Multi-target tracking method based on distributed PMHT

Abstract

The present invention belongs to the field of target tracking technology, and specifically relates to a multi-target tracking method based on distributed PMHT. In this scenario, the PMHT algorithm is used to process the data association problem of multi-target tracking, and multiple sensors are used to obtain a more stable and accurate tracking effect. The present invention extends it to a PMHT distributed algorithm, which has stronger flexibility and real-time performance and lower fusion calculation amount while ensuring tracking accuracy. The present invention can well perform multi-target tracking in complex environments such as proximity and intersection. Under the distributed PMHT algorithm, the tracking results of each sensor on the target state tend to be consistent, and have a tracking accuracy that is better than that of a single-sensor PMHT algorithm. Compared with the centralized algorithm, the distributed PMHT algorithm has a smaller amount of calculation, higher flexibility and timeliness, and has a tracking effect close to that of the centralized algorithm.

Description

Technical Field

[0001] The present invention belongs to the technical field of target tracking, and in particular relates to a multi-target tracking method based on distributed PMHT in a clutter environment. Background Art

[0002] In the multi-target tracking scenario, since the radiation source measured by the receiving end is unknown, it is necessary to associate the measurement with the target in a clutter environment to achieve the purpose of tracking, that is, data association. Classic data association algorithms include the nearest neighbor data association algorithm (NNAD), the multiple hypothesis tracking algorithm (MHT), and the joint probability data association algorithm (JPDA). These algorithms inevitably face the problem of combinatorial explosion caused by the increase in the number of measurements and the number of targets. The probabilistic multiple hypothesis algorithm (PMHT) based on the expectation maximization algorithm (EM) is a batch processing algorithm that updates the track in iterations. Its computational complexity increases linearly with the increase in the number of targets, and it can handle association problems in complex environments such as adjacent and cross-motion scenarios.

[0003] Compared with a single sensor, a multi-sensor system can achieve more accurate and stable tracking results. Multi-sensor systems are divided into centralized and distributed systems. Compared with centralized systems, distributed tracking has stronger real-time performance and greater flexibility in the face of emergencies such as sensor damage.

[0004] This method further applies the PMHT algorithm to a multi-sensor system and compares the tracking effects. Obviously, the distributed PMHT tracking algorithm not only has a smaller amount of calculation and a faster fusion speed than the centralized one, but also has a significantly better tracking effect than the single-sensor system and close to the centralized one. Summary of the invention

[0005] In view of the above problems, the present invention proposes a multi-target tracking method based on distributed PMHT, uses the PMHT algorithm to deal with the data association problem of multi-target tracking, adopts multiple sensors to obtain a more stable and accurate tracking effect, and expands it to a PMHT distributed algorithm with stronger flexibility, real-time performance and lower fusion calculation amount.

[0006] The technical solution adopted by the present invention is:

[0007] Define the total number of targets in the multi-target tracking scenario as M, the number of sensors as S, and U s Represents the coordinates of sensor s

[0008] X={x m (t)}, represents the state of target m at time t

[0009] Used to characterize the target's x and y axis movement speed information and location information x m (t),y m (t)

[0010] represents the rth measurement value of sensor s at time t

[0011] Indicates the target corresponding to the rth measurement of sensor s

[0012] Probability value π p =Pr(k r,s (t) = p, p = 1...M), represents the prior probability that the rth measurement of sensor s at time t comes from target p. In addition, the clutter number φ follows a Poisson distribution, V represents the detection range of the sensor, λ represents the clutter density, and the probability density function of the clutter number is expressed as follows:

[0013]

[0014] S1. Let the motion of the mth target conform to the linear model. The state equation and observation equation are given by the following model:

[0015] x m (t+1)=F m (t)x m (t)+v m (t)

[0016] Z m,s (t) = h s (t)x m (t)+w m,s (t)

[0017] Among them, Z m,s (t) represents the measurement of the mth target received by sensor s at time t, and the process noise v m (t) and the measurement noise w m,s (t) are independent zero-mean Gaussian white noises, and Q m (t) and R m,s (t) are their covariance matrices respectively: Q m (t) = E{v m (t)v m (t) T},R m,s (t) = E{w m,s (t)w m,s (t) T};h s (t) and F m (t) are the observation matrix and the state transfer matrix respectively, △t is the sampling interval:

[0018]

[0019]

[0020] S2. Based on the hidden variables of the probability model Observation The maximum likelihood solution for the state parameter X can be written as:

[0021]

[0022] S3. Use PMHT algorithm to obtain new measurements and covariance. PMHT algorithm is a batch tracking algorithm based on EM algorithm. First, perform E-step and define Q function as follows:

[0023]

[0024] Then perform the M-step of the EM algorithm

[0025] (1) First calculate the posterior probability:

[0026]

[0027] The rth measurement of sensor s at time t is obtained by target k r,s (t) produces the posterior probability, represents the Gaussian distribution of variable χ with μ as mean and Σ as covariance. The above formula reflects the possibility of association between measurement and target to a certain extent. Among them, It means that the rth measurement of sensor s at time t is obtained by target k r,s (t) the prior probability of generation, and represents the target k r,s (t) The mean and covariance of the measurements. Similarly, With R p,s (t) represents the mean and covariance of the sensor s's measurement of the target p. V represents the sensor's reconnaissance area, π p (p=1...M) is the same as defined in S1, represents the probability that the rth measurement of sensor s at time t is a false alarm.

[0028] (2) Q(X (n+1) ,X (n) ) can be maximized to obtain the iterative function Q(X) of the state variables based on the PMHT algorithm in the multi-sensor scenario. (n+1) ,X (n) ):

[0029]

[0030] in:

[0031]

[0032] Next, in order to maximize the iterative function, we need to calculate the derivative The former is the same as the derivative of the following equation, and the maximization of the following equation can be completed by the extended Kalman filter (EKF):

[0033]

[0034] in and The two variables calculated by the PMHT algorithm are used as the "new" measurement and covariance, usually called the centroid measurement and centroid covariance:

[0035]

[0036]

[0037] Among them, R m,s (t) is the covariance of the sensor s’s measurement of the target m; The posterior probability that the rth measurement of sensor s at time t, calculated by formula (1), is generated by target m.

[0038] S4. Data fusion and state prediction

[0039] For the distributed PMHT algorithm, data fusion is performed on each sensor node in the Kalman filter stage. Let S be the sensor set, and for each node i∈S,S i represents the neighboring nodes with which data can be fused, π i,j represents the fusion weight, where j∈S i , where the fusion matrix formed by the fusion weights is a row-random primitive matrix.

[0040] Set the number of fusion iterations to L, and the fusion steps are as follows:

[0041] (1) Measurement of sensor i at time t Sampling is performed to obtain intermediate variables in the fusion process and in, is the prior state information of the current target, is the derivative of the measurement equation to the prior estimate of the target state. If it is linear, it can be simplified to the observation matrix, is the covariance matrix of the measurement error of sensor i at time t. For convenience, the differences between different targets are ignored.

[0042]

[0043]

[0044]

[0045] (2) Data fusion. The initial iteration value of the current sensor node is set by the intermediate variable obtained in the previous step, and π is selected through the fusion matrix i,j As the weight value, data is fused at different nodes, where q i With Ω i is the information vector, and data fusion is performed on its prior information and intermediate variables:

[0046]

[0047]

[0048] right

[0049]

[0050]

[0051]

[0052]

[0053] (3) State estimation. The data fusion result of the previous step is used to obtain the posterior estimate of the current target state of the i-th sensor. and the posterior estimate of the information vector and (For the same target, the state estimates of each sensor after data fusion tend to be consistent, and the variable This will be explained in step (4):

[0054]

[0055]

[0056]

[0057] (4) Obtain a priori estimates of the target state and information vector To iterate at the next moment. m is the state transfer function, A t is the derivative of the posterior estimate of the target state. If it is linear, it can be simplified to the state transfer matrix. t is the covariance matrix of the state estimation error at time t. For convenience, the differences between different sensors are ignored:

[0058]

[0059]

[0060]

[0061]

[0062] In (3) the variable The introduction of is to prevent the node from overestimating the information vector and the weight value The update method is as follows:

[0063]

[0064]

[0065] For each sensor node, set the initial value In fact, the effect of this weight is and Multiplied by a coefficient according to The iterative process, this coefficient is The constraint will not exceed 1 to achieve the effect of suppressing overestimation.

