Improved adaptive tracking gate target tracking method

Abstract

The invention belongs to the field of data association in radar target tracking, and particularly relates to an improved adaptive tracking gate target tracking method. According to the method, transition probability parameters can be dynamically adjusted according to target motion characteristics, and a uniform measurement predicted value and a uniform covariance matrix are formed by combining the measurement predicted value and the covariance matrix of each model. In addition, the adaptive position correlation gate is constructed based on the unified measurement prediction value and the measurement prediction covariance matrix, and the measurement value is effectively screened to reduce the calculation amount. In order to deal with the problem of joint matrix exponential growth in multi-target tracking, a JPDA method is improved, and a threshold value is set to remove a small probability event, so that the calculation complexity is reduced. Compared with a current IMM-PDA method, the method provided by the invention can realize effective tracking of multiple targets in a noise environment.

Description

Technical Field

[0001] The invention belongs to the field of data association in radar target tracking, and in particular relates to an improved adaptive tracking gate target tracking method. Background Art

[0002] Radar target tracking refers to the process of using a radar system to continuously observe and measure a target, thereby obtaining the target's motion state information (such as position, velocity, acceleration, etc.) in real time. The radar system's transmitting antenna sends radio waves, which are reflected back when encountering a target and received by the radar system's receiving antenna. By processing and analyzing the received reflected waves, the radar system can calculate the target's distance, velocity, azimuth, and pitch angle, and then track the target. In radar target tracking, the accuracy of data association directly affects the performance and reliability of the tracking system. When the radar system receives observation data from multiple targets, it is necessary to determine which target these data belong to in order to ensure the continuity and accuracy of tracking.

[0003] Interacting Multiple Model (IMM) is a multi-model method for state estimation of systems with time-varying characteristics. It was first introduced by Shalom in 1989. The IMM method has excellent performance in both estimation accuracy and computational complexity, and occupies a mainstream position in the field of maneuvering target tracking. Despite this, the traditional IMM method still needs to be optimized. There are three main ways to optimize. The first is to change the size of the model set, increase the number of models to include more models to deal with the various motion states of the target, and achieve robust performance. The second is to optimize the type of model set, and strive to solve the complex maneuvers of the target with a smaller number of models. For example, models such as CV, CT, and CS are included in the model set. The third is to improve the filters used by the sub-models. The traditional IMM method uses Kalman Filter (KF) as the filter for each model, which can be modified to use nonlinear filtering methods such as unscented particle filtering as the filter. The IMM model set should include models that are as close to the real motion as possible, so that tracking is more accurate. In addition, the Markov transition probability matrix determines the interaction and switching between models, so it strongly affects the tracking performance of the IMM method. However, the fixed prior transition probability in the standard IMM is unreasonable, and the transition probability parameters cannot be adaptively and dynamically adjusted according to the target motion characteristics, which affects the target tracking accuracy.

[0004] Tracking gate plays an important role in target tracking. It is used iteratively during the track initiation and data association filtering process. It is designed to ensure tracking accuracy while effectively reducing the number of measurements. The tracking gate is a subspace in the tracking space, centered at the predicted position of the tracked target, and its size is determined by the probability of receiving the correct measurement. This area is used to determine whether there is a target that needs to be tracked. The gate size determines the number of verified measurements. Only those measurements within the gate are called candidate measurements and will be associated with the existing trajectory. Candidate measurements may be true measurements or clutter. The probability of detecting a true measurement through the correlation gate is called the detection probability, and vice versa, it is the false alarm probability. Commonly used tracking gates include rectangular tracking gates, ellipsoidal tracking gates, etc. Using these tracking gates can effectively remove invalid observation data and reduce the amount of calculation. However, these tracking gates cannot be adjusted adaptively, resulting in high computational complexity and reducing the accuracy of target tracking to a certain extent. Summary of the invention

