work, the aerosol extinction coefficient and scattering coefficient changed dynamically according to the different smoke density variation, aerosol particle distribution, and photon spatial positions. Based on , in this(1)v, and the target is detected for consecutive k times, each time interval is R is the distance between fuze and target. If the transmission power is D is the diameter of aperture of the receiving optical system, For the first case, the photon is directly reflected by the target and then received by the receiving optical system. During the multiple scattering process, the optical path length accumulated, and time delay occurred between the echo signal and the transmitted signal. During the approach of the projectile-target encounter, if the forward speed of the fuze is (2)For the second case, received photons don’t reach the target surface and are all scattered by smoke. Assuming that the laser emission power is ng model , if the i times scattering is:i-th scattering. According to the Mie scattering theory, the scattering phase function g is asymmetric factor and its value range is .We construct multiple scattering models based on single scattering model ,21, the xpressed :(9)P(θ)The delay time The echo signal power composed of the second type of photons after In the study, it is assumed that there are (3)i-th scattering, the target is the Lambert scatterer, and the reflection coefficient of the target is For the third case, photons that reach the target surface are scattered by the aerosol and eventually return to the fuze receiving system. The scattering process of photons in smoke is consistent with the first case, assuming that the power of the laser-emitting signal is The multiple scattering process caused the optical path length to accumulate and generated time delay. The delay time Therefore, the echo signal power composed of the third type of photons after the If there are According to the transmission process of the laser in the smoke environment, three types of echo signal photons can be received by the fuze receiving system at a certain time, including: (1) photons that are directly transmitted to the target surface after being emitted, and are directly received by the fuse after being reflected by the target; (2) photons that do not reach the target surface scattered by the aerosol and return to the receiving syatem; (3) photons that reach the target surface scattered by the aerosol during transmission and eventually return to the receiving system. At this time, the power If the photoelectric conversion efficiency of the photodetector is In this study, the local oscillator signal expression is:According to the principle of FMCW laser detection system, shown in If the mixing process of the local oscillator signal and the echo signal does not consider the signal attenuation and filters out the higher harmonic term, the IF signal of the FMCW laser fuze in the approach of the projectile can be expressed as:Under smoke interference conditions, the target echo signal Visibility is represented by smoke density during simulation. The relationship between smoke density and visibility is as follows :23)C=c0C=c0(23)Cd γ=1.07 . NormallCSD can compare the similarity of two signals in the frequency domain. Therefore, when using CSD algorithm for fixed-distance, computers are used to calculate IF signal frequency under ideal conditions according to the expected distance, and get the signal waveform, that is, the waveform of the reference IF signal. Ideally, an IF signal is a single frequency cosine signal whose frequency has a linear relationship with the distance between fuze and target. The IF signal under ideal conditions is referred to as the reference IF signal. According to the principle of FMCW laser detection, the reference IF signal Equation :(24)fIFeThis paper uses the CSD to compare the similarity in frequency domain between the reference IF signal and the measured IF signal as a criterion for fuze determining distance. If a spectral peak appears at a is standard deviation of the sampled signal and In this paper, the correntropy expression ,25 of metimation :(26)σ=4aThe Mercer kernel function  pattern . When thIn the implementation of laser fuze engineering,  formula :(27)V^(mFourier transform of ssion is :(28)C(f)Whether the two signals are similar can be discriminated by the presence or absence of a peak at a reference frequency in the correntropy spectral density distribution. When identifying the frequency peaks in the CSD distribution, a rectangular window function such as Equation  can be uIf the effective bandwidth In the absence of smoke interference, there is only target signal (1)Obtain the currently measured IF signal.