A low-computational-complexity particle smoothing estimation method for tracking multiple maneuvering targets' trajectories

Abstract

The present invention relates to a method for tracking the trajectories of multiple maneuvering targets using particle smoothing estimation with low computational complexity. Aiming at the application scenario of multiple maneuvering target tracking, a hybrid system model with unknown mixed states is established to identify the maneuvering modes and motion states of multiple maneuvering targets. A low-complexity smoothing calculation method is designed when the particle weights are not degraded, and the unknown maneuvering modes and motion states of the targets are estimated by combining Gibbs sampling and Markov chain Monte Carlo methods. Compared with the traditional particle smoothing algorithm, the method of the present invention improves the estimation accuracy of the target maneuvering mode and motion state by introducing a reference trajectory, and improves the computational efficiency by using a particle smoothing algorithm with low computational complexity. Therefore, the method can achieve the same tracking accuracy in a shorter time.

Description

Technical Field

[0001] The present invention belongs to the application of hybrid system theory and random process analysis in signal processing. The application object scenario is target maneuvering pattern recognition and trajectory tracking. It involves a multi-maneuvering target trajectory tracking method with low computational complexity particle smoothing estimation. The specific methods involve particle smoothing, Gibbs sampling, Markov chain Monte Carlo method, etc. Background Art

[0002] With the rapid development of science and technology, the increasing prevalence of aircraft technology poses significant risks and threats to public and national security. Therefore, there is an urgent need to establish an aerial target surveillance and management system, and the research on trajectory tracking strategies for these flying targets is crucial and imperative. In this field, due to the uncertainty and variability of target motion, tracking algorithms for multiple maneuvering targets are essential for achieving accurate and rapid target tracking. Therefore, the research on trajectory tracking algorithms for multiple maneuvering targets has important practical applications.

[0003] In practical applications of maneuvering target tracking, tracking algorithms often require faster response speeds and higher tracking accuracy. Researchers have proposed various algorithms based on these two requirements. Lopez et al. (R. Lopez and P. Danès, "Low-Complexity IMM Smoothing for Jump Markov Nonlinear Systems," in IEEE Transactions on Aerospace and Electronic Systems, vol. 53, no. 3, pp. 1261-1272, 2017) proposed a low-complexity smoothing estimation algorithm based on multiple interacting models. This algorithm can quickly estimate target trajectories. However, multiple interacting model algorithms perform interactive predictions of maneuvering patterns, making them incapable of accurately determining target maneuvers. Furthermore, tracking suffers from low accuracy and proneness to divergence in situations with high noise and complex maneuvers. Another algorithm for tracking multiple maneuvering targets is primarily based on Monte Carlo sampling. By establishing a nonlinear target motion model with jump characteristics, particle filtering or particle smoothing algorithms are used to estimate the maneuver patterns and target trajectories. Representative ones include the traditional particle smoothing algorithm (TTAshley and SBAndersson,"ASequential Monte Carlo framework for the system identification of jump Markovstate space models,"2014American Control Conference,2014,pp.1144-1149), the Markov chain Monte Carlo method combining Rao-Blackwellized particle filter and Gibbs prior sampling (C. Cheng,J.-Y.Tourneret and X.Lu,"A Rao-Blackwellized Particle Filter With VariationalInference for State Estimation With Measurement Model Uncertainties,"in IEEE Access, vol.8,pp.55665-55675,2020), etc.

[0004] The above research methods can effectively realize multi-maneuvering target tracking, but the following problems still exist:

[0005] (1) The method based on the multi-target interaction model is more sensitive to the probability of maneuver mode transfer, which leads to inaccurate maneuver mode estimation. It cannot guarantee tracking accuracy in situations such as high noise and complex maneuvering conditions, and is prone to divergence.

