An event-triggered multi-sensor multi-model fusion estimation algorithm resistant to thick-tail interference

Abstract

This invention discloses an event-triggered multi-sensor multi-model fusion estimation algorithm with resistance to heavy-tailed interference, belonging to the field of multi-sensor target tracking and information fusion technology. This method addresses the problems of heavy-tailed noise in sensor observation data and limited network transmission in real-world environments. It unifies the observations of targets by multiple sensors into a multi-model linear discrete dynamic system, and utilizes an improved Student's t-distribution interactive multi-model filtering algorithm to fully leverage multi-sensor information and achieve high-precision estimation of the target state. The algorithm design incorporates an event-triggered mechanism, allowing each sensor to independently determine whether its observation data should be transmitted and participate in fusion, effectively reducing the transmission of redundant information and saving network bandwidth and node energy consumption. Simultaneously, through a sequential information fusion structure and heavy-tailed noise modeling, the robustness and estimation accuracy of the system under extreme noise interference are further improved. This algorithm has low computational cost, low energy consumption, and is easy to implement, making it suitable for applications such as multi-target tracking, integrated navigation, distributed sensing, and fault detection in complex environments, and has broad engineering application value.

Description

Technical Field

[0001] This invention relates to target state estimation and data fusion technology in multi-sensor systems, and in particular to a heavy-tailed noise sequential single-sensor and multi-sensor fusion estimation algorithm based on an event-triggered mechanism and an interactive multi-model approach. It belongs to the technical fields of intelligent sensing, wireless sensor networks, automatic control, and information processing. Background Technology

[0002] With the rapid development of intelligent sensing and wireless sensor network technologies, multi-sensor fusion estimation has been widely applied in target tracking, intelligent transportation, robot control, and industrial monitoring. In real-world system environments, sensor observation data are often affected by various non-ideal factors, especially measurement noise, which exhibits significant non-Gaussian heavy-tailed characteristics such as sudden interference and outliers. Traditional state estimation algorithms based on the Gaussian noise assumption are poorly robust to heavy-tailed noise, easily leading to large estimation errors or even failure.

[0003] Furthermore, many complex dynamic systems possess multi-model characteristics, and the target state may exhibit maneuvering abrupt changes or multiple dynamic models. Filtering algorithms based on a single dynamic model struggle to adapt to changes in the system model. The Interactive Multiple Model (IMM) algorithm, by processing multiple dynamic models in parallel and integrating model probabilities, achieves adaptive tracking of the system's dynamic characteristics, effectively improving the accuracy and adaptability of state estimation. However, the performance of the classic IMM algorithm is still affected when the observation noise has a heavy-tailed distribution.

[0004] On the other hand, traditional time-triggered data transmission mechanisms in practical multi-sensor systems tend to generate a large amount of redundant data transmission, leading to increased communication energy consumption and network congestion, which is detrimental to the efficient and low-energy operation of the system. In recent years, event-triggered mechanisms have gradually attracted attention. By designing trigger criteria such as innovation normalization, sensors only upload data when the observed data makes a significant contribution to state estimation, effectively reducing communication load and system energy consumption, and improving the real-time performance and efficiency of the system.

[0005] In summary, designing a multi-sensor sequential fusion estimation algorithm that can improve estimation accuracy and robustness while effectively reducing communication load under conditions of heavy-tailed noise and multi-model dynamic systems has become a critical technical challenge that urgently needs to be addressed in the field of target tracking and state estimation. Summary of the Invention

[0006] The purpose of this invention is to propose a target tracking and localization method suitable for wireless sensor networks in radar systems. Addressing the common problems of thick-tailed noise and abrupt changes in system dynamic models in actual sensor observation data, this invention designs a single-sensor target tracking algorithm and a multi-sensor sequential fusion estimation algorithm based on an event-triggered mechanism and an interactive multi-model framework. This is achieved by employing a multivariate student... The distribution describes the heavy-tailed characteristics of sensor measurement noise and system process noise. Combined with an event-triggered strategy, it significantly reduces data transmission bandwidth and energy consumption while ensuring estimation accuracy and robustness, thus achieving efficient and reliable target tracking and state estimation.

[0007] The method is characterized by being implemented on a computer in the following steps:

[0008] 1. A multi-model target tracking method based on an event-triggered mechanism under thick-tailed noise, for radar target tracking systems with thick-tailed noise interference and network transmission limitations; the method describes the sensor's observation of the target as a linear discrete-time dynamic system with Markov jump characteristics, the system state including the target's position and velocity; characterized in that the method includes the following steps:

[0009] Step 1: Establish a single-sensor Markov transition system, acquire initial data of the tracked target, and set the initial state of the target. Follow the mean The scale matrix is The degrees of freedom are The system exhibits a thick-tailed distribution; assuming the system noise during sensor tracking of the target has a mean of 0, and the scaling matrix is... The degrees of freedom are The target has a heavy-tailed distribution; assuming the moving target has M dynamic models, the transitions between models are determined by Markov chains. express, for The system model variables at any given time represent the current dynamic model of the system. express The system state transition matrix at time t, It is a positive integer;

[0010] Step 2, at time Acquire sensor data Observational data at time The measurement matrix is The measurement noise follows a mean of 0, and the scale matrix is... Independent thick-tailed noise with v degrees of freedom;

[0011] Step 3, in At any given moment, define the model. probability ,Model probability The probability transition matrix between the model and the model Calculate the normalization constant. Mixed probabilities of the model ;

[0012] Step 4, from the model mixture probability Calculate the mixed state matrix and mixed covariance matrix ;

[0013] Step 5, according to Mixed state matrix at time step and mixed covariance matrix Calculate the current Target state prediction value at time 1 With state prediction error covariance matrix ;

[0014] Step 6, in At that time, the sensor measurement value obtained in step 2 is used. And the target state prediction value calculated in step 5 With state prediction error covariance matrix ,calculate The new covariance matrix at time 1 And calculate the event triggering parameters. ;when When the event is triggered, the measured value... Transmitted to the remote estimator; when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator;

[0015] Step 7, in At that time, using the observation data obtained in step 2 Step 5 calculates the target state prediction value With state prediction error covariance matrix and the event triggering parameters calculated in step 6. Calculate the mixture covariance matrix Filter gain and state estimates and the estimated error covariance matrix ;

[0016] Step 8, in At time, using the likelihood function and the normalization constant calculated in step 3 Update model probabilities ;

[0017] Step 9, in At time 1, the state estimates based on all models Estimation error covariance and model probability Calculate the weighted fusion system state estimate and the corresponding estimation error covariance matrix ,get The results of constant target tracking;

[0018] Step 10, Assign to Repeat steps 2 to 9 to obtain the target state estimate and the estimation error covariance matrix at any time.

[0019] In step 3, at the transmission time According to the model probability ,Model probability With the transition probabilities in the model transition matrix Calculate the normalization constant. Model mixture probability ,as follows:

[0020]

[0021]

[0022] in, ;

[0023] In step 4, the model mixture probability is used. Calculate the mixed state matrix and mixed covariance matrix ,as follows:

[0024]

[0025]

[0026] in, and Representing the model respectively The state estimate and the estimation error covariance matrix, , Superscript Indicates transpose; Indicates degrees of freedom.