[0005] Based on the problems existing in the prior art, the present invention describes an improved adaptive tracking gate target tracking method, which is improved from the IMM model, tracking gate and data association method to improve tracking accuracy and reduce the amount of calculation of the system. Specifically, it includes the following steps: first, through the measurement prediction value and measurement prediction covariance matrix of each model in the interactive multi-model, a unified measurement prediction value and measurement prediction covariance matrix are formed by probability weighting of each model. Based on the calculated unified measurement prediction value and measurement prediction covariance matrix, an adaptive position tracking gate is established to screen the measurement value. The improved JPDA method is used to calculate the association probability of each valid measurement, and a centralized measurement is obtained to correct the prediction value of each sub-model. According to the changes in the calculated probabilities of each model, the transfer probability matrix is ​​adjusted to achieve more effective tracking of the target.

[0006] An improved adaptive tracking gate target tracking method of the present invention comprises:

[0007] 101. Using a sensor to receive observation data from a target in real time; the observation data of the target is an actual observation value of the target at a current moment;

[0008] 102. Based on the preset transition probability parameters, the initial interaction values ​​of each sub-model in the interactive multi-model are calculated and the target is predicted respectively, and a unified prediction value of the target at the current moment is obtained by probability weighting; the unified prediction value includes a unified measurement prediction value and a unified measurement prediction covariance matrix;

[0009] 103. Calculate an adaptive tracking gate according to the unified measurement prediction value of the target at the current moment and the unified measurement prediction covariance matrix;

[0010] 104. Screening the actual observation value of the target at the current moment according to the adaptive tracking gate to obtain the effective observation value of the target at the current moment;

[0011] 105. Use an improved joint probability data association method to perform probability association on valid observation values ​​of the target at the current moment to obtain a centralized unified observation value of the target at the current moment; the centralized unified observation value of the target at the current moment is used to update the estimated value of the motion state of the target at the current moment;

[0012] 106. Update the transition probability parameters of each sub-model in the interactive multi-model according to the estimated value of the motion state of the target at the current moment;

[0013] 107. Repeat steps 101-106 until target tracking is completed.

[0014] Beneficial effects of the present invention:

[0015] The present invention enables the transfer probability parameters to be dynamically adjusted according to the target motion characteristics, and combines the measurement prediction values ​​and covariance matrix of each model to form a unified measurement prediction value and covariance matrix. The present invention constructs an adaptive position correlation gate based on the unified measurement prediction value and error covariance matrix to effectively filter the measurement value to reduce the amount of calculation. The present invention reduces the computational complexity by improving the joint probability data association method and setting a threshold to remove low-probability events, thereby solving the problem of exponential growth of the joint matrix in multi-target tracking, and can achieve effective tracking of multiple targets in a noisy environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a flow chart of an adaptive target tracking method according to an embodiment of the present invention;

[0017] Figure 2 is a schematic diagram of a real motion trajectory of a target in an embodiment of the present invention;

[0018] Figure 3 It is a schematic diagram of the target motion trajectory predicted in a clutter environment according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] The present invention describes an improved adaptive tracking gate target tracking method, which is improved from the IMM model, tracking gate and data association method to improve tracking accuracy and reduce the amount of calculation of the system. Specifically comprising the following steps: first, through the measurement prediction value and measurement prediction covariance matrix of each model in the interactive multi-model, a unified measurement prediction value and measurement prediction covariance matrix are formed by probability weighting of each model. Based on the calculated unified measurement prediction value and measurement prediction covariance matrix, an adaptive position tracking gate is established to screen the measurement value. The improved JPDA method is used to calculate the association probability of each valid measurement, and a centralized measurement is obtained to correct the prediction value of each sub-model. According to the changes in the calculated probabilities of each model, the transfer probability matrix is ​​adjusted to achieve more effective tracking of the target.

[0021] The following is a detailed description of the method:

[0022] 101. Using a sensor to receive observation data from a target in real time; the observation data of the target is an actual observation value of the target at a current moment;

[0023] In an embodiment of the present invention, the sensor is a device that can convert various information such as physical quantities and chemical quantities into electrical signals or digital signals that can be processed by computers or other devices. For example, in an intelligent transportation system, radar sensors, camera sensors, etc. can be used as sensors. The observation data of the target is the most real and direct reflection of the target at the current moment, that is, the actual observation value of the target at the current moment. These actual observation values ​​carry rich information, and they present various states and characteristics of the target at a specific moment in the form of data. For vehicles in an intelligent transportation system, the observation data may include the speed, position, direction of travel, etc. of the vehicle.