[0006] (2) Although the Monte Carlo sampling method can approximate the true probability density through a large number of sampling to obtain more accurate tracking results, its time efficiency is low and often fails to meet real-time requirements. Summary of the Invention

[0007] Technical problems to be solved

[0008] In order to avoid the shortcomings of the existing technology, the present invention proposes a multi-maneuvering target trajectory tracking method based on particle smoothing estimation with low computational complexity. Aiming at the problems that the multi-maneuvering target tracking algorithm based on traditional particle smoothing algorithm has low tracking accuracy and easy divergence when the number of particles is small, and poor time efficiency when the number of particles is large, a new particle smoothing algorithm is proposed to achieve higher time efficiency under the same tracking accuracy.

[0009] Technical Solution

[0010] A multi-maneuvering target trajectory tracking method using particle smoothing estimation with low computational complexity is characterized by the following steps:

[0011] Step 1: Establish a multi-maneuvering target motion model based on hybrid system theory: discrete random variables R∈Ω={1,…,M} represent the maneuvering mode, where M is the number of maneuvering modes, and continuous random variables X and Y represent the target motion state and observation quantity, respectively, where R and X are unknown and Y can be observed; the target maneuvering mode, motion state, and observation quantity at time n are r n 、x n and y n , the motion model of multiple maneuvering targets is:

[0012]

[0013] Among them, a lk is the transition probability of the maneuver mode from l to k, l,k∈Ω; nonlinear function f n+1 (x n ,r n+1 ) is the target motion equation, and the specific form of the motion equation is determined by the motion state at the previous moment and the maneuvering mode at the current moment; the nonlinear function g n+1 (x n+1 ,r n+1 ) is the observation equation; v x With v y are the target motion state error and observation error, both of which are Gaussian white noise;

[0014] The system model parameters are θ∈Θ={a lk ,θ f|l ,θ g|l ,Q x|l ,Q y|l} l,k∈Ω ,θ f|l ,θ g|l are the parameters of the target motion equation and the observation equation, Q x|l ,Q y|l is the error v x 、v y The covariance matrix of the continuous random variables X and Y represent the target motion state and the observation quantity respectively.

[0015] Step 2: Set up the particle collection Where K is the number of particles, and the number of particles represents the {x 1:n ,r 1:n The number of sampling times of probability distribution, the greater the number, the closer the particle set obtained by sampling is to the true distribution. The weight coefficient represents the corresponding particle value and The probability of occurrence, the particle weight at the nth moment satisfies Particle resampling threshold h s , the maximum number of iterations of the Markov chain Monte Carlo method is λ, and the iteration number flag d = 1;

[0016] Step 3: Set the target motion state and the initial state of the maneuvering mode, and obtain the observation sequence y according to the multi-maneuvering target motion model simulation 1:N ;

[0017] Step 4: Use particle filtering to obtain the initial reference trajectory {r′ 1:n ,x′ 1:n}:

[0018]

[0019]

[0020] in, To satisfy Conditional Dirac function; by introducing the reference trajectory {r′ 1:n ,x′ 1:n The estimated target motion state and maneuvering mode can be made closer to the real value;

[0021] Step 5: Let α n (r n ,x n )=p(r n+1:N,y n+1:N |r 1:n ,x 1:n ,y 1:n ), iteratively calculate α at all moments according to the following formula n (r′ n ,x′ n )

[0022]

[0023] Step 6: Execute the filtering algorithm based on Gibbs sampling from n=2 to n=N and update the particle weights

[0024] Step 7: Make From time n = N-1 to n = 1, iteratively execute the smoothing algorithm with low computational complexity, and obtain the particle smoothing weight

[0025] Step 8: Use the particle smoothing weights obtained in step 7 Calculate and update the reference trajectory for all n=1,…N moments:

[0026]

[0027]

[0028] The maneuver reference trajectory r′ obtained from the above formula n To make the weighted sum of the particle smoothing weights Maneuvering mode corresponding to the maximum value; x′ n is the weighted sum of the particle smoothing weights The obtained weighted sum average;

[0029] The obtained reference trajectory is recorded as the reference trajectory {r′ 1:n [d],x′ 1:n [d]}; If d≤λ, return to step 5, otherwise go to step 9;

[0030] Step 9: Output the estimated maneuver and target motion state

[0031]

[0032]

[0033] The nonlinear function f n+1 (x n ,r n+1 )'s target motion equation is determined by the motion state at the previous moment and the maneuvering method at the current moment.