[0027] In step 5, according to Given the mixture state matrix and mixture covariance matrix at time 1, calculate the current state matrix. Target state prediction value at time 1 With state prediction error covariance matrix ,as follows:

[0028]

[0029]

[0030] in, Represents the state transition matrix. Indicates in System noise during constant target observation The scaling matrix.

[0031] In step 6, the event triggering parameters of the sensor are calculated. The method is:

[0032] First, calculate The measurement value of the time sensor and based on The difference between the predicted value of the measured value and the state at time, i.e., the innovation. and the covariance matrix of the new information The following are examples:

[0033]

[0034]

[0035] The covariance matrix of the new information It is a positive semi-definite matrix, calculate eigenvalues , It is the dimension of the observation vector provided by the sensor, and is expressed as a diagonal matrix:

[0036]

[0037] Calculate the unitary matrix using the following formula :

[0038]

[0039] Then, set the matrix Then we can further obtain a normalized and decorrelated matrix. ;

[0040] Finally, obtain the event triggering parameters of the sensor. ;in, Denotes the infinity norm of a matrix. The threshold for triggering the event. .

[0041] In step 7, the mixed covariance matrix Filter gain and state estimates and estimation error covariance The calculation is as follows:

[0042]

[0043]

[0044]

[0045]

[0046] in, yes The predicted value of the measured value at any given time. It is a normalized new information, It is under the restricted interval The second moment of distribution is calculated as follows:

[0047]

[0048]

[0049]

[0050]

[0051] In step 8, the model probability is updated using the likelihood function and the normalization constant. The calculation is as follows:

[0052]

[0053]

[0054] In step 9, a weighted fusion system state estimate is calculated based on the state estimates, estimation error covariance, and model probabilities of all models. and the corresponding estimation error covariance matrix The calculation is as follows:

[0055]

[0056] 2. A multi-model sequential fusion estimation method based on an event-triggered mechanism under heavy-tailed noise, for a multi-sensor target tracking system with heavy-tailed noise interference and network transmission limitations; the multi-sensor observations of the target are described as a linear discrete-time dynamic system with Markov jump characteristics, and the system state includes the target's position and velocity; the method determines the timing of data transmission from each sensor through an event-triggered mechanism, effectively reducing network communication load, and uses a sequential fusion estimation strategy based on interactive multiple models (IMM) to achieve state estimation, characterized in that the method includes the following steps:

[0057] Step 1: Input the number of sensors N into the computer to establish a multi-sensor Markov hopping system, acquire the initial data of the tracked target, and set the initial state of the target. Follow the mean The scale matrix is The degrees of freedom are The system exhibits a thick-tailed distribution; assuming the system noise during sensor tracking of the target has a mean of 0, and the scaling matrix is... The degrees of freedom are The target has a heavy-tailed distribution; assuming the moving target has M dynamic models, the transitions between models are determined by Markov chains. express, for The system model variables at any given time represent the current dynamic model of the system. express The system state transition matrix at time t, It is a positive integer;

[0058] Step 2, at time Get the One sensor in Observational data at time , The measurement matrix is The measurement noise follows a mean of 0, and the scale matrix is... The degrees of freedom are Independent thick tail noise;

[0059] Step 3, in At any time, according to the model probability ,Model probability The probability transition matrix between the model and the model Calculate the normalization constant Mixed probabilities of the model ;

[0060] Step 4, from the model mixture probability Calculate the mixed state matrix and mixed covariance matrix ;

[0061] Step 5, according to Mixed state matrix at time step and mixed covariance matrix Calculate the current Target state prediction value at time 1 With state prediction error covariance matrix ;

[0062] Step 6, in At time 1, using the first time obtained in step 2 Measurement values ​​from each sensor Step 5 calculates the target state prediction value With state prediction error covariance matrix For sensors Calculate in sequence The new covariance matrix at time 1 And calculate the event triggering parameters. ;when When the event is triggered, the measured value... Transmitted to the remote estimator; when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator;

[0063] Step 7, in At that time, using the observation data obtained in step 2 Step 5 calculates and and the event triggering parameters calculated in step 6. For sensors Calculate the mixture covariance matrix sequentially. Filter gain and state estimates and estimation error covariance ,remember , ;

[0064] Step 8, in At time, using the likelihood function and the normalization constant calculated in step 3 For sensors Update the model probabilities sequentially ,remember ;

[0065] Step 9, in At time 1, the state estimates based on all models Estimation error covariance and model probability Calculate the weighted fusion system state estimate and the corresponding estimation error scaling matrix ,get The results of all sensors tracking the target at any given time;

[0066] Step 10, Assign to Repeat steps 2 to 9 until all data at all observation times have been processed. Then you can obtain the target state estimate and the estimation error covariance matrix of the multi-sensor sequential fusion at any time.

[0067] In step 3, at the transmission time According to the model probability ,Model probability With the transition probabilities in the model transition matrix Calculate the normalization constant. Model mixture probability ,as follows:

[0068]

[0069]

[0070] in, ;

[0071] In step 4, the model mixture probability is used. Calculate the mixed state matrix and mixed covariance matrix ,as follows:

[0072]

[0073]

[0074] in, and Representing the model respectively The state estimate and the estimation error covariance matrix, , Superscript Indicates transpose; Indicates degrees of freedom.

[0075] In step 5, according to Given the mixture state matrix and mixture covariance matrix at time 1, calculate the current state matrix. Target state prediction value at time 1 With state prediction error covariance matrix ,as follows:

[0076]

[0077]

[0078] in, Represents the state transition matrix. Indicates in System noise during constant target observation The scaling matrix.

[0079] In step 6, the sensor... Calculate the event trigger parameters of the sensor sequentially. The method is:

[0080] First, calculate The measurement value of the time sensor and based on The difference between the predicted value of the measured value and the state at time, i.e., the innovation. and the covariance matrix of the new information The following are examples:

[0081]

[0082]

[0083] It is the state transition matrix and the covariance matrix of the innovation. It is a positive semi-definite matrix, calculate eigenvalues , It is the dimension of the observation vector provided by the sensor, and is expressed as a diagonal matrix:

[0084]

[0085] Calculate the unitary matrix using the following formula :

[0086]

[0087] Then, let the matrix be... Then we can further obtain a normalized and decorrelated matrix. ;

[0088] Finally, obtain the event triggering parameters of the sensor. ;in, Denotes the infinity norm of a matrix. The threshold for triggering the event. .