[0024] 102. Based on the preset transition probability parameters, the initial interaction values ​​of each sub-model in the interactive multi-model are calculated and the target is predicted respectively, and a unified prediction value of the target at the current moment is obtained by probability weighting; the unified prediction value includes a unified measurement prediction value and a unified measurement prediction covariance matrix;

[0025] In an embodiment of the present invention, it is assumed that the interactive multi-model IMM with N sub-models follows a Markov process guided by a Markov chain of finite length when jumping, the state transition probability Π is as shown in formula (1), the transition probabilities in the state transfer matrix are as shown in formula (2), and the sum of the model transition probabilities of each state is 1 as shown in formula (3).

[0026] Π=[p ij ] N×N (1)

[0027] p ij=P{r(k)=j|r(k-1)=i} (2)

[0028]

[0029] Assume that the model probability of model i at time k-1 is The model transfer probability p ij Through interactive calculation, the model mixing probability of converting model i to model j can be obtained This value is the ratio of the model transition probability from model i to model j to the transition probability from all models to model j, as shown in formula (4):

[0030]

[0031] in As shown in formula (5):

[0032]

[0033] N represents the number of sub-models, and the state estimation of the target at time k-1 is The state posterior covariance matrix is The initial state of the model j mixed input at time k-1 can be obtained by weighting the model mixing probability and the initial covariance matrix As shown in formula (6) and formula (7):

[0034]

[0035] in, is the optimal state estimate of sub-model i at time k-1. It is preset during initialization, and the value used subsequently is the value obtained by recursion.

[0036]

[0037] in, represents the initial covariance matrix of model j obtained by weighting the model mixing probability, It is the posterior covariance matrix of sub-model i at time k-1. It is preset during initialization, and the value used subsequently is the value obtained by recursion.

[0038] After obtaining the initial state value and initial covariance matrix of each model through calculation, filtering calculation can be performed to obtain the prior state prediction value, prior error covariance matrix, measurement prediction value, measurement prediction covariance matrix, etc. of each model.

[0039] Therefore, the unified measurement prediction value can be calculated by formula (8) to form the center of the adaptive tracking gate, that is:

[0040]

[0041] in, represents the unified measurement prediction value from time k-1 to time k, is the measured prediction value of model i from time k-1 to time k, is the predicted probability of model i at time k.

[0042] Then, the covariance matrix of the unified measurement prediction value can be obtained through formula (9):

[0043]

[0044] In the above formula, S k is the unified measurement prediction covariance matrix at time k, is the measurement-prediction covariance matrix of model i.

[0045] 103. Calculate an adaptive tracking gate according to the unified measurement prediction value of the target at the current moment and the unified measurement prediction covariance matrix;

[0046] In the embodiment of the present invention, the unified measurement prediction value and the unified measurement prediction covariance matrix of the target at the current moment are used as input parameters. In this process, various factors such as the dynamic characteristics of the target, environmental noise, and measurement error are comprehensively considered. Through a series of matrix operations, logical judgments, and optimization adjustments, the range of the adaptive tracking gate can be finally determined according to formulas (8) and (9).

[0047] 104. Screening the actual observation value of the target at the current moment according to the adaptive tracking gate to obtain the effective observation value of the target at the current moment;

[0048] In the embodiment of the present invention, step 104 may include the following steps:

[0049] According to the sum of the products of the measured prediction value of each sub-model in the interactive multi-model at the current moment and the prediction probability of the corresponding sub-model, the center of the adaptive tracking gate at the current moment is obtained;

[0050] Based on the center of the adaptive tracking gate at the current moment and the unified measurement prediction covariance matrix, an adaptive tracking gate is established to filter the actual observation values ​​received;

[0051] If an actual observation falls within the adaptive tracking gate, the position and size of the adaptive tracking gate will not be changed;

[0052] If no actual observation falls within the adaptive tracking gate, the adaptive tracking gate is enlarged by increasing the unified measurement prediction covariance matrix to increase the probability that the actual observation falls within.

