Target tracking method based on probability data association in unknown clutter environment

Abstract

The invention provides a target tracking method based on probability data association in an unknown clutter environment, and belongs to the field of target tracking. In the prior art, an integrated probability data association (IPDA) is a method which is designed to be used for single target tracking, and the tracking precision in multi-target tracking is insufficient. According to the method, on the basis of the thought that a probabilistic Data Association (PDA) algorithm is subjected to multi-target tracking optimization to obtain a generalized Probabilistic Data Association (GPDA) algorithm, the multi-target tracking optimization is carried out on an IPDA algorithm to obtain a GIPDA algorithm, and the GIPDA algorithm is subjected to the multi-target tracking optimization on the basis of the thought that the GIPDA algorithm is subjected to the multi-target tracking optimization on the basis of the thought that the GIPDA algorithm is subjected to the multi-target tracking optimization on the basis of the multi-target tracking optimization on the basis of the multi-target tracking optimization on the basis of the multi-target tracking optimization. A simulation result shows that in a clutter environment in which multiple target positions are close / crossed, compared with an IPDA algorithm, the algorithm has more excellent tracking performance, and a more accurate target existence probability can be obtained.

Description

Technical Field

[0001] The invention belongs to the field of multi-target tracking. Aiming at a multi-target tracking method in a clutter environment where the existence of targets is unknown, the invention proposes an algorithm based on the GPDA algorithm idea derivation with the addition of a Markov chain. Background Art

[0002] The IPDA algorithm takes into account the situation that the target may not exist continuously on the basis of the PDA algorithm. It introduces an algorithm derived from the Markov chain on the basis of the PDA algorithm. During the target tracking process, the IPDA algorithm can obtain the target's existence probability in addition to the target's state, providing parameters for the start and end of the track.

[0003] However, the PDA algorithm itself is designed for single target tracking in a clutter environment, and is less effective when tracking multiple adjacent targets or targets in high clutter. The IPDA improved based on PDA also has this problem. Summary of the Invention

[0004] The present invention refers to the design idea of ​​GPDA, a multi-target generalization method of PDA, and improves the IPDA algorithm for multi-target situations to obtain better multi-target tracking effect.

[0005] The technical solution of the present invention is a target tracking method based on probabilistic data association in an unknown clutter environment. The motion equation of the discrete linear time-invariant system targeted by this method is:

[0006] x k =F*x k-1 +q k-1

[0007] z k =H*x k +r k

[0008] Among them, x k ∈R n is the state of the object at time k, F∈R n is the object state transfer matrix, q k-1 is the process noise of the object at time k-1; z k ∈R n is the observable quantity of the object at time k, H∈R nxn is the object's observation matrix, r k is the observation noise of the object at time k, where R n represents an n-dimensional real column vector, R nxn represents an n×n real matrix;

[0009] In a clutter environment, the existence of the target is uncertain. The state transfer matrix F and the process noise covariance Q are known. The observation matrix H is known and meets the conditions of complete controllability and observability and is a constant value. It is assumed that the observation matrix H is reversible and a quantity matrix. The observation quantity z of the system is k is measurable and bounded; assume that the process noise and observation noise are uncorrelated, their values ​​are completely unknown and are positive definite matrices, and that the noise values ​​are bounded; for the above discrete-time linear time-invariant system model, the steps at time k are as follows:

[0010] Step 1: Use the motion equation to estimate the state of the target at time k, and predict the corresponding observation value as the center of the relevant wave gate:

[0011] x t (k|k-1)=F*x t (k-1|k-1) Formula (1)

[0012] z t (k|k-1)=H*x t (k|k-1) Formula (2)

[0013] Among them, x t (k|k-1) represents the prior estimate of the target state t at time k based on the information at time k-1, F represents the state transfer matrix, x t (k-1|k-1) represents the posterior estimate of the state of the target t at time k-1; z t (k|k-1) represents the observation value corresponding to the prior predicted state of target t at time k according to the observation equation;

[0014] Step 2: According to the state transition formula, calculate the prior probability of the target t at time k: the probability of existence and being observed Probability of existing but not being observed and the probability that target t does not exist Indicates that the target t exists at time k and has a probability be detected; Indicates that target t exists at time k but is not detected; Indicates that the target t does not exist at time k; Z k-1 represents the set of measurements obtained up to time k-1;