[0034] The particle resampling threshold h in step 2 s The value is greater than 1 and less than 5.

[0035] The step 4 uses particle filtering to obtain the initial reference trajectory {r′ 1:n ,x′ 1:n The process of} is:

[0036] Step 4.1: Initialize all K particles: Let r1 (i) Randomly select a value in Ω, is an all-zero vector,

[0037] Step 4.2: Iterate and calculate the particles at each moment as follows

[0038]

[0039]

[0040]

[0041]

[0042] The symbol '~' indicates that the value on the left is a random sample that obeys the probability distribution on the right, and the symbol '∝' indicates that the value on the left is proportional to the value on the right. is the weight of n-1 at the previous moment The random sampling number of ; the function q(·) represents the probability density sampling function, so Indicates that the maneuvering mode is from the last moment to becomes The probability of sampling is Indicates that the Under the condition of the target motion state from the previous moment becomes Take samples; Represents the observed value y n exist The probability under the condition; if each iteration satisfies the following formula, the particle is weighted Resample K particles and make all particle weights

[0043]

[0044] Step 4.3: Calculate the initial reference trajectory {r′ 1:n ,x′ 1:n}

[0045]

[0046]

[0047] in, To satisfy Conditional Dirac function; by introducing the reference trajectory {r′ 1：n ,x′ 1:n} can make the estimated target motion state and maneuver mode closer to the real value.

[0048] The step 6 performs a filtering algorithm based on Gibbs sampling from n=2 to n=N to update the particle weights. The steps are:

[0049] Step 6.1: Sample K-1 particles according to the following formula,

[0050]

[0051]

[0052]

[0053] Step 6.2: Based on the reference trajectory {r′ 1:n ,x′ 1:n To obtain the Kth particle, first calculate the prior weight:

[0054]

[0055]

[0056] according to Sample the Kth particle number and let

[0057] Step 6.3: Update particle weights according to the following formula

[0058]

[0059] Step 6.4: If According to weight Resample K particles and make all particle weights Return to step 6.1 until n=N.

[0060] The step 7 calculates the complexity of the smoothing algorithm:

[0061] Step 7.1: Calculation

[0062] Step 7.2: If Represents the particle smoothing weight The degeneration phenomenon occurs, which means that the probability of the motion state and maneuvering mode values ​​represented by the vast majority of particles in the K particles is infinitely close to 0, and the number of effective particles is too small. Therefore, in order to ensure the accuracy of the calculation, the particle smoothing weight is calculated and normalized according to the traditional particle smoothing algorithm, as follows:

[0063]

[0064] If Neff>h s , represents the particle smoothing weight There is no degradation and there are enough effective particles. Therefore, in order to improve the computational efficiency, the particle smoothing method with low computational complexity is used to calculate the particle smoothing weight and normalize it.

[0065]

[0066] The weight of the obtained particle smoothing Can be approximately regarded as the corresponding particle value and In all observation sequences y 1:N The probability density of occurrence under the conditions.

[0067] Beneficial effects

[0068] The present invention proposes a method for tracking the trajectories of multiple maneuvering targets using particle smoothing estimation with low computational complexity. Aiming at the application scenario of multiple maneuvering target tracking, a hybrid system model with unknown mixed states is established to identify the maneuvering mode and motion state of multiple maneuvering targets. A low-complexity smoothing calculation method is designed when the particle weights are not degraded, combining Gibbs sampling and Markov chain Monte Carlo methods to estimate the unknown maneuvering mode and motion state of the target. Compared with the traditional particle smoothing algorithm, the method of the present invention improves the estimation accuracy of the target maneuvering mode and motion state by introducing a reference trajectory, and improves the computational efficiency through the low computational complexity particle smoothing algorithm. Therefore, this method can achieve the same tracking accuracy in a shorter time. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is a method flow chart.

[0070] Figure 2 This is a comparison chart of the changing trend of maneuver mode estimation error with calculation time.