[0066] The beneficial effects of the present invention are:

[0067] The present invention can well track multiple targets in complex environments such as proximity and intersection. The tracking results of each sensor on the target state under the distributed PMHT algorithm tend to be consistent, and the tracking accuracy is better than that of the single-sensor PMHT algorithm. Compared with the centralized algorithm, the distributed PMHT algorithm has a smaller amount of calculation, higher flexibility and timeliness, and has a tracking effect close to that of the centralized algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 This is a simulation diagram of PMHT multi-target tracking based on a single sensor;

[0069] Figure 2 This is a simulation diagram of centralized PMHT multi-target tracking under multiple sensors;

[0070] Figure 3 This is a simulation diagram of multi-target tracking of sensor 1 in a distributed PMHT scenario;

[0071] Figure 4 This is a simulation diagram of multi-target tracking of sensor 2 in a distributed PMHT scenario;

[0072] Figure 5This is a simulation diagram of multi-target tracking of sensor 3 in a distributed PMHT scenario;

[0073] Figure 6 It is a multi-target tracking simulation diagram of sensor 4 in the distributed PMHT scenario;

[0074] Figure 7 It is a multi-target tracking simulation diagram of sensor 5 in the distributed PMHT scenario;

[0075] Figure 8 This is a comparison chart of RMSE in three scenarios: single sensor, centralized, and distributed; DETAILED DESCRIPTION

[0076] The present invention is described in detail below in conjunction with embodiments:

[0077] In the simulation scenario, both single and multi-sensors observe four targets moving in a uniform linear motion. The four targets start from [-2500m, -1500m], [-2500m, -1400m], [-2500m, -1000m], and [-2500m, -900m]. The velocity vectors on the x-axis and y-axis are [8m / s, 10m / s], [8m / s, 8m / s], [8m / s, -8m / s], and [8m / s, -10m / s] respectively. Assume that the reconnaissance range of the x-axis is -2500m to -1700m, the y-axis is -1800m to -600m, the coordinates of the single sensor are set to [-2100m, -1800m], and four more sensors are set in the centralized and distributed multi-sensor scenarios, with coordinates of [-2500m, -600m], [-1700m, -1800m], [-1700m, -600m], [-2500m, -1800m]. The number of fusion iterations L under distributed conditions is set to 9, assuming that each sensor can fuse data with its two nearest sensors. The sampling period △t = 3, the total number of samples T = 30, the algorithm batch processing window length is 3, and it slides 2 units of length each time. The number of clutter in the scene follows the Poisson distribution and the clutter density value is set to 10 -4 , the measurement covariance is set to the unit matrix, and the system noise covariance is:

[0078]

[0079] Multi-target tracking simulation experiments were carried out in three scenarios respectively. Finally, the RMSE in the three scenarios were compared through 100 Monte Carlo experiments.

[0080] Tracking results:

[0081] In order to verify the tracking effect of the distributed PMHT algorithm, the tracking effects of the single sensor, centralized and distributed PMHT algorithms are shown respectively. Figure 1 It can be seen that the accuracy of tracking with a single sensor will decrease significantly as time increases. Figure 8 It can also be seen from the simulation Figure 2-Figure 7 It can be seen intuitively that the distributed and centralized tracking have higher accuracy, and the real trajectory and the tracking trajectory are almost coincident. Figure 3-Figure 7 It can also be shown that the estimated states of each distributed sensor tend to be consistent, and a high number of fusion iterations is not required. The RMSE comparison chart shows that the distributed tracking accuracy is significantly better than that of a single sensor, and the tracking effect is close to that of a centralized one, which confirms the good tracking effect and superiority of the distributed PMHT algorithm proposed in the present invention.