[0053] In the embodiment of the present invention, whether the actual observation value is a valid observation value can be determined by determining whether the actual observation value is within the threshold of the adaptive tracking gate.

[0054] Specifically, based on the unified position tracking gate center and the measurement prediction covariance matrix, an adaptive tracking gate is established to screen the received measurement values. If an actual observation value falls within the adaptive tracking gate, the position and size of the adaptive tracking gate are not changed. If no actual observation value falls within the adaptive tracking gate, the adaptive tracking gate is appropriately enlarged by increasing the unified measurement prediction covariance matrix as shown in formula (10), thereby increasing the probability of the observation value falling within.

[0055]

[0056] In formula (10): represents the unified measurement prediction covariance matrix after amplification at time k, S k represents the unified measurement prediction covariance matrix at time k; is the i-th expansion step, which is set here as the covariance matrix of the sub-model corresponding to the maximum maneuvering level at time k; p is the number of times the tracking gate is expanded, which is generally in the range of 3-5 in actual situations; H is the observation matrix, and the superscript T is the matrix transpose. Assuming that the maneuvering level of model j'' at time k is the largest, then equation (11) is satisfied

[0057]

[0058] Among them, j" represents the sub-model corresponding to the maximum maneuverability level, represents the unified measurement prediction value from time k-1 to time k, represents the measured predicted value of sub-model j from time k-1 to time k, and the superscript T represents transposition. It can reflect the measurement prediction covariance matrix of the sub-model corresponding to the maximum maneuvering level at time k.

[0059] After this operation, if the actual observation value falls within the adaptive tracking gate, the center position of the tracking gate is adjusted according to the measured value within the adaptive tracking gate.

[0060]

[0061] in, It represents the information of the j'th observation point falling into the relevant wave gate obtained by the k'th scan, that is, the j'th valid observation value. k Represents the total number of measurement points falling into the relevant wave gate obtained in the kth scan. and They represent the position coordinates of the j'th effective measurement value in the kth scan in the spatial rectangular coordinate system. The center position of the adjusted adaptive tracking gate can be obtained through equation (13).

[0062]

[0063] in, represents the center position of the adaptive tracking gate determined by the adjusted k-th scan.

[0064] In a preferred embodiment of the present invention, within a preset period, the size of the adaptive tracking gate is changed back to the size before the enlargement to remove more false measurement values ​​and reduce the amount of calculation for data association.

[0065] 105. Use an improved joint probability data association method to perform probability association on valid observation values ​​of the target at the current moment to obtain a centralized unified observation value of the target at the current moment; the centralized unified observation value of the target at the current moment is used to update the estimated value of the motion state of the target at the current moment;

[0066] In the embodiment of the present invention, step 105 may include:

[0067] The approximate posterior probability of the association between the valid observation and the target is calculated based on the probability that the valid observation falls into the adaptive tracking gate, the measurement innovation, the covariance matrix and the clutter density;

[0068] If the valid observation value at the current moment is only within one wave gate, there is no need to adjust the measurement association probability;

[0069] If the valid observation value at the current moment is in the intersection gate, the measurement association probability needs to be adjusted;

[0070] According to the weighted summation of the associated probabilities of each valid observation value, the centralized unified observation value of the target at the current moment is calculated.