[0071] The data on the vertical axis in the figure is the average error in maneuver estimation for all maneuver patterns within one second, calculated by running the tracking algorithm 100 times for various values ​​of K and λ, using different particle numbers, K, and Markov Chain Monte Carlo method iterations. This shows that the proposed method can more accurately estimate maneuver patterns within the same computational time compared to traditional algorithms.

[0072] Figure 3 This is a comparison chart of the changing trend of motion state estimation error with calculation time.

[0073] The vertical axis in the figure shows the average motion state estimation error calculated within 1 second by running the tracking algorithm 100 times for different values ​​of K and λ, using different particle numbers, K, and Markov Chain Monte Carlo method iterations. This shows that the proposed method can more accurately estimate the target's motion state than traditional algorithms within the same computational time.

[0074] Figure 4 This is a comparison chart of trajectory tracking results with a calculation time of 49.5-50.5 seconds.

[0075] The target trajectory tracking result in the figure is the average value of the tracking trajectory when the calculation time is 49.5-50.5 seconds. It can be seen that the tracking trajectory obtained by the method of the present invention is closer to the real target trajectory than the traditional particle smoothing algorithm. DETAILED DESCRIPTION

[0076] The present invention will now be further described with reference to the embodiments and accompanying drawings:

[0077] This paper proposes a multi-maneuvering target tracking method based on low-complexity smooth estimation. The whole method combines hybrid system theory, particle smoothing algorithm, Markov chain Monte Carlo method and Gibbs prior sampling. The specific steps are as follows:

[0078] Step 1:

[0079] A multi-maneuvering target motion model is established based on hybrid system theory. Let the discrete random variable R∈Ω={1,…,M} represent the maneuvering mode, where M is the number of maneuvering modes, and the continuous random variables X and Y represent the target motion state and observation quantity, respectively. In the model, R and X are unknown, only Y can be observed, and at time n, the target maneuvering mode, motion state, and observation quantity take the values ​​of r respectively. n 、x n and y n , then the entire system model can be expressed as

[0080]

[0081] Among them, a lk is the transition probability of the maneuver mode from l to k, l,k∈Ω; nonlinear function f n+1 (x n ,r n+1 ) is the target motion equation, and the specific form of the motion equation is determined by the motion state at the previous moment and the maneuvering mode at the current moment; the nonlinear function g n+1(x n+1 ,r n+1 ) is the observation equation;

[0082] v x With v y are the target motion state error and observation error, both of which are Gaussian white noise. The system model parameters are established as θ∈Θ={a lk ,θ f|l ,θ g|l ,Q x|l ,Q y|l} l,k∈Ω ,θ f|l ,θ g|l are the parameters of the target motion equation and the observation equation, Q x|l ,Q y|l is the error v x 、v y The covariance matrix of .

[0083] Step 2:

[0084] Setting up particle collection Where K is the number of particles, and the number of particles represents the 1:n ,r 1:n The number of sampling times of probability distribution, the greater the number, the closer the particle set obtained by sampling is to the true distribution. The weight coefficient represents the corresponding particle value and The probability of occurrence, the particle weight at the nth moment satisfies Particle resampling threshold h s (The value is generally greater than 1 and less than 5), the maximum number of iterations of the Markov chain Monte Carlo method is λ, and the iteration number flag d=1.

[0085] Step 3:

[0086] By setting the target motion state and the initial state of the maneuver mode, the observation sequence y is obtained according to the system model simulation. 1:N .

[0087] Step 4:

[0088] Use particle filtering to obtain the initial reference trajectory of the Markov Chain Monte Carlo method:

[0089] Step 4.1: Initialize all K particles: Let r1 (i) Randomly select a value in Ω, is an all-zero vector,

[0090] Step 4.2: Iterate and calculate the particles at each moment as follows

[0091]

[0092]

[0093]

[0094]

[0095] The symbol '~' indicates that the value on the left is a random sample that obeys the probability distribution on the right, and the symbol '∝' indicates that the value on the left is proportional to the value on the right. is the weight of n-1 at the previous moment The random sampling number of ; the function q(·) represents the probability density sampling function, so Indicates that the maneuvering mode is from the last moment to becomes The probability of sampling is Indicates that the Under the condition of the target motion state from the previous moment becomes Take samples; Represents the observed value y n exist If the following formula is satisfied at each iteration, the particles are weighted according to Resample K particles and make all particle weights

[0096]

[0097] Step 4.3: Calculate the initial reference trajectory {r′ 1:n ,x′ 1:n}

[0098]

[0099]

[0100] in, To satisfy Conditional Dirac function. By introducing the reference trajectory {r′ 1:n ,x′ 1:n} can make the estimated target motion state and maneuver mode closer to the real value.