[0089] In step 7, the sensor... Calculate the mixture covariance matrix sequentially. Filter gain and state estimates and estimation error covariance The calculation is as follows:

[0090]

[0091]

[0092]

[0093]

[0094] in, yes Time of the first The predicted value of the sensor for the measured value, It is a normalized new information, It is under the restricted interval The second moment of distribution is calculated as follows:

[0095]

[0096]

[0097]

[0098]

[0099] make ,

[0100] In step 8, the sensor... The model probabilities are updated sequentially using the likelihood function and the normalization constant. The calculation is as follows:

[0101]

[0102]

[0103] make

[0104] In step 9, a weighted fusion system state estimate is calculated based on the state estimates, estimation error covariance, and model probabilities of all models. and the corresponding estimation error covariance matrix The calculation is as follows:

[0105]

[0106] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0107] (1) The present invention adopts an event-triggered transmission mechanism. By designing an event-triggered criterion based on information normalization, data is uploaded only when the observed data makes a significant contribution to the system state estimation. This significantly reduces unnecessary communication load and system energy consumption. Under the premise of ensuring target tracking accuracy, it effectively improves the utilization rate of network resources and system real-time performance, and has the characteristics of low energy consumption and high efficiency.

[0108] (2) This invention adopts a multi-student approach. The distribution model uses a heavy-tailed approach to model measurement noise and system noise, overcoming the limitations of traditional fusion algorithms in non-Gaussian noise environments such as outliers and sudden disturbances in real systems, thus improving the anti-interference ability and robustness of state estimation.

[0109] (3) Based on the Interactive Multi-Model (IMM) algorithm, this invention can dynamically capture multiple motion models or state changes of the system, enhance the system's adaptability to target maneuvering changes and complex dynamic environments, and improve the accuracy and stability of target tracking estimation.

[0110] (4) This invention proposes a sequential multi-sensor fusion strategy, which makes full use of the observation information of each sensor to update the system state in sequence, realizing efficient information fusion and recursive estimation, which is easy to implement in engineering and applicable to large-scale, multi-type sensor systems.

[0111] (5) The overall algorithm of this invention has the advantages of simple structure, high computational efficiency and convenient implementation. It can be directly applied to actual scenarios such as target tracking, intelligent transportation and environmental monitoring, and has good promotion prospects and engineering application value. Attached Figure Description

[0112] Figure 1 This is a computer flowchart of the event-triggered multi-model target tracking algorithm (ET-tIMM algorithm) under thick-tailed noise environment described in this invention.

[0113] Figure 2 This is a computer flowchart of the event-triggered multi-model sequential fusion method (ET-tIMM-SF algorithm) under thick-tailed noise environment described in this invention.

[0114] Figure 3The graph shows the relationship between the root mean squared error (RMSE) of position and velocity for different algorithms in computer simulation curves as a function of time step. The upper graph represents the position RMSE, and the lower graph represents the velocity RMSE. The blue curve represents the RMSE of the Student-t interactive multi-model sequential fusion algorithm (NET-tIMM-SF) without the event-triggered mechanism, and the red curve represents the RMSE of the Student-t interactive multi-model sequential fusion algorithm (ET-tIMM-SF) with the event-triggered mechanism.

[0115] Figure 4 This section compares the root mean square error (RMSE) of position and velocity for a single sensor under different noise modeling conditions using computer simulation curves, with the event trigger threshold uniformly set to θ=0.5. The top figure shows the position RMSE variation over time, and the bottom figure shows the velocity RMSE variation over time. The blue curve represents the single-sensor event-triggered interactive multi-model estimation algorithm ET-gIMM-S1 based on Gaussian noise modeling, and the red curve represents the single-sensor event-triggered interactive multi-model estimation algorithm ET-tIMM-S1 based on heavy-tailed noise modeling, used to compare the robustness and estimation accuracy differences of the algorithms under the two noise assumptions.

[0116] Figure 5 This figure compares the root mean square error (RMSE) of position and velocity estimation algorithms with event-triggered mechanisms under heavy-tailed noise conditions for single-sensor and multi-sensor estimation, as well as under Gaussian noise conditions, using computer simulation curves. The event-triggered threshold is uniformly set to θ=0.5. In the figure, the red curve ET-tIMM-S1 represents the RMSE of the event-triggered single-sensor 1 estimation algorithm under heavy-tailed noise; the green curve ET-tIMM-S2 represents the RMSE of the event-triggered single-sensor 2 estimation algorithm under heavy-tailed noise; the blue curve ET-tIMM-SF represents the RMSE of the event-triggered sequential fusion estimation algorithm under heavy-tailed noise; and the black curve ET-gIMM-SF represents the RMSE of the event-triggered sequential fusion estimation algorithm under Gaussian noise. The comparison of the curves shows that the proposed heavy-tailed Student-t event-triggered sequential fusion algorithm (ET-tIMM-SF) outperforms the comparative algorithms in terms of position and velocity estimation accuracy, verifying its robustness and superior performance under heavy-tailed noise and communication-constrained conditions.

[0117] Figure 6The graphs show the root mean square error (RMSE) of the position and velocity of the multi-model sequential fusion estimation algorithm (ET-tIMM-SF algorithm) based on the Student-t distribution described in this invention under different event triggering thresholds in computer simulation curves. The upper graph shows the change of the target position RMSE with time step under a heavy-tailed noise environment, and the lower graph shows the change of the target velocity RMSE with time step under the same environment. The red, green, blue, and black lines in the graphs correspond to event triggering thresholds θ=0, θ=0.5, θ=0.8, and θ=1.0, respectively, illustrating that adjusting the triggering thresholds can achieve a trade-off between reducing sensor communication load and maintaining estimation accuracy. Detailed Implementation

[0118] The present invention will now be described in further detail with reference to the accompanying drawings and examples.

[0119] This invention addresses single-sensor and multi-sensor systems operating in heavy-tailed noise environments. Based on linear discrete-time dynamic systems and primarily applied to radar target tracking, it aims to obtain high-precision and robust target state information. The invention investigates state estimation algorithms based on event-triggered mechanisms and interactive multi-model (IMM) frameworks, achieving efficient fusion and robust estimation of sequential observation information from single and multi-sensor systems.

[0120] In this embodiment of the invention, the hardware environment and software configuration for implementing the method of the present invention are as follows:

[0121] Hardware environment: Computer; Correlator;

[0122] Software requirements: Windows 7 / 8 / 9 / 10; any language environment such as MATLAB, C, or C++.

[0123] A multi-sensor Markov jump system can be described as

[0124]

[0125]

[0126] in, Indicates the system at time 10:00 The state vector, Indicates the first Each sensor at time The observed values, . Assuming it is a Markov chain with finite states, This represents the total number of dynamic models. Probability transition matrix. ,in For any ,satisfy . and Based on model The system state transition function and observation transition function.

[0127] Assuming system noise and measuring noise These are independent thick-tailed noises and satisfy...

[0128]

[0129]

[0130] in , indicating that the mean is The scale matrix is Degrees of freedom are diversity distributed.

[0131] initial state Follow the mean The scale matrix is The degrees of freedom are diversity distributed:

[0132]

[0133] in, also with and They are mutually independent. Under the above problem description, the sequential fusion estimation results of the system state will be obtained below.

[0134] like Figure 1 As shown, the multi-model single-sensor estimation method under the heavy-tailed noise and event-triggered mechanism provided by the present invention is described in the following steps.