Claims

1. Based on the distributed PMHT multi-target tracking method, the total number of targets in the multi-target tracking scenario is defined as M, the number of sensors is S, and the coordinates of the sensor s are represented as U s , Indicates the movement speed information of target m on the x and y axes and location information x m (t),y m (t), then the state parameter of the target m at time t is expressed as X = {x m (t)}, the rth measurement value of sensor s at time t is expressed as The relationship between measurement and target is expressed as The prior probability that the rth measurement of sensor s at time t comes from target p is π p , p = 1...M, and π p =Pr(k r,s (t) = p); characterized in that The multi-target tracking method comprises the following steps: S1. Define the motion of the mth target to conform to the linear model, and its state equation and observation equation are: x m (t+1)=F m (t)x m (t)+v m (t) Z m,s (t)=h s (t)x m (t)+w m,s (t) Among them, Z m,s (t) represents the measurement of the mth target received by sensor s at time t, and the process noise v m (t) and the measurement noise w m,s (t) are independent zero-mean Gaussian white noises, and Q m (t) and R m,s (t) are their covariance matrices respectively: Q m (t) = E{v m (t)v m (t) T },R m,s (t) = E{w m,s (t)w m,s (t) T };h s (t) and F m (t) respectively observe the matrix and the state transfer matrix, and the sampling interval is △t, then: S2. Based on the relationship between measurement and target, the latent variables of the probability model By observation The maximum likelihood solution for the state parameter X is obtained: S3. Use PMHT algorithm to obtain new measurements and covariance. PMHT algorithm is a batch tracking algorithm based on EM algorithm. First, perform E-step and define Q function as follows: Then proceed to M-step, including: First calculate the posterior probability: The rth measurement of sensor s at time t is obtained by target k r,s (t) produces the posterior probability, represents the Gaussian distribution of the variable χ with μ as mean and Σ as covariance; It means that the rth measurement of sensor s at time t is obtained by target k r,s (t) the prior probability of generation, and represents the target k r,s (t) The mean and covariance of the measurements. Similarly, With R p,s (t) represents the mean and covariance of the sensor s's measurement of the target p, V represents the sensor's reconnaissance area, represents the probability that the rth measurement of sensor s at time t is a false alarm; Q(X (n+1) ,X (n) ) is maximized to obtain the iterative function Q(X) of the state variables based on the PMHT algorithm in the multi-sensor scenario. (n+1) ,X (n) ): in: Next, in order to maximize the iterative function, we need to calculate the derivative This is the same as the derivative of the following equation, and the maximization of the following equation is done by the extended Kalman filter: in and The variables calculated by the PMHT algorithm are used as new measurements and covariances, defined as centroid measurements and centroid covariances: Among them, R m,s (t) is the covariance of the sensor s’s measurement of the target m; is the calculated a posteriori probability that the rth measurement of sensor s at time t is generated by target m; S4. Data fusion and state prediction: In the Kalman filter stage, data fusion is performed on each sensor node. Let S be the sensor set, and for each node i∈S,S i represents the neighboring nodes with which data can be fused, π i,j represents the fusion weight, where j∈S i , the fusion matrix composed of fusion weights is a row-random primitive matrix; the number of fusion iterations is set to L, and the fusion steps are as follows: S41. Measurement of sensor i at time t Sampling is performed to obtain intermediate variables in the fusion process and in, is the prior state information of the current target, is the derivative of the measurement equation with respect to the prior estimate of the target state. If it is linear, it is simplified to the observation matrix, is the covariance matrix of the measurement error of sensor i at time t; S42, data fusion: Set the initial iteration value of the current sensor node by the intermediate variable obtained, and select π through the fusion matrix i,j As the weight value, data is fused at different nodes, and q is defined i With Ω i is the information vector, and data fusion is performed on the prior information and intermediate variables: right S43, state estimation: The posterior estimation of the current target state of the i-th sensor is obtained through the data fusion result of S42 and the posterior estimate of the information vector and in This is to prevent the node from overestimating the information vector. The update method is as follows: for each sensor node, set the initial value S44, obtain the prior estimate of the target state and information vector To iterate at the next moment: Among them, F m is the state transfer function, A t is the derivative of the posterior estimate of the target state. If it is linear, it can be simplified to the state transfer matrix; W t is the covariance matrix of the state estimation error at time t.

Images