Group target tracking method under pure azimuth measurement

Abstract

The invention provides a group target tracking method under pure azimuth measurement, which can provide an efficient group target tracking strategy for a sensor platform adopting pure azimuth measurement, and particularly shows relatively high accuracy and robustness under the conditions of multi-target dynamic complexity and limited signal observation. According to the method, under the condition of only azimuth measurement, the AIVKF algorithm is provided to estimate the group target state in combination with the annular navigation motion of the observation platform and the GNN algorithm, so that the estimation precision is greatly improved; the RM algorithm is applied to the pure azimuth tracking model, the appearance estimation of the group target under the passive tracking condition is realized, and the estimation precision is close to the level of active tracking.

Description

Technical Field

[0001] The present invention relates to the field of group target tracking and identification, and specifically to a method for tracking group targets under bearing-only measurement. Background Art

[0002] In both military and civilian fields, group target tracking has become an important research direction, especially in application scenarios such as unmanned aerial vehicle swarms and fleet formations. With the wide application of group targets in modern warfare, how to achieve effective passive tracking of group targets in complex environments has become the focus of research. As a common passive tracking method, bearing-only measurement locates and tracks targets by passively receiving target signals, and has good concealment and anti-interference capabilities. However, group target tracking under bearing-only measurement faces a series of challenges.

[0003] The core of the method for tracking group targets under bearing-only measurement lies in estimating the motion trajectory by analyzing the change in the target azimuth angle. Due to the lack of distance information, such problems typically manifest as non-linear and non-Gaussian tracking problems, and traditional tracking methods are difficult to directly apply. Common solutions include Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Particle Filter (PF), and pseudo linear Kalman filter (PLKF), etc. These methods combine azimuth information with the target motion model by constructing a state space model to achieve real-time tracking of group targets. However, EKF approximates non-linear functions through first-order Taylor expansion, but this approximation will introduce truncation errors; although UKF and PF have advantages in dealing with non-linearity, their computational complexity is relatively high; PLKF has a relatively low computational complexity, but there are still significant biases in target state estimation. Therefore, the core difficulty in this field is to study how to reduce the computational complexity while improving the tracking accuracy and achieve tracking of maneuvering targets.

[0004] In addition, group targets usually exhibit the characteristics of cluster motion. Therefore, recent research tends to treat group targets as a whole, focusing on the estimation of the centroid motion and extended shape of group targets. Current group target shape modeling methods include Random Matrix (RM), Random Hypersurface Model (RHM), and Gaussian Process (GP). Among them, the RHM and GP methods can model relatively complex target shapes, but the computational cost is relatively high and they are applicable to targets with large shape variations; the RM method is widely used due to its simple filtering process and strong robustness. However, most of these shape estimation algorithms rely on the active tracking process. How to accurately estimate the shape of group targets when only azimuth information is available remains another key problem.

[0005] Therefore, designing a tracking algorithm that can effectively handle the complex dynamic characteristics of group targets under pure azimuth measurement conditions has become a research topic that urgently needs to be solved. This not only involves high-precision angle information processing technology, but also requires reasonable modeling of the shape of group targets and accurate estimation of the state of group targets through advanced filtering algorithms. Such research will provide a new technical path for low-cost and low-complexity group target tracking, with important theoretical value and practical application significance. Summary of the Invention

[0006] In order to overcome the deficiencies of the prior art, the present invention provides a method for tracking group targets under pure azimuth measurement. The present invention aims to solve the problems of low tracking accuracy and difficult shape estimation existing in the prior art when tracking group targets only relying on azimuth measurement, and provides a method for state estimation and shape recognition of group targets based on pure azimuth measurement. This method can provide an efficient group target tracking strategy for sensor platforms using pure azimuth measurement, especially showing high accuracy and robustness in the case of complex multi-target dynamics and limited signal observations.