[0135] Multi-model single-sensor estimation method under heavy-tailed noise and event-triggered mechanism

[0136] Step 1: Establish a single-sensor Markov hopping system model and acquire the initial data of the tracked target. Specifically, this includes the following: the target's initial state vector is... The mean of its initial state estimate is The scale matrix is Assume the initial state of the target follows a set of degrees of freedom. Diverse students distributed:

[0137]

[0138] in, This represents the mean of the initial state. It is a positive definite covariance matrix. for Degrees of freedom of distribution.

[0139] System noise and measuring noise All are independent, thick-tailed noises. The scaling matrix of the system noise is... The scale matrix for measuring noise is Both obey a set of degrees of freedom. Diverse students Distribution, that is:

[0140] ,

[0141] in, and These are the scale matrices for system noise and measurement noise, respectively.

[0142] The system has a finite number of dynamic models, and the transitions between models are modeled by Markov chains. The total number of models is denoted as . The sensor is at all times The observation data used The system state transition matrix and measurement matrix are respectively... and .in, For the first The system model variables at time t represent the current dynamic model of the system.

[0143] In summary, a single-sensor Markov skipping system can be represented as:

[0144]

[0145]

[0146] in, For the system at time The state vector, For the sensor at any time The observed values.

[0147] Step 2, at each recursive time step It is necessary to obtain information from the sensor. The observation data at each time point and the corresponding observation transition matrix are obtained through the following steps:

[0148] Acquire sensor data The observation data collected at each moment is denoted as Obtain the observation transition matrix at the corresponding time point. This matrix is ​​used to map the current state of the system to the sensor observation space. Among them, It is a positive integer, representing the current global time step in the recursion.

[0149] Step 3: In the multi-model estimation process, at each observation time... It is necessary to normalize the model probabilities based on the current probabilities and transition probability matrices of each model in the system.

[0150] The specific process is as follows:

[0151] Assume the system has There are three dynamic models, and the model probability vector is denoted as...

[0152]

[0153] in, Indicates time The lower model The probability satisfies .

[0154] The state transitions between the various models in the system are determined by the Markov chain probability transition matrix. control, According to Bayes' theorem, first, based on the model probability from the previous time step... With transition probability Computational model Normalization constant:

[0155]

[0156] in, Indicates the transition to the model The sum of the probabilities of all paths at that time. This represents the total number of dynamic models in the system.

[0157] For each model and Calculate the mixture probability:

[0158]

[0159] in, Indicates the state of the model at the previous time step. And transfer to the current time-instance model The normalized probability.

[0160] Previous time step model The probability of;

[0161] Previous time step model The probability of;

[0162] : Model arrive The state transition probability;

[0163] Step 4: Obtain the model from the mixture probability. The prior mean and mixture covariance matrix of the mixed states provide priors for subsequent recursion:

[0164]

[0165]

[0166] , Previous time step model The state estimate and the estimation error covariance matrix;

[0167] : Degrees of freedom of distribution;

[0168] superscript This represents a weighted mixed prior over all possible transition paths.

[0169] Step 5: Based on the mixed state matrix obtained in Step 4 and mixed covariance matrix Calculate each model at the current time. Target state prediction value With state prediction error covariance matrix The specific calculation formula is as follows:

[0170]

[0171]

[0172] : indicates that it corresponds to the model The state transition matrix;

[0173] : indicates in System noise during constant target observation The covariance matrix;

[0174] Step 6, at each moment Combined with the sensor measurements obtained in step 2 and the target state prediction value calculated in step four. and error covariance The innovation and covariance criteria are calculated to obtain the event triggering parameters. And decide whether to transmit the observation data. First, calculate the measurement value at the current time and the value based on... The difference between the predicted and observed values ​​at any given time, i.e., the innovation and the covariance matrix of the new information :

[0175]

[0176]

[0177] in, Representation Model The observation transition matrix, This represents the covariance matrix of the measurement noise.

[0178] The covariance matrix of the new information Given a positive semi-definite matrix, perform eigenvalue decomposition on it, and denote the eigenvalues ​​as... ,in The dimension of the observation vector is expressed as a diagonal matrix:

[0179]

[0180] orthogonal matrix composed of eigenvectors Makes the following equation true:

[0181]

[0182] Define the normalized and decorrelated innovation matrix:

[0183]

[0184] in, .

[0185] Using the infinite norm of the normalized innovation as the event trigger criterion, a threshold is set. Then the event triggering parameters Determined by the following formula:

[0186]

[0187] in, Denotes the infinity norm of a matrix. This is the threshold for triggering the event.

[0188] when When the event is triggered, the measured value... It is transmitted to the remote estimator;

[0189] when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator.

[0190] Step 7, at time Using the observation data obtained in step 2 Step 5 calculates the target state prediction value. Covariance of state prediction error and the event triggering parameters calculated in step 6. Recursively calculate the mixed covariance matrix Filter gain And update the target state estimate. and estimation error covariance The specific process is as follows:

[0191] The mixed covariance matrix, filter gain, and state update formulas are as follows:

[0192]

[0193]

[0194]

[0195]

[0196] in, For a moment For the predicted values ​​of the observed quantities, To normalize new energy, Under the restricted interval The second moment of distribution is calculated as follows:

[0197]

[0198]

[0199]

[0200]

[0201] in, To normalize the new information.

[0202] Step 8, at time Using the likelihood function and the normalization constant calculated in step 3 The probabilities of each dynamic model are updated to obtain the new probabilities of each model at the current time. The specific calculation method is as follows:

[0203] Current Time Model probability The calculation formula is:

[0204]

[0205] The denominator is normalized to ensure that the sum of all model probabilities is 1. Likelihood function Adopting multiple The distribution pattern, specifically expressed as:

[0206]

[0207] in, For the current observation data, For the predicted value of the observed quantity, The new information covariance matrix, for Degrees of freedom of distribution.

[0208] Step 9, at each moment State estimates based on all dynamic models Estimation error covariance and model probability Calculate the weighted fusion system state estimate and its estimated error covariance matrix This yields the final global target tracking result. The specific calculation formula is as follows:

[0209]

[0210] This is the weighted and fused system state estimate;

[0211] This is the weighted fusion estimation error covariance matrix;

[0212] , The models are respectively The state estimate and covariance;

[0213] For the model The probability weights;

[0214] For diversity Degrees of freedom of distribution;

[0215] This represents the total number of dynamic models in the system.

[0216] Step 10, Assign to By repeating steps 2 to 9, the estimated value and the covariance matrix of the estimation error at any time can be obtained, thus realizing continuous multi-model adaptive estimation of the system over the entire time domain.

[0217] like Figure 2 As shown, the multi-model, multi-sensor sequential fusion estimation method under the heavy-tailed noise and event-triggered mechanism provided by this invention is described in the following steps.

[0218] Multi-model, multi-sensor sequential fusion estimation method under heavy-tailed noise and event-triggered mechanisms:

[0219] Step 1: Establish a multi-sensor Markov hopping system model and acquire initial data of the tracked target. This includes the following: initial state. Follow the mean The scale matrix is The degrees of freedom are diversity distributed:

[0220]

[0221] in, This represents the mean of the initial state. It is a positive definite covariance matrix. for Degrees of freedom of distribution.