[0015] Step 3: Update covariance:

[0016] P t (k|k-1)=F*P t (k-1|k-1)F T +Q formula (3)

[0017] S t (k)=H*P t (k|k-1)H T +R formula (4)

[0018] P t (k|k-1) is the prior target state x at time k predicted by formula (1) t (k|k-1) Same as target t actual state x t The covariance of (k), P t (k-1|k-1) is the posterior target state x at time k-1 t (k-1|k-1) Same as target t actual state x t (k-1) covariance, Q is the process error covariance of the target motion; S t (k) is the innovation covariance matrix at time k, which is used to filter observations in step 3. R is the observation error covariance of the device observation. T represents the transpose of the matrix [.];

[0019] Step 4: Obtain multiple actual observations at time k, establish a correlation gate with the prior state observation value obtained by formula (2) as the center, and filter out the set of observations that fall into the correlation gate from the actual observations:

[0020]

[0021] Z(k) is the set of observations that fall into the relevant gate at time k, m means there are m observations that fall into the relevant gate, z i (k) represents the i-th observation in the set;

[0022] Step 5: Calculate the posterior probability matrix B = [β it ], the probability of each target t existing and being observed at time k Probability of existing but not being observed and the probability that target t does not exist

[0023] Step 6: Use the calculated probability as the weight to perform weighted calculation on the observation value to obtain the conditional mean as the observation value of each target at time k, and use this to calculate the new information V at time k of the combination. t (k);

[0024] Step 7: Update the Kalman gain K t (k), posterior estimate x for each target t (k|k), update the posterior state estimate covariance P t (k|k):

[0025]

[0026] x t (k|k)=x t (k|k-1)+K t (k)V t (k) Formula (7)

[0027]

[0028] Among them, x it (k|k) represents the posterior estimated state value of target t corresponding to measurement i when it comes from target t, β 0t (k) represents the probability that all measured values ​​at time k do not originate from target t, S represents the innovation covariance of target t at time k t The inverse matrix of (k), K t (k) represents the Kalman gain at time k, x t (k|k) represents the posterior estimate of the target state at time k.

[0029] Furthermore, the specific calculation method of step 2 is: according to the state transfer matrix:

[0030]

[0031] Represents the state transition probability from state i to state j, satisfying

[0032] Furthermore, the specific calculation method of step 5 is:

[0033] Let Z(k) be the candidate echo set that falls into the target waves at time k, Z k is the set of confirmed measurements up to time k, that is Where, mk represents the total number of valid echoes confirmed by each target tracking unit at time k, z i (k) represents the i-th measurement in the candidate echo;

[0034] Step 5.1: Calculate the initial attribution matrix F = [f it ] represent the prior probability density between each measurement i and each target t;

[0035] Construct the initial attribution matrix F = [f it ],i=0,1,…,mk,t=0,1,…,T;

[0036] Where F is the basic information matrix of the interconnection time between target t and measurement i, which is composed of the probability statistical distance between the measurement and the target, and f it is the probability density function between measurement i and target t, mk is the number of valid echoes detected at the current moment, and T is the total number of targets detected at the current moment;

[0037] Assume that the state variable of target t has a mean of X t (k|k-1), with a variance of P t The normal distribution of (k|k-1) is:

[0038]

[0039] Then the probability density function f of measurement i corresponding to target t is it , i≠0, t≠0:

[0040]

[0041] Where: v it (k) = z i (k)-Z t (k|k-1), v′ it (k) represents the matrix v it The transpose of (k), P represents the prior probability that the target t exists and is observed at the kth moment based on the information obtained at the previous k-1 moments. G is the probability that the target t falls into the observation gate, S t (k) represents the new information covariance of target t at time k, z i (k) represents the i-th measurement observed at time k;

[0042] The probability density function f between the measurement 0 and the target t=0 0t Indicates that the target is not detected, which is:

[0043]

[0044] Among them, P D is the detection probability, V is the volume of the waves, and n is the coefficient, which is generally a positive integer;

[0045] The probability density function of the i-th measurement and the 0 target means that the measurement does not belong to any target of interest to the system, i≠0, that is, the probability density function of the measurement belongs to the false target event, which is:

[0046] f i0 =λ Formula (15)