[0007] The technical solution adopted by the present invention to solve its technical problems is as follows:

[0008] Step 1, establish a target state transition model and a pseudo-measurement model under pure azimuth measurement;

[0009] By combining the circum-navigation strategy of the observation station and the Global Nearest Neighbour (GNN) algorithm, obtain the azimuth measurement information of the target, and use the Instrumental Variable PLKF (IVKF) algorithm to update the preliminary state estimate of the target. The preliminary state estimate includes position and velocity;

[0010] Step 2: Introduce an adaptive adjustment mechanism to dynamically adjust the process noise covariance Q in the IVKF algorithm. k The updated covariance is used in the prediction and update steps of the next moment to improve the system's tracking ability of the target trajectory. The IVKF algorithm is used to obtain the state estimation result of the target.

[0011] Step 3: Use the state estimation result obtained in Step 2 as a pseudo-measurement and input it into the RM algorithm to model the shape of the group target. The centroid position and shape parameters of the group target are recursively updated through Kalman filtering.

[0012] In Step 1, a state transition model and a pseudo-measurement model of the target under bearing-only measurement are established. Combining with the GNN algorithm and using the IVKF filter, the target state estimation at the current moment is obtained. The specific steps are as follows:

[0013] Assume that the observation station and the target are flying at a fixed altitude, and there are N targets moving at a constant speed in the observation area. The BOT model of a single target is expressed as:

[0014] x k = Fx k-1 + w k-1

[0015] z k = H k x k + η k (1)

[0016] where represents the target state at time k, p T,k = [x k , y k T and represent the position and velocity of the target respectively. Among them, x k and y k represent the coordinates of the target on the x-axis and y-axis respectively. and represent the velocities of the target on the x-axis and y-axis respectively. The position of the observer is p k = [p x,k , p y,k T where p x,k and p y,k represent the coordinates of the observer on the x-axis and y-axis respectively; F is the state transition matrix, and the process noise w k-1 obeys Gaussian white noise with zero mean and variance Q k-1 ; is the pseudo-linear measurement, is the pseudo-measurement matrix, and η k = -||D k ​​||sinv k is the pseudo-linear measurement noise, η k The variance of which is expressed as:

[0017]

[0018] where is the azimuth angle with noise, v k is the measurement noise with variance D k = p T,k - p k ;

[0019] For the association problem between the measurement and the target track, calculate the association cost a ij ;

[0020]

[0021] where, θ thresh is the association threshold, θ ij > 0 represents the difference between the predicted azimuth angle of track i at time k and the measurement j; Denote the optimal problem of the GNN algorithm as:

[0022]

[0023] where, δ ij is a binary function representing the association situation between the i-th track and the j-th measurement:

[0024]

[0025] Use the Hungarian algorithm for the optimal problem to find the global optimal solution, obtain the matching result between each target and the measurement, and then obtain the state estimate of the target through the IVKF algorithm Covariance matrix and the Kalman gain K k .

[0026] Introduce an adaptive adjustment mechanism in step 2 to dynamically adjust the process noise covariance Q k in the IVKF algorithm, and the specific steps are as follows:

[0027] Randomly select a window with length M, and take the new residual d k :

[0028]

[0029] Obtain the covariance estimate of the new residual through the sliding window method

[0030]

[0031] Among them, m represents the time index, which is used to traverse M moments before the k-th moment, and d m represents the residual at the m-th moment, and the estimated value of the process noise covariance is:

[0032]

[0033] Among them, ε k = x k - x k|k-1 x k|k-1 = Fx k-1 is the prediction of the target state at the k-th moment. Under the steady-state assumption, it is necessary to ensure that the error does not diverge and the state estimate remains within an acceptable range after the algorithm converges, and we get:

[0034]

[0035] Among them, F T represents the transpose of matrix F, and the estimated is used as Q k and substituted into the state update process.