[0222] System noise and measuring noise All are independent, thick-tailed noises. The scaling matrix of the system noise is... The scale matrix for measuring noise is Both obey a set of degrees of freedom. Diverse students Distribution, that is:

[0223]

[0224]

[0225] in, and These are the scale matrices for system noise and measurement noise, respectively.

[0226] The system has a finite number of dynamic models, and the transitions between models are modeled by Markov chains. The total number of models is denoted as . In a multi-sensor system, the first... Each sensor at time The observation data used express, The system state transition matrix and measurement matrix are respectively... and .in, For the first The system model variables at time t represent the current dynamic model of the system.

[0227] In summary, the multi-sensor Markov skipping system can be represented as:

[0228]

[0229]

[0230] in, For the system at time The state vector, For the first Each sensor at time The observed values.

[0231] Step 2, at each recursive time step It is necessary to obtain data from all sensors. The observation data at each time point and the corresponding observation transition matrix are obtained through the following steps:

[0232] Acquire each sensor At the present moment The observation data is denoted as ,in , Indicates the number of sensors. For each sensor Obtain the observation transition matrix at the corresponding time. This matrix is ​​used to map the current state of the system to the sensor observation space. For each sensor... Each can have an independent observation matrix format to support different observation characteristics or layouts, reflecting differences in measurement type and geometric configuration. `x` is a positive integer representing the current global time step in the recursion. Simultaneously, the measurement noise scale matrix for each sensor is obtained. This is used for calculating the information covariance and filter gain in subsequent fusion steps.

[0233] Step 3: In the multi-model sequential fusion estimation process, at each observation time... This requires normalizing the model probabilities and calculating the mixed states under each model based on the current probabilities and transition probability matrices of each model in the system, providing prior knowledge for subsequent recursion. The specific process is as follows:

[0234] Assume the system has There are three dynamic models, and the model probability vector is denoted as...

[0235]

[0236] in, Indicates time The lower model The probability satisfies .

[0237] The state transitions between the various models in the system are determined by the Markov chain probability transition matrix. control, According to Bayes' theorem, first, based on the model probability from the previous time step... With transition probability Computational model Normalization constant:

[0238]

[0239] in, Indicates the transition to the model The sum of the probabilities of all paths at that time. This represents the total number of dynamic models in the system.

[0240] For each model and Calculate the mixture probability:

[0241]

[0242] in, Indicates the state of the model at the previous time step. And transfer to the current time-instance model The normalized probability.

[0243] Previous time step model The probability of;

[0244] Previous time step model The probability of;

[0245] : Model arrive The state transition probability;

[0246] Step 4: Obtain the model from the mixture probability. The prior mean and mixture covariance matrix of the mixed states provide priors for subsequent recursion:

[0247]

[0248]

[0249] , Model at time l-1 of the previous time step The state estimate and the estimation error covariance matrix; : Degrees of freedom of distribution; superscript This represents a weighted mixed prior over all possible transition paths.

[0250] Step 5: Within the multi-sensor sequential fusion framework, at each time step... For each sensor in turn The target state prediction and error covariance are recursively calculated. The specific process is as follows:

[0251] For current sensors With each dynamic model Based on the state estimate and covariance output from the previous sensor (or fused from the previous time step), predict the system state before the current sensor. And calculate the state prediction error covariance matrix. :

[0252]

[0253]

[0254] : indicates that it corresponds to the model The state transition matrix;

[0255] : indicates in System noise during constant target observation The covariance matrix;

[0256] Step 6, at each moment Each sensor Combined with the self-observation data obtained in step 3 and the target state prediction value calculated in step 4 and error covariance The innovation and covariance criteria are calculated to obtain the event triggering parameters. To independently determine whether to transmit observations. First, for each model Calculate the measured value at the current time and based on The difference between the predicted and observed values ​​at any given time, i.e., the innovation and the covariance matrix of the new information :

[0257]

[0258]

[0259] in, Indicates the first Model in each sensor The observation transition matrix, This represents the covariance matrix of the measurement noise.

[0260] The covariance matrix of the new information Given a positive semi-definite matrix, perform eigenvalue decomposition on it, and denote the eigenvalues ​​as... ,in The dimension of the observation vector is expressed as a diagonal matrix:

[0261]

[0262] orthogonal matrix composed of eigenvectors Makes the following equation true:

[0263]

[0264] Define the normalized and decorrelated innovation matrix:

[0265] ;

[0266] in, .

[0267] Using the infinite norm of the normalized innovation as the event trigger criterion, a threshold is set. Then the event triggering parameters Determined by the following formula:

[0268]

[0269] in, Denotes the infinity norm of a matrix. This is the threshold for triggering the event.

[0270] when When the event is triggered, the measured value... It is transmitted to the remote estimator;

[0271] when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator.

[0272] Step 7, at time Each sensor Based on the observation data at this moment Step 4: Calculate the target state prediction value Covariance of state prediction error and the event triggering result calculated in step 5. Recursively calculate the mixed covariance matrix Filter gain And update the target state estimate. and estimation error covariance The specific process is as follows:

[0273] For each model Calculate the mixture covariance matrix Filter gain ,time Predicted values ​​of observed quantities and normalized new energy :

[0274]

[0275]

[0276]

[0277]

[0278] Based on the event triggering results, the state estimation and error covariance are recursively derived:

[0279]

[0280]

[0281] in, Taken from the normalized new information The second moment of distribution, For the observation dimension, For degrees of freedom.

[0282]

[0283]

[0284] make , ,in, To normalize the new information.

[0285] Step 8, at time In each sensor After completing the state recursion, the model probabilities need to be dynamically updated based on the observed likelihoods under each dynamic model. The specific process is as follows:

[0286] For each model Using the likelihood function of current observation data and model predictions and normalization constant Calculate the model probability under the current sensor:

[0287]

[0288] in, It is the normalization constant (or initial value) of the previous time step. To observe the likelihood, This represents the total number of models. The denominator is normalized to ensure that the sum of the probabilities of all models is 1. (Multi-model) The observation likelihood function under the distribution is:

[0289]

[0290] make

[0291] in, Based on current sensor observations, For the predicted value of the observed quantity, The new information covariance matrix, for Degrees of freedom of distribution.

[0292] Step 9: After all sensors have completed their sequential recursion, at time [time missing] State estimation based on all current models Covariance and model probability This achieves weighted fusion of multiple models to obtain the system's globally optimal state estimate and error covariance. The specific calculations are as follows:

[0293]

[0294] The system state estimate after global weighted fusion;

[0295] The estimated error covariance matrix after global weighted fusion;

[0296] , : respectively models The state estimate and the covariance of the estimation error;

[0297] :Model The probability weights;

[0298] : Diversity Degrees of freedom of distribution;

[0299] Total number of system dynamic models.

[0300] Step 10: Complete a certain moment After multi-sensor, multi-model weighted fusion estimation, Assign to Repeat steps 2 through 9 to achieve recursive operation of the multi-sensor sequential fusion algorithm across the entire time domain. Through this recursive process, the globally optimal state estimate and estimation error covariance at any given time can be obtained, meeting the needs of continuous target tracking and state estimation in practical engineering.