[0047] Where λ represents the clutter distribution density, and when it is unknown, As a reference value, where mk is the measurement number and V is the volume or area of ​​the observation area;

[0048] Step 5.2: Normalize the initial attribution matrix based on the measurement and the target to obtain the probability matrix

[0049]

[0050] and

[0051] Step 5.3: Obtain the posterior probability matrix corresponding to each target t and each measurement, as well as the existence probability of each target;

[0052] Find the posterior comprehensive probability matrix:

[0053]

[0054] where ε it and ε′ it are θ t and θ i The element in row i+1 and column t+1 of the matrix; ε rtr , ε′ rtr Also expressed as θ t and θ i The matrix corresponds to the elements in r+1 rows and tr+1 columns;

[0055] Then the posterior probability that no measurement originates from target t is:

[0056]

[0057] f′ 0t represents the element in row 1 and column t+1 of the F′ matrix;

[0058] The posterior probability that target t exists but is not detected is:

[0059]

[0060] The posterior probability that target t exists and can be detected, but no measurement originates from it, is:

[0061]

[0062] represents the probability of target t being detected, represents the probability that the target t falls into the detection gate;

[0063] The posterior probability that target t exists and can be detected, and that measurement i originates from this target, is:

[0064]

[0065] f′ it represents the element in row i+1 and column t+1 of the F′ matrix;

[0066] The posterior probability that the target exists and can be detected is:

[0067]

[0068] From equations (19)-(23), the interconnection probability of different measurements and target t is:

[0069]

[0070] Furthermore, the specific calculation method of step 6 is:

[0071]

[0072] where β it is the interconnection probability between measurement i and target t calculated in the previous step, z it (k) is the i-th measurement at time k.

[0073] The present invention realizes the multi-target tracking expansion of IPDA by adopting the design concept of GPDA algorithm, and obtains significantly better tracking effect while maintaining the probability of target existence. At the same time, compared with the original GPDA algorithm, due to the introduction of Markov chain, better tracking effect is obtained under longer sampling time intervals. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A general flow chart of the operation of the present invention.

[0075] Figure 2 The position error of the algorithm is tracked at different sampling time intervals.

[0076] Figure 3 The algorithm tracking speed error at different sampling time intervals.

[0077] Figure 4 There are probability variations in the target 1 obtained by different algorithms.

[0078] Figure 5 There are probability variations in target 2 obtained by different algorithms. DETAILED DESCRIPTION

[0079] During target tracking, the target that existed at the previous moment may not exist at this moment. Considering this situation, the events related to track existence are defined as follows: (1) Indicates that target t exists at time k; (2) Indicates that target t does not exist at time k.

[0080] These two events can be viewed as a Markov chain with two states, i.e., a type of Markov chain, and their probabilities are expressed as and where Z k Represents the set of measurements obtained up to time k, and defines the state transition probability matrix

[0081]

[0082] Represents the state transition probability from state i to state j, satisfying

[0083] have

[0084]

[0085] For the GIPDA algorithm of the second-class Markov chain, it is necessary to consider both the existence and visibility of the target. The events related to the existence of the target are defined as follows:

[0086] (1) Indicates that the target t exists at time k and has a probability be detected;

[0087] (2) Indicates that target t exists at time k but is not detected;

[0088] (3) Indicates that target t does not exist at time k.

[0089] Their corresponding probabilities are expressed as and State transition matrix

[0090]

[0091] Represents the state transition probability from state i to state j, satisfying

[0092] have

[0093]

[0094] The first-class Markov chain can be regarded as the second-class Markov chain. use replace, It is replaced by 0, so the following only introduces the second-class Markov chain GIPDA algorithm.

[0095] The feasibility rule of the present invention considers that: a target may have multiple measurements; a measurement may also come from multiple targets. Based on this, the concept of generalized joint events is proposed. A generalized joint event is a combination of the following two generalized events.

[0096] ① Each target has a measurement (one or more, including 0 measurement).

[0097] ② Each measurement has a target source (one or more, including 0 target).

[0098] Here, 0 target means no target, that is, false targets generated by new targets, interference, clutter, etc. other than the target of interest; 0 measurement means no measurement.

[0099] Under the above assumptions, calculate the association probability β between the measurement and the target it (k).