[0036] Optionally, the updated state estimate of the group target is used as the pseudo-measurement set and the RM algorithm is used to estimate the centroid state and extended shape of the group target, specifically including:

[0037] Denote the pseudo-measurement set at the k-th moment as n k is the number of measurements; all the target measurement sets before the k-th moment are The centroid state x k is obtained by Kalman filter recursion, and the covariance matrix of the centroid state is The extended shape matrix is denoted as X k X k The prediction process is:

[0038]

[0039] Among them, is the posterior estimate of the shape matrix at the (k - 1)-th moment, δ k is the degree of freedom of the Wishart distribution,

[0040] is the degree of freedom of the inverse Wishart distribution, and the parameter A k is the shape evolution matrix, and B k is the shape observation matrix;

[0041] X kThe update process is as follows:

[0042]

[0043] N k is the correction term for the shape matrix estimation, is the predicted state of the group centroid at time k, is the centroid of the pseudo-measurement, and the corresponding scattering matrix is

[0044] An electronic device includes: one or more processors; a memory; one or more programs, where the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs are configured to execute the method as described above.

[0045] A computer-readable storage medium stores program codes, and the program codes can be called by a processor to execute the method as described above.

[0046] The beneficial effects of the present invention are as follows:

[0047] (1) In the case of only bearing measurement, combining the circumferential motion of the observation platform and the GNN algorithm, the AIVKF algorithm is proposed to estimate the state of the group target, greatly improving the estimation accuracy;

[0048] (2) Applying the RM algorithm to the pure bearing tracking model realizes the shape estimation of the group target under passive tracking conditions, and its estimation accuracy is close to the level of active tracking. Description of the Drawings

[0049] Figure 1 is a flowchart of a method for tracking a group target under pure bearing measurement provided by an embodiment of the present application.

[0050] Figure 2 is a schematic diagram of the planar projection of the circumferential tracking of the target by the observation station provided by an embodiment of the present application.

[0051] Figure 3 is a comparison chart of the RMSE of the centroid position estimation of the group target in an embodiment of the present application (σ1 = 1°), Figure 3 (a) is a comparison chart of the RMSE of the X channel, Figure 3 (b) is a comparison chart of the RMSE of the Y channel, Figure 3 (c) is a comparison chart of the RMSE of the distance.

[0052] Figure 4 is a comparison chart of the RMSE of the centroid position estimation of the group target in an embodiment of the present application (σ2 = 10°), Figure 4 (a) is a comparison chart of the RMSE of the X channel,Figure 4 (b) is a comparison graph of RMSE for the Y channel Figure 4 (c) is a comparison graph of RMSE for distance.

[0053] Figure 5 This is the trajectory graph of the group target circular navigation tracking in the embodiment of the present application.

[0054] Figure 6 This is the overall tracking effect diagram of the group target in the embodiment of the present application.

[0055] Figure 7 This is the RMSE comparison graph of the centroid position estimation of the group target in the embodiment of the present application. Figure 7 (a) is a comparison graph of RMSE for the X channel Figure 7 (b) is a comparison graph of RMSE for the Y channel Figure 7 (c) is a comparison graph of RMSE for the centroid position.

[0056] Figure 8 This is the comparison graph of the pseudo Jaccard distance for the shape estimation of the group target in the embodiment of the present application. Detailed implementation manners

[0057] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0058] The present invention discloses a method for tracking the state and extended shape of a group target under the condition of only bearing measurement at a single observation station. First, a pure bearing measurement model is constructed, and combined with the circular navigation strategy of the observation station and the GNN algorithm to obtain the measurement information of the target, and the target state is preliminarily estimated by the IVKF algorithm. Subsequently, an adaptive process noise covariance adjustment mechanism is introduced to further improve the estimation accuracy of the target state. Finally, the state estimation result of the group target is used as pseudo-measurement input, and the RM algorithm is used to model the shape of the group target, and the accurate state estimation and shape estimation of the centroid of the group target are recursively obtained.