[0301] The effectiveness of the method of the present invention will be tested through simulation experiments below.

[0302] A radar tracking system with two sensors can be described by the following formula:

[0303]

[0304] For the tracked target, two motion models are used for description: constant velocity (CV) motion model and constant turning (CT) motion model, respectively. and This indicates that the goal is at a certain moment. The state vector is four-dimensional, containing position and velocity components: .

[0305] The system matrix and system noise matrix of the CV and CT models are represented as follows:

[0306] , ,

[0307] The measurement equation is

[0308]

[0309] in

[0310] ,

[0311] The initial state and the initial scale matrix are as follows: , . Indicates the sampling interval, and the target rotation rate is... The initial model probabilities are assumed to be equal. The state transition probability matrix is ​​as follows:

[0312]

[0313] In this example, the heavy-tailed system noise and measurement noise are generated in the following ways:

[0314]

[0315]

[0316] in, , For the first The intensity coefficient of each model, The scaling matrix for measuring noise is: ,in , Degrees of freedom .

[0317] A total of Sub-Monte Carlo simulation. To analyze the filtering performance, the root mean square error (RMSE) of position and velocity was used as an evaluation metric, defined as follows:

[0318]

[0319]

[0320] To comprehensively verify the effectiveness and advantages of the proposed fusion algorithm in scenarios with heavy-tailed noise and event-triggered noise, four sets of comparative simulation experiments were designed and conducted. Each experiment systematically evaluated the algorithm's performance under different event-triggered noise conditions, including those with single-sensor and multi-sensor fusion, Gaussian noise, and heavy-tailed noise, as well as under different event-triggered thresholds. These simulation experiments fully demonstrate the comprehensive advantages of the proposed method in terms of state estimation accuracy, robustness, and resource utilization efficiency.

[0321] In Experiment 1, for a heavy-tailed noise environment, the state estimation performance of the multi-sensor sequential fusion estimation algorithm with and without an event-triggered mechanism (NET-tIMM-SF) was compared. The event trigger threshold θ was set to 0.5, and the other parameters were the same as described above. 500 Monte Carlo simulations were performed with 400 steps each, and the statistical index was the root mean square error (RMSE) of the target position and velocity.

[0322] from Figure 3 The RMSE curves show that the blue curve represents the case without event triggering (NET-tIMM-SF), while the red curve represents the case with event triggering (ET-tIMM-SF). Both curves exhibit similar overall trends, stabilizing after a brief convergence phase. However, with event triggering, both position and velocity RMSEs are slightly higher than without, indicating that triggering filtering results in some measurements being unused, leading to a slight decrease in estimation accuracy at certain moments.

[0323] Table 1 presents the quantitative results of the time-averaged RMSE:

[0324] Location RMSE: NET-tIMM-SF is 0.515, ET-tIMM-SF is 0.526, difference +0.013 (approximately +2.7%).

[0325] Speed ​​RMSE: NET-tIMM-SF is 0.237, ET-tIMM-SF is 0.250, the difference is +0.013 (approximately +6.3%).

[0326] The above results and Figure 3 The curves in the data are consistent: at the selected threshold θ=0.5, the event-triggered mechanism results in minimal accuracy loss (only a slight increase in position and velocity RMSE), but its advantage lies in significantly reducing invalid / redundant measurement uploads and fusion, thereby reducing communication load and energy consumption, and improving the system's availability and robustness in bandwidth- and energy-constrained scenarios. Overall, the sequential fusion under the event-triggered mechanism still maintains stable and reliable estimation performance, balancing estimation accuracy and resource consumption, making it suitable for engineering applications in resource-constrained scenarios.

[0327] To further analyze the impact of different noise distributions on the performance of single-sensor fusion algorithms under the event-triggered mechanism, Experiment 2 compares the single-sensor event-triggered IMM algorithm (ET-tIMM-S1) with heavy-tailed noise processing and the single-sensor event-triggered IMM algorithm (ET-gIMM-S1) under the Gaussian noise assumption, under the same event trigger threshold θ=0.5 and other parameters. The simulation uses Monte Carlo simulation with MC=500 times and N=400 steps, and the root mean square error (RMSE) of position and velocity is used as the evaluation index.

[0328] from Figure 4 It can be seen that both curves are relatively stable after convergence, but ET-tIMM-S1 is significantly lower than ET-gIMM-S1 overall, and occasional spikes are effectively suppressed, showing stronger robustness to outlier observations.

[0329] Table 2 further presents the quantitative results of the time-averaged RMSE:

[0330] Location RMSE (mean): ET-tIMM-S1 = 0.41965, ET-gIMM-S1 = 0.48391, difference 0.06426, relative decrease of approximately 14.0%;

[0331] Speed ​​RMSE (mean): ET-tIMM-S1 = 0.18621, ET-gIMM-S1 = 0.20062, difference 0.01441, relative decrease of about 8.0%.

[0332] Since both algorithms use the same event triggering threshold (θ=0.5), their communication triggering strategies and resource overhead can be considered essentially the same; the performance difference mainly stems from noise modeling. Compared to the Gaussian assumption, the Student-t model can naturally apply heavy weighting penalties to large residuals (equivalent to reducing the weighting of outlier observations), thereby significantly reducing the interference of heavy-tailed noise on the estimation and achieving lower RMSEs for both position and velocity estimations. This result verifies the effectiveness and superiority of the heavy-tailed noise modeling + event triggering mechanism used in this invention in complex noise environments.

[0333] To comprehensively evaluate the performance of the proposed event-triggered sequential fusion in multi-sensor scenarios, Experiment 3 uniformly set the event trigger threshold to θ=0.5, with other parameters remaining the same as described above. Under the conditions of MC=300 and N=400, the following were tested:

[0334] The position and velocity RMSE were compared and evaluated using single-sensor (ET-tIMM-S1, ET-tIMM-S2) under thick-tailed noise, multi-sensor sequential fusion (ET-tIMM-SF) under thick-tailed noise, and multi-sensor sequential fusion (ET-gIMM-SF) under Gaussian noise. Experimental curves are shown below. Figure 5 The time-averaged RMSE results are shown in Table 3.

[0335] from Figure 5 As can be seen, all algorithms maintain a relatively stable error level after convergence. Among them, the ET-tIMM-SF curve of the multi-sensor under the heavy-tailed assumption is the lowest overall, which is significantly better than the two single-sensor cases (ET-tIMM-S1 / ET-tIMM-S2), and has a stronger ability to suppress occasional spikes. Compared with ET-gIMM-SF under the Gaussian assumption, ET-tIMM-SF still maintains a lower error in the heavy-tailed scenario, demonstrating its robustness to outlier observations.

[0336] Table 3 provides a quantitative comparison of time-averaged RMSE:

[0337] Position RMSE: ET-tIMM-SF was 0.50406, which was 0.19899 (approximately 28.8%) and 0.10781 (approximately 17.0%) lower than ET-tIMM-S1 (0.70305) and ET-tIMM-S2 (0.61187), respectively; and 0.09788 (approximately 16.6%) lower than ET-gIMM-SF (0.60194).