[0101] Step 5:

[0102] Let α n (r n ,x n )=p(r n+1:N ,y n+1:N |r1:n ,x 1:n ,y 1:n ), iteratively calculate α at all moments according to the following formula n (r′ n ,x′ n )

[0103]

[0104] Step 6:

[0105] Filtering algorithm based on Gibbs sampling from n=2 to n=N is performed:

[0106] Step 6.1: Sample K-1 particles according to the following formula,

[0107]

[0108]

[0109]

[0110] Step 6.2: Based on the reference trajectory {r′ 1:n ,x′ 1:n To obtain the Kth particle, first calculate the prior weight:

[0111]

[0112]

[0113] according to Sample the Kth particle number and let

[0114] Step 6.3: Update particle weights according to the following formula

[0115]

[0116] Step 6.4: If According to weight Resample K particles and make all particle weights Return to step 6.1 until n=N.

[0117] Step 7:

[0118] make From time n=N-1 to n=1, iteratively execute a smoothing algorithm with low computational complexity:

[0119] Step 7.1: Calculation

[0120]

[0121] Step 7.2: If Neff < h s , represents the particle smoothing weight The degeneration phenomenon occurs, which means that the probability of the motion state and maneuvering mode values ​​represented by the vast majority of particles in the K particles is infinitely close to 0, and the number of effective particles is too small. Therefore, in order to ensure the accuracy of the calculation, the particle smoothing weight is calculated according to the traditional particle smoothing algorithm as follows:

[0122]

[0123] And normalized.

[0124] If Neff>h s , represents the particle smoothing weight There is no degradation and there are enough effective particles. Therefore, in order to improve the computational efficiency, a particle smoothing method with low computational complexity is used to calculate the particle smoothing weight.

[0125]

[0126] And normalized.

[0127] The weight of the particle smoothing obtained in this step Can be approximately regarded as the corresponding particle value and In all observation sequences y 1:N The probability density of occurrence under the conditions.

[0128] Step 8:

[0129] The particle smoothing weight obtained in step 7 Calculate and update the reference trajectory for all n=1,…N moments:

[0130]

[0131]

[0132] The maneuver reference trajectory r′ obtained from the above formula n To make the weighted sum of the particle smoothing weights Maneuvering mode corresponding to the maximum value; x′ n is the weighted sum of the particle smoothing weights The obtained weighted sum average value is recorded as the reference trajectory {r′ 1:n [d],x′ 1:n [d]}. If d≤λ, return to step 5, otherwise go to step 9.

[0133] Step 9:

[0134] Output estimated maneuver mode and target motion state

[0135]

[0136]

[0137] The present invention will now be further described with reference to specific examples and accompanying drawings:

[0138] Let the maneuver be selected from the finite set Ω∈{1,2,3}. The three maneuvers represent the target velocity direction: counterclockwise rotation at an angular rate of 10° / s, linear motion (angular velocity is zero), and clockwise rotation at an angular rate of 10° / s. The transition between maneuvers has Markov properties. The target motion state is represented by x=[p1,υ1,p2,υ2] Τ , where p1 and p2 represent the projection coordinates of the target position on the horizontal and vertical axes of the two-dimensional plane, respectively, and υ1 and υ2 represent the projection coordinates of the target velocity on the horizontal and vertical axes of the two-dimensional plane, respectively; the observed two-dimensional vector includes the distance between the target and the coordinate origin, and the angle between the vector from the coordinate origin to the target position and the horizontal axis of the coordinate. Then, the motion model of multiple maneuvering targets in a two-dimensional plane can be established:

[0139] p(r n+1 =k|r n =l)=a lk

[0140]

[0141]

[0142]

[0143]

[0144] where ω is the angular velocity of the maneuver and T is the observation time interval.