[0059] Step 1: Establish a target state transition model and a pseudo-measurement model under pure bearing measurement, combine the circular navigation strategy of the observation station and the GNN algorithm to obtain the measurement information of the corresponding target, and preliminarily estimate the target state by the IVKF algorithm;

[0060] Step 2: Introduce an adaptive adjustment of the process noise variance into the IVKF algorithm, calculate the adaptive process noise covariance as the Q for the next moment k , and obtain the accurate estimation result of the target state;

[0061] Step 3: Use the state estimation result of the group target as pseudo-measurement input, and adopt the RM algorithm to model the shape of the group target, and recursively obtain the accurate state estimation and shape estimation of the centroid of the group target.

[0062] Specifically, in step 1, a motion model of the target under pure bearing measurement is established, and the current target state estimate is obtained by using the IVKF filter in combination with the GNN algorithm, including:

[0063] The single-target BOT model can be expressed as:

[0064] x k = Fx k-1 + w k-1 (14)

[0065] z k = H k x k + η k (15)

[0066] Where, represents the target state at time k, and the position and velocity of the target on the x-axis and y-axis are represented by p T,k = [x k , y k T and The observer position is p k = [p x,k , p y,k T ; F is the state transition matrix, and the process noise w k obeys Gaussian white noise with zero mean and variance Q k .

[0067] η k = -||D k ||sinv k is the pseudo-linear noise, and its variance is expressed as:

[0068]

[0069] Where, is the azimuth angle with noise, v k is the measurement noise with variance , D k = p T,k - p k .

[0070] For the association problem between measurement j and target i, calculate the association cost a ij ;

[0071]

[0072] Where, θ thresh is the association threshold, θ​​ij > 0 is the difference between the predicted azimuth angle of target i at time k and measurement j; Denote the optimal problem of the GNN algorithm as

[0073]

[0074] where, δ ij is a binary function representing the association between the i-th track and the j-th measurement:

[0075]

[0076] Use the Hungarian algorithm for the above optimal problem to find the global optimal solution and obtain the matching results between each target and measurement. Then, obtain the state estimation and covariance matrix Kalman gain K k .

[0077] In step 2, an adaptive adjustment system covariance Q k is introduced:

[0078] Randomly select a window of length M, and take the new residual as:

[0079]

[0080] Obtain the covariance estimate of the new residual through the sliding window method:

[0081]

[0082] Estimate the process noise as:

[0083]

[0084] where, ε k = x k - x k|k-1 . Under the steady-state assumption, the estimated process noise can be expressed as:

[0085]

[0086] The filtering result calculated according to the above formula is prone to divergence, so an adjustment factor is added on this basis to ensure the stability of the algorithm:

[0087]

[0088] Substitute into the estimation process of IVKF at the next moment.

[0089] In step 3, the state estimation of the group target is used as pseudo-measurement information, and the RM algorithm is used to estimate the centroid state and extended shape of the group target. It includes:

[0090] Denote the pseudo-measurement set at time k as All target measurement sets before time k are The centroid state is obtained by Kalman filter recursion The covariance matrix is The extended shape matrix is denoted as X k , and its prediction process is:

[0091]

[0092] Among them, δ k is the degree of freedom of the Wishart distribution, A k is the shape evolution matrix, B k is the shape observation matrix.

[0093] X k The update process of is:

[0094]

[0095] is the centroid of the pseudo-measurement, and the corresponding scattering matrix is

[0096] The technical solution of the present invention will be described in detail below, but the protection scope of the present invention is not limited to the described embodiments.

[0097] Embodiment

[0098] The method provided by the present application will be further elaborated below in combination with specific embodiments. This embodiment is described for the following environment. Assume there is a cross-shaped group target composed of 5 group members. The edge group members are 20m or 30m away from the center, and the initial position is set to p T,0 = [0, 0, 0, -30, 30; 0, 20, 40, 20, 20] m. The members within the group target have the same speed, and the relationship between the motion state of the target and time is shown in Table 1.