[0338] Speed ​​RMSE: ET-tIMM-SF is 0.23665, which is 0.03318 (approximately 12.9%) lower than ET-tIMM-S1 (0.26983) and 0.02474 (approximately 8.7%) lower than ET-tIMM-S2 (0.26139); it also shows an improvement of 0.00166 (approximately 0.9%) compared to ET-gIMM-SF (0.23831).

[0339] It should be noted that all the above algorithms use the same event trigger threshold (θ=0.5), and the communication trigger rate and bandwidth / energy consumption can be considered to be basically the same; therefore, the performance difference is mainly determined by the noise modeling and information fusion methods. In the heavy-tailed environment, ET-tIMM-SF achieves the best global RMSE in position and velocity estimation by (1) using Student-t noise modeling to naturally reduce the weight of large residuals and (2) using sequential multi-sensor fusion to make full use of complementary observations. This experiment further proves the robustness and practical value of "heavy-tailed modeling + event triggering + sequential fusion of multiple models" in complex noise scenarios.

[0340] To analyze the impact of the event triggering threshold on the estimation accuracy of the fusion algorithm, Experiment 4 was conducted under a heavy-tailed noise environment. The event triggering threshold θ was set to 0, 0.5, 0.8, and 1.0, respectively, and the position and velocity RMSE performance of the multi-sensor event triggering sequence fusion algorithm was compared under different thresholds. When θ=0, triggering was constant (equivalent to not discarding any observations); when θ=1.0, triggering was the most stringent, and observations were only uploaded when the residuals were significant. The remaining algorithm parameters were consistent with the previous experiments, the time step remained unchanged, and the number of Monte Carlo trials was 400.

[0341] Figure 6The curves showing the evolution of position and velocity RMSE over time under four thresholds are presented. From the curve shape, all four thresholds experience a brief convergence in the initial stage before entering a steady-state oscillation range. The position and velocity curve at θ=0 maintains the lowest envelope across the entire time domain, indicating that fully utilizing measurements under heavy-tailed observations can significantly improve estimation accuracy and robustness. Increasing the threshold to θ=0.5 and θ=0.8 both increase the mean and fluctuation amplitude of the steady-state RMSE; among them, θ=0.5 performs better overall than θ=0.8, indicating that under this setting, a moderate threshold can better balance communication overhead and correction effect. Further increasing to θ=1.0 results in the most "thick" position and velocity curves, with more significant local peaks, reflecting that an excessively high threshold leads to a large suppression of effective observations, causing the fusion unit to rely more on model extrapolation, accelerating error accumulation, and resulting in the worst steady-state accuracy. Overall, increasing the threshold lengthens the continuous prediction segment and reduces the effective correction frequency, thus first manifesting as a significant deterioration in the position dimension in heavy-tailed environments. As can be seen from the curve shape, the event triggering threshold not only changes the communication frequency, but also changes the temporal structure of "observation-prediction": the higher the threshold, the longer the continuous prediction segment, and the random burst effects of model mismatch and heavy-tailed observations are amplified. Therefore, the "peak-valley difference" and steady-state mean of the RMSE curve increase accordingly.

[0342] Table 4 shows the time average and rate of change relative to θ=0 for position and velocity RMSE under different thresholds:

[0343] θ=0: Position RMSE=0.50884, velocity RMSE=0.24203, which is the optimal baseline among the four settings;

[0344] θ=0.5: Position RMSE=0.51351 (+0.92%), Velocity RMSE=0.24212 (+0.04%).

[0345] θ=0.8: Position RMSE=0.53239 (+4.63%), Velocity RMSE=0.24243 (+0.17%).

[0346] θ=1.0: Position RMSE= 0.55824 (+9.31%), Velocity RMSE= 0.24297 (+0.39%).

[0347] Meanwhile, the average trigger rate of the two sensors monotonically decreases with the threshold (see Table 4), from 100% at θ=0 to approximately 78% / 79% at θ=0.5, approximately 59% / 60% at θ=0.8, and approximately 47% / 50% at θ=1.0. This is consistent with the aforementioned accuracy changes: when the threshold is too high and the upload speed is significantly reduced, the fusion performance will decline accordingly. Under the settings of this invention, θ=0 offers the best accuracy but has the highest communication cost; θ=0.5 achieves a considerable decrease in trigger rate with only a minimal speed penalty (+0.04%) and slight position degradation (+0.92%), demonstrating a more balanced communication-performance trade-off; θ≥0.8 is not suitable for applications where accuracy is paramount.

[0348] In summary, the experimental results further illustrate the crucial role of event-triggered mechanisms in fusion algorithms, and that setting appropriate thresholds is essential for balancing estimation accuracy and communication resource consumption. The above conclusions are consistent with... Figure 6 The consistent performance across the entire time domain and the time-averaged statistics in Table 4 demonstrate that a reasonable event-triggered setting can maintain high estimation performance while controlling communication costs, reflecting the engineering usability of the thick-tailed-event-triggered-multi-sensor sequential fusion framework proposed in this invention.

[0349] Table 1. Average RMSE of different algorithms with and without event triggering (MC=500, N=400, θ=0.5)

[0350] Table 2. Average RMSE of different algorithms under different noise processing methods (MC=500, N=400, θ=0.5)

[0351] Table 3. Average RMSE of different algorithms under event triggering (MC=300, N=400, θ=0.5)

[0352] Table 4. Average RMSE of the ET-tIMM-SF algorithm under different event trigger thresholds (MC=400) .

Claims

1. A multi-model target tracking algorithm based on an event-triggered mechanism under thick-tailed noise, for radar target tracking systems with thick-tailed noise interference and network transmission limitations; describing the sensor's observation of the target as a linear discrete-time dynamic system with Markov jump characteristics, the system state including the target's position and velocity; characterized in that, The method includes the following steps: Step 1: Establish a single-sensor Markov transition system, acquire initial data of the tracked target, and set the initial state of the target. Follow the mean The scale matrix is The degrees of freedom are The system exhibits a thick-tailed distribution; assuming the system noise during sensor tracking of the target has a mean of 0, and the scaling matrix is... The degrees of freedom are The target has a heavy-tailed distribution; assuming the moving target has M dynamic models, the transitions between models are determined by Markov chains. express, for The system model variables at any given time represent the current dynamic model of the system. express The system state transition matrix at time t, It is a positive integer; Step 2, at time Acquire sensor data Observational data at time The measurement matrix is The measurement noise follows a mean of 0, and the scale matrix is... Independent thick-tailed noise with v degrees of freedom; Step 3, in At any given moment, define the model. probability ,Model probability The probability transition matrix between the model and the model Calculate the normalization constant. Mixed probabilities of the model ,as follows: Where, assuming ; Step 4, from the model mixture probability Calculate the mixed state matrix and mixed covariance matrix ,as follows: in, and Representing the model respectively The state estimate and the estimation error covariance matrix, , Superscript Indicates transpose; Indicates degrees of freedom; Step 5, according to Mixed state matrix at time step and mixed covariance matrix Calculate the current Target state prediction value at time 1 With state prediction error covariance matrix ,as follows: in, Represents the state transition matrix. Indicates in System noise during constant target observation The scale matrix; Step 6, in At that time, the sensor measurement value obtained in step 2 is used. And the target state prediction value calculated in step 5 With state prediction error covariance matrix ,calculate The new covariance matrix at time 1 And calculate the event triggering parameters. ;when When the event is triggered, the measured value... Transmitted to the remote estimator; when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator; Step 7, in At that time, using the observation data obtained in step 2 Step 5 calculates the target state prediction value With state prediction error covariance matrix and the event triggering parameters calculated in step 6. Calculate the mixture covariance matrix Filter gain and state estimates and the estimated error covariance matrix ; Step 8, in At time, using the likelihood function and the normalization constant calculated in step 3 Update model probabilities ; Step 9, in At time 1, the state estimates based on all models Estimation error covariance and model probability Calculate the weighted fusion system state estimate and the corresponding estimation error covariance matrix ,get The results of constant target tracking; Step 10, Assign to Repeat steps 2 to 9 to obtain the target state estimate and the estimation error covariance matrix at any time.