[0100] Construct the initial attribution matrix

[0101] Where F is the basic information matrix of the interconnection time between target t and measurement i, which is composed of the probability statistical distance between the measurement and the target, and f it is the probability density function between measurement i and target t, mk is the number of valid echoes detected at the current moment, and T is the total number of targets detected at the current moment.

[0102] Assume that the state variable of target t has a mean of X t (k|k-1), with a variance of P t The normal distribution of (k|k-1) is:

[0103]

[0104] Then the probability density function of measurement i (i≠0) corresponding to target t (t≠0) is:

[0105]

[0106] Where: v it (k) = z i (k)-Z t (k|k-1), P represents the prior probability that the target t exists and is observed at the kth moment based on the information obtained at the previous k-1 moments. G is the probability that the target t falls into the observation gate, S t (k) represents the new information covariance of target t at time k, z i (k) represents the i-th measurement observed at time k.

[0107] The probability density function f between the measurement 0 and the target t (t = 0) 0t Indicates that the target is not detected, which is:

[0108]

[0109] Among them, P D is the detection probability, V is the volume of the waves, and n is the coefficient, which is generally a positive integer.

[0110] The probability density function of the i-th (i≠0) measurement and the 0 target means that the measurement does not belong to any target of interest to the system, that is, the probability density function of the measurement belonging to the false target event is:

[0111] f i0 =λ Formula (4)

[0112] Where λ represents the clutter distribution density, and when it is unknown, As a reference value, mk is the measurement number and V is the volume or area of ​​the observation area.

[0113] The matrices based on measurement and target are obtained by rule ① and rule ② respectively, and the probability matrix is ​​obtained by normalizing the initial attribution matrix.

[0114] and

[0115] The posterior probability matrix corresponding to each target t and each measurement, as well as the existence probability of each target, are further derived.

[0116] The conditional Bayes formula for multiple events can be derived as follows:

[0117]

[0118] Then, based on the Markov chain, the probability of the target's existence is further corrected, where ε it and ε′ it are θ t and θ i Corresponding elements.

[0119] Then the posterior probability that no measurement originates from target t is

[0120]

[0121] The posterior probability that target t exists but is not detected is

[0122]

[0123] The posterior probability that target t exists and can be detected, but no measurement originates from it is

[0124]

[0125] The posterior probability that target t exists and can be detected and measurement i originates from the target is

[0126]

[0127] The posterior probability that the target exists and can be detected is

[0128]

[0129] From equations (19)-(23), the interconnection probability of different measurements and target t is

[0130]

[0131] Comparison of simulation results and demonstration of method effectiveness:

[0132] Simulation environment 1:

[0133] Simulation purpose: Compare the tracking performance of GPDA, GIPDA1, GIPDA2, IPDA1, and IPDA2 algorithms

[0134] Target state: The five target initial states are [55000m,200m / s,55000m,-50m / s], [45000m,350m / s,45000m,-20m / s], [35000m,550m / s,35000m,70m / s], [25000m,300m / s,25000m,80m / s], and [15000m,440m / s,15000m,70m / s] (initial x coordinate, initial x-direction velocity, initial y coordinate, and initial y-direction velocity, respectively).

[0135] Noise matrix: The Q value of the noise matrix in the simulation process is:

[0136] [(T 5 / 20)m 2 ,(T 4 / 8)m 2 / s 2 ,0m 2 ,0m 2 / s 2 ;(T 4 / 8)m 2 ,(T 3 / 3)m 2 / s 2 ,0m 2 ,0m 2 / s 2 ;

[0137] 0m 2 ,0m 2 / s 2 ,(T 5 / 20)m 2 ,(T 4 / 8)m 2 / s 2 ;0m 2 ,0m 2 / s 2 ,(T 4 / 8)m 2 ,(T 3 / 3)m 2 / s 2 ;], where T is the scanning interval; the observation noise R value is diag([10m 2 ,10m 2 ]).

[0138] The probability of the target falling into the door is Pg = 0.99, and the probability of target detection is Pd = 0.95.

[0139] Markov chain: The first-class Markov chain matrix is ​​[0.98, 0.02; 0, 1], with an initial probability of existence of 0.2. The second-class Markov chain matrix is ​​[0.93, 0.05, 0.02; 0.23, 0.75, 0.02; 0, 0, 1], with an initial probability of existence and detection of 0.2 and an initial probability of existence but not detection of 0.3.