[0099] Table 1 Relationship table of the speed and time of the target Set the filter window length M = 3. Assume that each group member only generates one measurement, and set the initial position of the observation station to (10, 1000) T , and its ideal circular tracking distance r d from the center of the group target is 350m, the gain coefficient of the controller is set to K c = 45, and the circular tracking speed is set to v A= 165 m / s.

[0100] (1) For different measurement noises, two different simulation scenarios (σ1 = 1°, σ2 = 10°) are designed to track the group targets; in each scenario, the IVKF and the proposed AIVKF in this paper are simulated and compared. Without considering the initial convergence time, that is, the target tracking time is set as 40 ≤ k ≤ 150, and 100 Monte Carlo (MC) simulation experiments are carried out. The simulation results of the root mean square error (RMSE) of the centroid position of the group targets are as Figure 3 , Figure 4 shown.

[0101] It can be seen from Figure 3 that when the measurement noise σ1 = 1°, the deviation of the IVKF algorithm is large and unstable. Especially when the target maneuvers, the positioning error increases significantly. However, the proposed AIVKF algorithm in this paper compensates for the error caused by model mismatch through the adaption of the process noise variance, thus having better robustness and high precision. When the measurement noise increases to σ2 = 10°, the filtering error of the IVKF algorithm without adaptive compensation increases significantly, and the positioning accuracy of the AIVKF algorithm is significantly better than that of the IVKF algorithm, and it can track and predict the target state more quickly and accurately.

[0102] (2) Set the BOT measurement noise σ = 0.3°, and the active tracking (AT) measurement noise follows a normal distribution N(0, R A ), R A = R k ≈ diag([2 2 , 2 2 ) m 2 , and other parameters remain unchanged. Based on the random matrix theory, the centroid model is set as the CV model, and the shape evolution matrix is set with ο = 3, and the shape observation matrix . The RM parameter settings of the two algorithms are the same. The simulation time is taken as 0 - 120 s, and the comparison results of BOT-RM and AT-RM are as Figures 5 - 8 shown.

[0103] Figure 5 is the circular tracking trajectory diagram of the group targets, Figure 6 is the overall tracking effect diagram of the group targets, Figure 7 Figure 8 is the estimation results of the centroid position and shape of the target by the two tracking algorithms under 100 MC simulation experiments. It can be seen from Figure 7 that the positioning accuracy and stability of the AT algorithm for the target are significantly better than those of the BOT algorithm. Although the state estimation error of the BOT algorithm for the target is large at the initial moment, it can quickly converge to the neighborhood of the true position.Figure 8 The Jaccard distance is used to represent the difference between the two, and the smaller the difference, the higher the similarity. Figure 8 It reflects that when the measurement noise σ of AT-RM A = 2m, the BOT-RM algorithm proposed in this application shows an equivalent effect to the AT-RM algorithm in estimating the shape of the group target; when σ A increases to 5m, the BOT-RM algorithm shows better performance. It can overcome the influence of positioning errors, effectively estimate the shape of the group target, and thus reduce the tracking cost.

Claims

1. A tracking method for group targets under pure bearing measurement, characterized in that Including the following steps: Step 1, establish a target state transition model and a pseudo-measurement model under pure bearing measurement; By combining the circum-navigation strategy of the observation station and the global nearest neighbor algorithm, obtain the bearing measurement information of the target, and use the auxiliary vector PLKF algorithm to update the preliminary state estimate of the target. The preliminary state estimate includes position and velocity; Step 2, introduce an adaptive adjustment mechanism to dynamically adjust the process noise covariance Q in the IVKF algorithm k , and the updated covariance is used for the prediction and update steps at the next moment to improve the system's tracking ability of the target trajectory. Use the IVKF algorithm to obtain the state estimation result of the target; Step 3, input the state estimation result obtained in Step 2 into the RM algorithm as a pseudo-measurement to model the shape of the group target, and recursively update the centroid position and shape parameters of the group target through Kalman filtering.