2. The method according to claim 1, characterized in that, In step 6, the event triggering parameters of the sensor are calculated. The method is: First, calculate The measurement value of the time sensor and based on The difference between the predicted value of the measured value and the state at time, i.e., the innovation. and the covariance matrix of the new information The following are examples: The covariance matrix of the new information It is a positive semi-definite matrix, calculate eigenvalues , It is the dimension of the observation vector provided by the sensor, and is expressed as a diagonal matrix: Calculate the unitary matrix using the following formula : Then, set the matrix Then we can further obtain a normalized and decorrelated matrix. ; Finally, obtain the event triggering parameters of the sensor. ;in, Denotes the infinity norm of a matrix. The threshold for triggering the event. .

3. The method according to claim 1, characterized in that, In step 7, the mixed covariance matrix Filter gain and state estimates and estimation error covariance The calculation is as follows: in, yes The predicted value of the measured value at any given time. It is a normalized new information, It is under the restricted interval The second moment of distribution is calculated as follows: 。 4. The method according to claim 1, characterized in that, In step 8, the model probability is updated using the likelihood function and the normalization constant. The calculation is as follows: 。 5. The method according to claim 1, characterized in that, In step 9, a weighted fusion system state estimate is calculated based on the state estimates, estimation error covariance, and model probabilities of all models. and the corresponding estimation error covariance matrix The calculation is as follows: 。 6. A multi-model sequential fusion estimation method based on an event-triggered mechanism under heavy-tailed noise, for a multi-sensor target tracking system with heavy-tailed noise interference and network transmission limitations; the multi-sensor observations of the target are described as a linear discrete-time dynamic system with Markov jump characteristics, and the system state includes the target's position and velocity; the method determines the timing of data transmission from each sensor through an event-triggered mechanism, effectively reducing network communication load, and employs a sequential fusion estimation strategy based on interactive multiple models (IMM) to achieve state estimation, characterized in that... The method includes the following steps: Step 1: Input the number of sensors N into the computer to establish a multi-sensor Markov hopping system, acquire the initial data of the tracked target, and set the initial state of the target. Follow the mean The scale matrix is The degrees of freedom are The system exhibits a thick-tailed distribution; assuming the system noise during sensor tracking of the target has a mean of 0, and the scaling matrix is... The degrees of freedom are The target has a heavy-tailed distribution; assuming the moving target has M dynamic models, the transitions between models are determined by Markov chains. express, for The system model variables at any given time represent the current dynamic model of the system. express The system state transition matrix at time t, It is a positive integer; Step 2, at time Get the One sensor in Observational data at time , The measurement matrix is The measurement noise follows a mean of 0, and the scale matrix is... The degrees of freedom are Independent thick tail noise; Step 3, in At any time, according to the model probability ,Model probability The probability transition matrix between the model and the model Calculate the normalization constant Mixed probabilities of the model ,as follows: Where, assuming ; Step 4, from the model mixture probability Calculate the mixed state matrix and mixed covariance matrix ,as follows: in, and Representing the model respectively The state estimate and the estimation error covariance matrix, , Superscript Indicates transpose; Indicates degrees of freedom; Step 5, according to Mixed state matrix at time step and mixed covariance matrix Calculate the current Target state prediction value at time 1 With state prediction error covariance matrix ,as follows: in, Represents the state transition matrix. Indicates in System noise during constant target observation The scale matrix; Step 6, in At time 1, using the first time obtained in step 2 Measurement values ​​from each sensor Step 5 calculates the target state prediction value With state prediction error covariance matrix For sensors Calculate in sequence The new covariance matrix at time 1 And calculate the event triggering parameters. ;when When the event is triggered, the measured value... Transmitted to the remote estimator; when When the event is not triggered, the measurement data... It will not be transmitted to the remote estimator; Step 7, in At that time, using the observation data obtained in step 2 Step 5 calculates and and the event triggering parameters calculated in step 6. For sensors Calculate the mixture covariance matrix sequentially. Filter gain and state estimates and estimation error covariance ,remember , ; Step 8, in At time, using the likelihood function and the normalization constant calculated in step 3 For sensors Update the model probabilities sequentially ,remember ; Step 9, in At time 1, the state estimates based on all models Estimation error covariance and model probability Calculate the weighted fusion system state estimate and the corresponding estimation error scaling matrix ,get The results of all sensors tracking the target at any given time; Step 10, Assign to Repeat steps 2 to 9 until all data at all observation times have been processed. Then you can obtain the target state estimate and the estimation error covariance matrix of the multi-sensor sequential fusion at any time.

7. The method according to claim 6, characterized in that, In step 6, the sensor... Calculate the event trigger parameters of the sensor sequentially. The method is: First, calculate The measurement value of the time sensor and based on The difference between the predicted value of the measured value and the state at time, i.e., the innovation. and the covariance matrix of the new information The following are examples: It is the state transition matrix and the covariance matrix of the innovation. It is a positive semi-definite matrix, calculate eigenvalues , It is the dimension of the observation vector provided by the sensor, and is expressed as a diagonal matrix: Calculate the unitary matrix using the following formula : Then, let the matrix be... Then we can further obtain a normalized and decorrelated matrix. ; Finally, obtain the event triggering parameters of the sensor. ;in, Denotes the infinity norm of a matrix. The threshold for triggering the event. .

8. The method according to claim 6, characterized in that, In step 7, the sensor... Calculate the mixture covariance matrix sequentially. Filter gain and state estimates and estimation error covariance The calculation is as follows: in, yes Time of the first The predicted value of the sensor for the measured value, It is a normalized new information, It is under the restricted interval The second moment of distribution is calculated as follows: make , .

9. The method according to claim 6, characterized in that, In step 8, the sensor... The model probabilities are updated sequentially using the likelihood function and the normalization constant. The calculation is as follows: make .

10. The method according to claim 6, characterized in that, In step 9, a weighted fusion system state estimate is calculated based on the state estimates, estimation error covariance, and model probabilities of all models. and the corresponding estimation error covariance matrix The calculation is as follows: 。

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