[0145] The specific implementation steps of multi-maneuvering target tracking are as follows:

[0146] Step 1: Set the parameters of the multi-maneuvering target tracking system as shown in the following table

[0147]

[0148] In this way, the particle's maneuvering mode at a given moment can be obtained Maneuvering mode at the current moment under the conditions Sampling Satisfy the distribution law

[0149]

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] The particle is in the current maneuver mode and the motion state at the previous moment Sampling under conditions Satisfies the following Gaussian distribution

[0159]

[0160] The particle is in the current maneuver mode and motion status The probability density of the observation under the condition is

[0161]

[0162] Step 2: Set the number of particles to K and the particle resampling threshold to h s =4, the maximum number of iterations λ of the Markov chain Monte Carlo method, and the iteration number flag k=1.

[0163] Step 3: Let the observation time interval T = 1s, and the target initial motion state x1 = [100, 0, 0, 10] Τ The initial maneuver mode is r1=1, the simulation time is 200 seconds, and a total of N=200 length data {r 1:N ,x 1:N ,y 1:N}.

[0164] Step 4: Assume that only the observed quantity y 1:N It is known that {r 1:N ,x 1:N} unknown, the multi-maneuvering target tracking algorithm based on low computational complexity particle smoothing of the present invention is used to estimate the maneuvering mode and motion state of the target, and obtain and compare the estimated values With the true value {r1:N ,x 1:N}The error between them.

Claims

1. A multi-maneuvering target trajectory tracking method based on particle smoothing estimation with low computational complexity, characterized in that Here are the steps: Step 1: Establish a multi-maneuvering target motion model based on hybrid system theory: discrete random variables R∈Ω={1,…,M} represent the maneuvering mode, where M is the number of maneuvering modes, and continuous random variables X and Y represent the target motion state and observation quantity, respectively, where R and X are unknown and Y can be observed; the target maneuvering mode, motion state, and observation quantity at time n are r n 、x n and y n , the motion model of multiple maneuvering targets is: Among them, a lk is the transition probability of the maneuver mode from l to k, l,k∈Ω; nonlinear function f n+1 (x n ,r n+1 ) is the target motion equation, and the specific form of the motion equation is determined by the motion state at the previous moment and the maneuvering mode at the current moment; the nonlinear function g n+1 (x n+1 ,r n+1 ) is the observation equation; v x With v y are the target motion state error and observation error, both of which are Gaussian white noise; The system model parameters are θ∈Θ={a lk ,θ f|l ,θ g|l ,Q x|l ,Q y|l } l,k∈Ω ,θ f|l ,θ g|l are the parameters of the target motion equation and the observation equation, Q x|l ,Q y|l is the error v x 、v y The covariance matrix of the continuous random variables X and Y represent the target motion state and the observation quantity respectively. Step 2: Set up the particle collection Where K is the number of particles, and the number of particles represents the {x 1:n ,r 1:n The number of sampling times of probability distribution, the greater the number, the closer the particle set obtained by sampling is to the true distribution. The weight coefficient represents the corresponding particle value and The probability of occurrence, the particle weight at the nth moment satisfies Particle resampling threshold h s , the maximum number of iterations of the Markov chain Monte Carlo method is λ, and the iteration number flag d = 1; Step 3: Set the target motion state and the initial state of the maneuvering mode, and obtain the observation sequence y according to the multi-maneuvering target motion model simulation 1:N ; Step 4: Use particle filtering to obtain the initial reference trajectory {r′ 1:n ,x′ 1:n }: in, To satisfy Conditional Dirac function; by introducing the reference trajectory {r′1: n ,x′ 1:n The estimated target motion state and maneuvering mode can be made closer to the real value; Step 5: Let α n (r n ,x n )=p(r n+1:N ,y n+1:N |r 1:n ,x 1:n ,y 1:n ), iteratively calculate α at all moments according to the following formula n (r′ n ,x′ n ) Step 6: Execute the filtering algorithm based on Gibbs sampling from n=2 to n=N and update the particle weights Step 7: Make From time n = N-1 to n = 1, iteratively execute the smoothing algorithm with low computational complexity, and obtain the particle smoothing weight Step 8: Use the particle smoothing weights obtained in step 7 Calculate and update the reference trajectory for all n=1,…N moments: The maneuver reference trajectory r′ obtained from the above formula n To make the weighted sum of the particle smoothing weights Maneuvering mode corresponding to the maximum value; x′ n is the weighted sum of the particle smoothing weights The obtained weighted sum average; The obtained reference trajectory is recorded as the reference trajectory {r′ 1:n [d],x′ 1:n [d]}; If d≤λ, return to step 5, otherwise go to step 9; Step 9: Output the estimated maneuver and target motion state 2. The multi-maneuvering target trajectory tracking method with low computational complexity particle smoothing estimation according to claim 1, characterized in that: The nonlinear function f n+1 (x n ,r n+1 )'s target motion equation is determined by the motion state at the previous moment and the maneuvering method at the current moment.