2. The tracking method for group targets under pure bearing measurement according to claim 1, wherein: In the said Step 1, establish a target state transition model and a pseudo-measurement model under pure bearing measurement, combine the GNN algorithm and use the IVKF filter to obtain the target state estimate at the current moment. The specific steps include: Assume that the observation station and the target fly at a fixed altitude, there are N targets moving at a constant speed in the observation area, and the BOT model of a single target is expressed as: x k = Fx k-1 + w k-1 z k = H k x k + η k (1) Among them, represents the target state at time k, p T,k = [x k , y k T and respectively represent the position and velocity of the target, where x k and y k respectively represent the coordinates of the target on the x-axis and y-axis. and respectively represent the velocities of the target on the x-axis and y-axis. The observer position is p k = [p x,k , p y,k T , where p x,k and p y,k respectively represent the coordinates of the observer on the x-axis and y-axis; F is the state transition matrix, and the process noise w k-1 obeys Gaussian white noise with zero mean and variance Q k-1 ; is the pseudo-linear measurement, is the pseudo-measurement matrix, and η k = -||D k ||sinv k is the pseudo-linear measurement noise, and the variance of η k is expressed as:​​ Among them, is the azimuth angle with noise, v k is the measurement noise with variance , D k = p T,k - p k ; Regarding the association problem between measurements and target tracks, calculate the association cost a between each track i and measurement j ij ; where, θ thresh is the association threshold, and θ ij > 0 represents the difference between the predicted azimuth of track i at time k and measurement j; Denote the optimal problem of the GNN algorithm as: where δ ij is a binary function representing the association between the i-th track and the j-th measurement: The Hungarian algorithm is used for the optimal problem to find the global optimal solution, obtaining the matching results between each target and measurement, and then the state estimation of the target is obtained through the IVKF algorithm Covariance matrix and the Kalman gain K k .

3. The tracking method for group targets under pure bearing measurement according to claim 1, wherein: In step 2, an adaptive adjustment mechanism is introduced to dynamically adjust the process noise covariance Q in the IVKF algorithm k , and the specific steps are as follows: Randomly select a window of length M and take the new residual d k : Obtain the covariance estimate of the new residual through the sliding window method where m represents the time index, which is used to traverse M moments before time instant k, and d m represents the residual at time instant m, and the estimated value of the process noise covariance is as follows: where ε k = x k - x k|k-1 , x k|k-1 = Fx k-1 is the prediction of the target state at time step k. Under the steady-state assumption, it is necessary to ensure that the error does not diverge after convergence and the state estimation remains within an acceptable range, resulting in: Among them, F T represents the transpose of matrix F, and the estimated is used as Q k and substituted into the state update process.

4. The tracking method for group targets under pure bearing measurement according to claim 1, wherein: In step 3, the updated state estimate of the group target is used as the pseudo-measurement set The RM algorithm is used to estimate the centroid state and extended form of the group target, specifically including: Denote the pseudo-measurement set at time k as n k which is the number of measurements; the set of all target measurements before time k is the centroid state obtained by Kalman filter recursion, and the covariance matrix of the centroid state is The extended shape matrix is denoted as X k , X k The prediction process is as follows: Among them, is the posterior estimate of the shape matrix at time k - 1, and δ k is the degree of freedom of the Wishart distribution, is the degree of freedom of the inverse Wishart distribution, and the parameter A k is the shape evolution matrix, and B k is the shape observation matrix; X k The update process of N k is the correction term for the shape matrix estimation, is the predicted state of the group centroid at time k, is the centroid of the pseudo-measurement, and the corresponding scattering matrix is 5. An electronic device, characterized in that, Including: One or more processors; A memory; One or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors. The one or more programs are configured to execute the method according to any one of claims 1-4.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores program codes, and the program codes can be called by the processor to execute the method according to any one of claims 1-4.

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