[0071] Specifically, the effective observations in the latest adaptive tracking gate are used to calculate the association probability of the effective observations by using the improved JPDA method. The improved JPDA data association method first approximately calculates the posterior probability, and then removes the events with lower posterior probabilities to reduce the amount of calculation for splitting. If there is only one target or the tracking gates do not intersect, the posterior probability calculation formula is:

[0072]

[0073] in, represents the association probability between the valid observation value j' falling within a gate of the tracking gate and the target t at the current moment, where:

[0074]

[0075] Among them, m k is the total number of valid observations within the target t-wave gate, P D is the detection probability of target t, P G is the probability that a valid observation falls into the gate, is the new information of effective observation, which is obtained by subtracting the measured prediction value of each sub-model from the unified actual observation value. k is the unified measurement prediction covariance matrix at time k, and λ is the clutter density.

[0076] If the valid observation j is only in one gate, the probability does not need to be changed. If the valid observation j is in the intersecting gates, the probability needs to be reduced. The specific formula is formula (17):

[0077]

[0078] in, It represents the corrected association probability between the valid observation value j' and the target t at the current moment, and α is the attenuation coefficient.

[0079] After calculating the source probability of each valid observation value, a threshold is set, and events with probability less than the threshold are considered impossible events. The corresponding positions of the confirmation matrix are set to zero, as shown in formula (18), and then the final association probability is calculated according to the steps of the JPDA method. ε is the threshold. By setting the threshold, low-probability events can be removed, thereby reducing the computational complexity.

[0080]

[0081] The final calculated association probability is weighted and summed with the corresponding observation value to obtain a unified observation value as shown in formula (19):

[0082]

[0083] In the formula, m k is the total number of valid observations, is the j'th valid observation value, It represents the final association probability between the effective observation value j' and the target t at the current moment calculated by the decomposed and corrected confirmation matrix. The calculated unified observation value result is used to update the subsequent posterior state estimation, posterior error covariance matrix and the probability value of each model.

[0084] Using formula (20), the model likelihood function Λ j (k) and the model transition probability update the probability of model j at the current time k:

[0085]

[0086] in The likelihood function is given by formula (21):

[0087]

[0088] in is the filtered information of model j at time k, is the measurement-prediction covariance matrix of model j at time k.

[0089] The total state estimation and error covariance matrix of the target at time k can be obtained, as shown in equations (22) and (23):

[0090]

[0091] in, is the optimal state estimate at time k, is the optimal state estimate of sub-model i at time k, is the model probability of model i at time k, P kk is the posterior covariance matrix at time k, is the posterior covariance matrix of sub-model i at time k.

[0092] 106. Update the transition probability parameters of each sub-model in the interactive multi-model according to the estimated value of the motion state of the target at the current moment;

[0093] In the embodiment of the present invention, step 106 may specifically include:

[0094] According to the model likelihood function and the transition probability parameter, updating the transition probability of each sub-model in the interactive multi-model at the current moment;

[0095] Constructing a correction function according to the model likelihood function to adaptively adjust the state transition probability of each sub-model in the interactive multi-model;

[0096] After adjusting the transition probability matrix using the correction function, comparing the magnitudes of all diagonal elements and the first parameter, and the magnitudes of non-diagonal elements and the second parameter;

[0097] If the transition probability matrix is ​​greater than the first parameter, the first transition calculation function is used to calculate the transition probability of each sub-model in the interacting multi-model;

[0098] If the transition probability matrix is ​​less than the second parameter, the second transition calculation function is used to calculate the transition probability of each sub-model in the interacting multi-model.

[0099] Specifically, based on the likelihood function of the model, the transition probability matrix of IMM is adaptively adjusted according to equations (24), (25), and (26) to make the model transition probability values more reasonable.

[0100]

[0101] To address the situation where, during iterative calculations, the transition probability from a non-matching model to a matching model becomes increasingly large, resulting in the transition probability of the non-matching model becoming increasingly small. If the transition probability of the model is very small when the non-matching model becomes a matching model, it will cause a lag in model jumps and a decrease in the efficiency of model state switching. Therefore, element adjustment is required to ensure that the values are not too low. A threshold value, i.e., the first parameter a and the second parameter b, can be set for the diagonal elements and non-diagonal elements of the transition matrix respectively. After adjusting the transition probability matrix using the correction function, compare the magnitudes of all diagonal elements with a and non-diagonal elements with b. When p ii (k) > a, adjust the transition probability magnitude according to equation (27):