3. The multi-maneuvering target trajectory tracking method with low computational complexity particle smoothing estimation according to claim 1, characterized in that: The particle resampling threshold h in step 2 s The value is greater than 1 and less than 5.

4. The method for tracking multiple maneuvering targets using particle smoothing estimation with low computational complexity according to claim 1, characterized in that: The step 4 uses particle filtering to obtain the initial reference trajectory {r′ 1:n ,x′ 1:n The process of} is: Step 4.1: Initialize all K particles: Let r1 (i) Randomly select a value in Ω, is an all-zero vector, Step 4.2: Iterate and calculate the particles at each moment as follows The symbol '~' indicates that the value on the left is a random sample that obeys the probability distribution on the right, and the symbol '∝' indicates that the value on the left is proportional to the value on the right. is the weight of n-1 at the previous moment The random sampling number of ; the function q(·) represents the probability density sampling function, so Indicates that the maneuvering mode is from the last moment to becomes The probability of sampling is Indicates that the Under the condition of the target motion state from the previous moment becomes Take samples; Represents the observed value y n exist The probability under the condition; if each iteration satisfies the following formula, the particle is weighted Resample K particles and make all particle weights Step 4.3: Calculate the initial reference trajectory {r′ 1:n ,x′ 1:n } in, To satisfy Conditional Dirac function; by introducing the reference trajectory {r′ 1:n ,x′ 1:n } can make the estimated target motion state and maneuver mode closer to the real value.

5. The multi-maneuvering target trajectory tracking method with low computational complexity particle smoothing estimation according to claim 1, characterized in that: The step 6 performs a filtering algorithm based on Gibbs sampling from n=2 to n=N to update the particle weights. The steps are: Step 6.1: Sample K-1 particles according to the following formula, Step 6.2: Based on the reference trajectory {r′ 1:n ,x′ 1:n To obtain the Kth particle, first calculate the prior weight: according to Sample the Kth particle number and let Step 6.3: Update particle weights according to the following formula Step 6.4: If According to weight Resample K particles and make all particle weights Return to step 6.1 until n=N.

6. The method for tracking multiple maneuvering targets using particle smoothing estimation with low computational complexity according to claim 1, characterized in that: The step 7 calculates the complexity of the smoothing algorithm: Step 7.1: Calculation Step 7.2: If Neff < h s , represents the particle smoothing weight The degeneration phenomenon occurs, which means that the probability of the motion state and maneuvering mode values ​​represented by the vast majority of particles in the K particles is infinitely close to 0, and the number of effective particles is too small. The weight of particle smoothing is calculated and normalized according to the traditional particle smoothing algorithm as follows: If Neff>h s , represents the particle smoothing weight There is no degradation and there are enough effective particles; Use particle smoothing method with low computational complexity to calculate the weight of particle smoothing and normalize it; The weight of the obtained particle smoothing Approximately regarded as the corresponding particle value and In all observation sequences y 1:N The probability density of occurrence under the conditions.

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