[0140] The clutter is randomly distributed on the x-axis [0m,10 5 m]y axis is [0m,10 5 m] square area, the clutter density is 300*10 -10 pcs / m 2 , 5000 Monte Carlo simulations were performed at different time intervals, and the MAE between the target coordinates and the true coordinates, and the MAE between the target speed and the true speed at 120 seconds were statistically analyzed under different sampling time intervals to observe the impact of the sampling interval on the algorithm tracking accuracy.

[0141] Simulation results:

[0142]

[0143] As can be seen from the table and figure, the tracking accuracy trends for position and velocity are similar across the algorithms. The GIPDA algorithm consistently outperforms the IPDA algorithm in tracking accuracy at all time intervals. Compared to the GPDA algorithm, GIPDA2's tracking accuracy is comparable to that of GPDA at short time intervals, while GIPDA1's tracking accuracy is inferior. However, to conserve system computing resources, after gradually adjusting the sampling interval, both GIPDA1 and GIPDA2 achieve better accuracy than GPDA.

[0144] Figure 2 is the tracking position error of the algorithms under different sampling time intervals. It can be seen that GIPDA and GPDA algorithms are far superior to IPDA algorithm under any circumstances. At short sampling intervals, the tracking accuracy of GIPDA2 and GPDA is similar, and the tracking accuracy of GIPDA1 is poor. When the time interval is 6 seconds or longer, the tracking accuracy of both GIPDA algorithms is better than that of GPDA algorithm.

[0145] Figure 3 is the algorithm tracking speed error under different sampling time intervals of each algorithm. It can be seen that GIPDA and GPDA algorithms are far superior to IPDA algorithm under any circumstances. At short sampling intervals, the tracking accuracy of GIPDA2 and GPDA is similar, and the tracking accuracy of GIPDA1 is slightly lower than GPDA. When the sampling time interval is 6 seconds or longer, the tracking accuracy of both types of GIPDA algorithms is better than that of GPDA algorithm.

[0146] As an extension of the IPDA algorithm in multi-target situations, the GIPDA algorithm brings about a significant improvement in tracking effect; at the same time, compared with the original GPDA algorithm, when a larger sampling interval is selected to save system resources, it can also bring about a certain enhancement in tracking effect.

[0147] Simulation environment 2:

[0148] Simulation purpose: Compare the judgment accuracy of GIPDA1, GIPDA2, IPDA1, and IPDA2 on the probability of target existence

[0149] Target state: The two initial states are [15000m, 200m / s, 45000m, -350m / s] and [10000m, 450m / s, 40000m, -100m / s] (initial x-coordinate, initial x-direction speed, initial y-coordinate, initial y-direction speed, respectively), and last for 60 seconds and 55 seconds, respectively.

[0150] Noise matrix: The Q value of the noise matrix in the simulation process is:

[0151] 10*[(T 5 / 20)m 2 ,(T 4 / 8)m 2 / s 2 ,0m 2 ,0m 2 / s 2 ;(T 4 / 8)m 2 ,(T 3 / 3)m 2 / s 2 ,0m 2 ,0m 2 / s 2 ;

[0152] 0m 2 ,0m 2 / s 2 ,(T 5 / 20)m 2 ,(T 4 / 8)m 2 / s 2 ;0m 2 ,0m 2 / s 2 ,(T 4 / 8)m 2 ,(T 3 / 3)m 2 / s 2 ;], where T is the scanning interval; the observation noise R value is diag([10m 2 ,10m 2 ]).

[0153] T: The sampling time interval is 1s.

[0154] The probability of the target falling into the door is Pg = 0.99, and the probability of target detection is Pd = 0.95.

[0155] Markov chain: The first-class Markov chain matrix is ​​[0.98, 0.02; 0, 1], with an initial probability of existence of 0.2. The second-class Markov chain matrix is ​​[0.93, 0.05, 0.02; 0.23, 0.75, 0.02; 0, 0, 1], with an initial probability of existence and detection of 0.2 and an initial probability of existence but not detection of 0.3.

[0156] The clutter is randomly distributed on the x-axis [0m,5*10 4 m]y axis is [0m,5*10 4 m], the clutter density is 100*10 -10 pcs / m 2 , continue observing for 60 seconds, and compare the differences in target existence probabilities given by different algorithms.