(2)Calculate the reference frequency (3)Calculating (4)Do Fourier transform for the (5)Determine whether the peak appears in the CSD processing result. If the peak appears at the reference intermediate frequency (6)Recalculate the distance according to the motion speed of the fuze and the detection time interval, and begin the second detection at step The basic steps of the CSD-based fixed-distance algorithm are as follows:k is the number of detections, v is the motion speed of the fuze.This section studies the CSD algorithm to identify target signals in the case of target without smoke interference, smoke interference but no target, and the target is covered by smoke. The CSD algorithm processing results are compared with the FFT algorithm processing results to further verify the advantages of the CSD algorithm in terms of under smoke interference conditions. The specific parameters used in simulation are shown in Equation . Other pEquation .In this section, when expected distance is 3 m, the simulation results are compared when the distance is 3 m and 5 m between fuze and target. When expected distance is 9 m, the simulation results are compared when the distance is 9 m and 12 m between fuze and target. Each simulation result includes two consecutive detetion, the red curve represents the first detection, and the black curve represents the second detection.It can be seen from the simulation results that, when there is no smoke interference, if the distance between the fuze and the target is equal to the expected distance, both the CSD algorithm and the FFT algorithm processing results have obvious peaks at the reference intermediate frequency, both satisfying the fixed-distance condition. However, the amplitude of the spectral peak of the CDS algorithm is much larger than the peak of the FFT algorithm. When the distance between the fuze and the target is not equal to the expected distance, the processing results of the two methods have no peak near the reference intermediate frequency, indicating that the fixed-distance condition is not satisfied. Since the correntropy is always greater than zero, when the correntropy is Fourier transformed to obtain the correntropy spectral density, zero-frequency interference occurs in the result. Zero-frequency interference can be eliminated by the window function without affecting the identification of the peak of the target signal.When there is no target, it can be found that there is no obvious peak in the result of the CSD algorithm from the results of simulations. However, affected by smoke interference, the result of FFT algorithm has multiple peaks, which can’t achieve fixed-distance and may cause false alarms.From simulation results In summary, the CSD algorithm can effectively suppress smoke interference. When performing correntropy calculations, the Gaussian kernel function rapidly attenuates the components whose frequency is not equal to This section builds the FMCW laser fuze test platform, and conducts experiments in different environments. A typical semiconductor laser (In experiments, the fuze is facing the target, and the target surface is perpendicular to the emitted laser beam. The fuze adopts a triangular wave frequency modulation system, and the DDS generates a chirp signal with a bandwidth of 50 MHz, and the modulation period is 100 The spectrum of IF signal is obtained by fast Fourier transform. It can be found that, in the correntropy spectral density distribution, as shown in Equation . The absThis section verifies the anti-interference ability of FMCW laser fuze in the smoke environment. The test scenario schematic is shown in The experiment room size is 15 m × 4 m wide, test window size is 0.3 m × 0.3 m and confined diffusion space which is 2 m × 4 m wide. Gradually release smoke from smoke source in confined space to reduce visibility. We used an atmospheric visibility sensor to calibrate the visibility of the experimental environment to 10 m. The laser beam emitted by the prototype enters the smoke diffusion space through the test window. Because high speed movement of fuze cannot be simulated indoors, this paper lists the results of two detections of the target under the same conditions. From the experimental results, it can be found that the smoke interference increases the noise in the IF signal, and the time domain waveform is obviously distorted. The noise in the spectrum increases, and a high-amplitude interference peak appears on the left of the target signal peak. The smoke interference signal may be used as the target signal to cause false alarm. Under smoke interference conditions, significant peaks can still appear at the reference frequency in the CSD algorithm processing results. The peak frequencies at 3 m and 9 m from the target are 19.6 kHz and 59.5 kHz, respectively. In this paper, a multiple scattering model of photons in smoke environment is established. This model takes account of the multiple scattering of photons and multi-path propagation. The CSD algorithm is used to process the data, and an accurate fixed-distance algorithm of FMCW laser fuze is proposed. The experimental results show that the CSD algorithm has good anti-interference ability in smoke environments, and our experimental results are consistent with the simulation results. The relative error between measured peak frequency and theoretical value does not exceed 5%, and the absolute error of distance does not exceed 0.15 m. Our detection system uses single-quadrant and single-detector achieving high accuracy, so our system is simpler and easier to implement in engineering.