[0157] Simulation results:

[0158] according to Figure 4 It can be seen that for the target 1 that always exists, GIPDA1 and GIPDA2 always give extremely high probability of target existence. However, the probability of target existence given by IPDA1 and IPDA2 decreases rapidly with time. In this environment, the judgment of target existence given by IPDA is far less accurate than that of GIPDA algorithm. Figure 5 It can be seen that during the period of 1-55 seconds when target 2 persisted, both GIPDA algorithms continued to give extremely high existence probabilities. After target 2 disappeared, the existence probability quickly dropped to 1.7% within 3 seconds, indicating that the target disappeared. Subsequently, because the track was not set to terminate in the experiment, it matched clutter, resulting in an increase in the existence probability. The effects of the two types of IPDA were the same as those of target 1. Regardless of whether target 2 existed or not, the given target existence probability steadily decreased over time.

[0159] From the above results, it can be seen that in a multi-target intersection environment, the GIPDA algorithm is much better than the IPDA algorithm in judging the probability of target existence.

Claims

1. A target tracking method based on probabilistic data association in an unknown clutter environment. The motion equation of the discrete linear time-invariant system targeted by this method is: x k =F*x k-1 +q k-1 z k =H*x k +r k in, x k ∈R n is the state of the object at time k, F∈R n is the object state transfer matrix, q k-1 is the process noise of the object at time k-1; z k ∈R n is the observable quantity of the object at time k, H∈R nxn is the object's observation matrix, r k is the observation noise of the object at time k, where R n represents an n-dimensional real column vector, R nxn represents an n×n real matrix; In a clutter environment, the existence of the target is uncertain. The state transfer matrix F and the process noise covariance Q are known. The observation matrix H is known and meets the conditions of complete controllability and observability and is a constant value. It is assumed that the observation matrix H is reversible and a quantity matrix. The observation quantity z of the system is k is measurable and bounded; assume that the process noise and observation noise are uncorrelated, their values ​​are completely unknown and are positive definite matrices, and that the noise values ​​are bounded; for the above discrete-time linear time-invariant system model, the steps at time k are as follows: Step 1: Use the motion equation to estimate the state of the target at time k, and predict the corresponding observation value as the center of the relevant wave gate: x t (k|k-1)=F*x t (k-1|k-1) Formula (1) z t (k|k-1)=H*x t (k|k-1) Formula (2) Among them, x t (k|k-1) represents the prior estimate of the target state t at time k based on the information at time k-1, F represents the state transfer matrix, x t (k-1|k-1) represents the posterior estimate of the state of the target t at time k-1; z t (k|k-1) represents the observation value corresponding to the prior predicted state of target t at time k according to the observation equation; Step 2: According to the state transition formula, calculate the prior probability of the target t at time k: the probability of existence and being observed Probability of existing but not being observed and the probability that target t does not exist Indicates that the target t exists at time k and has a probability be detected; Indicates that target t exists at time k but is not detected; Indicates that target t does not exist at time k; Z k-1 represents the set of measurements obtained up to time k-1; Step 3: Update covariance: P t (k|k-1)=F*P t (k-1|k-1)F T +Q formula (3) S t (k)=H*P t (k|k-1)H T +R formula (4) P t (k|k-1) is the prior target state x at time k predicted by formula (1) t (k|k-1) Same as target t actual state x t The covariance of (k), P t (k-1|k-1) is the posterior target state x at time k-1 t (k-1|k-1) Same as target t actual state x t (k-1) covariance, Q is the process error covariance of the target motion; S t (k) is the innovation covariance matrix at time k, which is used to filter observations in step 3. R is the observation error covariance of the device observation. T represents the transpose of the matrix [.]; Step 4: Obtain multiple actual observations at time k, establish a correlation gate with the prior state observation value obtained by formula (2) as the center, and filter out the set of observations that fall into the correlation gate from the actual observations: Z(k) is the set of observations that fall into the relevant gate at time k, m means there are m observations that fall into the relevant gate, z i (k) represents the i-th observation in the set; Step 5: Calculate the posterior probability matrix B = [β it ], the probability of each target t existing and being observed at time k Probability of existing but not being observed and the probability that target t does not exist Step 6: Use the calculated probability as the weight to perform weighted calculation on the observation value to obtain the conditional mean as the observation value of each target at time k, and use this to calculate the new information V at time k of the combination. t (k); Step 7: Update the Kalman gain K t (k), posterior estimate x for each target t (k|k), update the posterior state estimate covariance P t (k|k): Among them, x it (k|k) represents the posterior estimated state value of target t corresponding to measurement i when it comes from target t, β 0t (k) represents the probability that all measured values ​​at time k do not originate from target t, S represents the innovation covariance of target t at time k t The inverse matrix of (k), K t (k) represents the Kalman gain at time k, x t (k|k) represents the posterior estimate of the target state at time k.

2. The target tracking method based on probabilistic data association in an unknown clutter environment according to claim 1, characterized in that: The specific calculation method of step 2 is: according to the state transfer matrix: Represents the state transition probability from state i to state j, satisfying 3. The target tracking method based on probabilistic data association in an unknown clutter environment according to claim 1, characterized in that: The specific calculation method of the step 5 is: Let Z(k) be the candidate echo set that falls into the target waves at time k, Z k is the set of confirmed measurements up to time k, that is Where, mk represents the total number of valid echoes confirmed by each target tracking unit at time k, z i (k) represents the i-th measurement in the candidate echo; Step 5.1: Calculate the initial attribution matrix F = [f it ] represent the prior probability density between each measurement i and each target t; Construct the initial attribution matrix F = [f it ],i=0,1,…,mk,t=0,1,…,T; Where F is the basic information matrix of the interconnection time between target t and measurement i, which is composed of the probability statistical distance between the measurement and the target, and f it is the probability density function between measurement i and target t, mk is the number of valid echoes detected at the current moment, and T is the total number of targets detected at the current moment; Assume that the state variable of target t has a mean of X t (k|k-1), with a variance of P t The normal distribution of (k|k-1) is: Then the probability density function f of measurement i corresponding to target t is it , i≠0, t≠0: Where: v it (k) = z i (k)-Z t (k|k-1), v′ it (k) represents the matrix v it The transpose of (k), P represents the prior probability that the target t exists and is observed at the kth moment based on the information obtained at the previous k-1 moments. G is the probability that the target t falls into the observation gate, S t (k) represents the new information covariance of target t at time k, z i (k) represents the i-th measurement observed at time k; The probability density function f between the measurement 0 and the target t=0 0t Indicates that the target is not detected, which is: Among them, P D is the detection probability, V is the volume of the waves, and n is the coefficient, which is generally a positive integer; The probability density function of the i-th measurement and the 0 target means that the measurement does not belong to any target of interest to the system, i≠0, that is, the probability density function of the measurement belongs to the false target event, which is: f i0 =λ Formula (15) Where λ represents the clutter distribution density, and when it is unknown, As a reference value, where mk is the measurement number and V is the volume or area of ​​the observation area; Step 5.2: Normalize the initial attribution matrix based on the measurement and the target to obtain the probability matrix Step 5.3: Obtain the posterior probability matrix corresponding to each target t and each measurement, as well as the existence probability of each target; Find the posterior comprehensive probability matrix: where ε it and ε′ it are θ t and θ i The element in row i+1 and column t+1 of the matrix; ε rtr , ε′ rtr Also expressed as θ t and θ i The matrix corresponds to the elements in r+1 rows and tr+1 columns; Then the posterior probability that no measurement originates from target t is: f′ 0t represents the element in row 1 and column t+1 of the F′ matrix; The posterior probability that target t exists but is not detected is: The posterior probability that target t exists and can be detected, but no measurement originates from it, is: represents the probability of target t being detected, represents the probability that the target t falls into the detection gate; The posterior probability that target t exists and can be detected, and that measurement i originates from this target, is: f′ it represents the element in row i+1 and column t+1 of the F′ matrix; The posterior probability that the target exists and can be detected is: From equations (19)-(23), the interconnection probability of different measurements and target t is:

4. The target tracking method based on probabilistic data association in an unknown clutter environment according to claim 1, characterized in that: The specific calculation method of step 6 is: where z 0t (k) = z t (k|k-1) formula (26) where β it is the interconnection probability between measurement i and target t calculated in the previous step, z it (k) is the i-th measurement at time k.

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