[0102]

[0103] where p ii (k) represents the probability that the sub-model i transfers to the sub-model i at time k, p ij (k) represents the probability that the sub-model i transfers to the sub-model j at time k, p in (k) represents the probability that the sub-model i transfers to the sub-model n at time k, a represents the first parameter; b represents the second parameter. When p ij (k) < b, the method for correcting the transition probability magnitude is similar to the above formula. By dynamically adjusting the transition probability values between models and keeping them within a reasonable range, the switching speed of the model and the robustness of the method can be improved, achieving better tracking performance. After the transition probability is adjusted, continue with the next recursive operation.

[0104] 107. Repeat steps 101 - 106 until the target tracking ends.

[0105] Through the above steps, continuous tracking of the target can be achieved.

[0106] In some embodiments, the following test conditions are given in this embodiment: Assume that the probability P D of detecting a moving target is 1, the probability P G that the correct measurement falls within the tracking gate is 0.99, the threshold of the adaptive tracking gate g_sigma has a value of 5, the number of simulated tracking targets is 4, and the interference in the target motion space is Gaussian noise with a density of 2 * 10 -9 per unit volume. Assume that all 4 targets perform uniformly accelerated linear motion, and verify the effectiveness of the method through simulation under the above conditions.

[0107] Figure 2 The real motion trajectories of multiple targets generated by simulation are displayed; Figure 3 The results of using this method to track moving targets in the presence of clutter interference are shown in Figure 2. It can be seen that the estimated motion trajectory can better reflect the simulated real motion trajectory, indicating that this method has certain robustness and accuracy in interference environments.

[0108] A person skilled in the art can understand that all or part of the steps in the various methods of the above embodiments can be completed by instructing the relevant hardware through a program, and the program can be stored in a computer-readable storage medium, which can include: ROM, RAM, disk or CD, etc.

[0109] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An improved adaptive tracking gate target tracking method, characterized in that: The method comprises:

101. Using a sensor to receive observation data from a target in real time; the observation data of the target is an actual observation value of the target at a current moment; 102. Based on the preset transition probability parameters, the initial interaction values ​​of each sub-model in the interactive multi-model are calculated and the target is predicted respectively, and a unified prediction value of the target at the current moment is obtained by probability weighting; the unified prediction value includes a unified measurement prediction value and a unified measurement prediction covariance matrix; 103. Calculate an adaptive tracking gate according to the unified measurement prediction value of the target at the current moment and the unified measurement prediction covariance matrix; 104. Screening the actual observation value of the target at the current moment according to the adaptive tracking gate to obtain the effective observation value of the target at the current moment; 105. Use an improved joint probability data association method to perform probability association on valid observation values ​​of the target at the current moment to obtain a centralized unified observation value of the target at the current moment; the centralized unified observation value of the target at the current moment is used to update the estimated value of the motion state of the target at the current moment; 106. Update the transition probability parameters of each sub-model in the interactive multi-model according to the estimated value of the motion state of the target at the current moment; 107. Repeat steps 101-106 until target tracking is completed.

2. The improved adaptive tracking gate target tracking method according to claim 1, characterized in that: The actual observation value of the target at the current moment is screened according to the adaptive tracking gate to obtain the valid observation value of the target at the current moment, including: According to the sum of the products of the measurement prediction value of each sub-model in the interactive multi-model at the current moment and the prediction probability of the corresponding sub-model, the unified measurement prediction value at the current moment, that is, the center of the adaptive tracking gate, is obtained; Based on the center of the adaptive tracking gate at the current moment and the unified measurement prediction covariance matrix, an adaptive tracking gate is established to filter the actual observation values ​​received; If an actual observation falls within the adaptive tracking gate, the position and size of the adaptive tracking gate will not be changed; If no actual observation falls within the adaptive tracking gate, the adaptive tracking gate is enlarged by increasing the unified measurement prediction covariance matrix to increase the probability that the actual observation falls within.

3. The improved adaptive tracking gate target tracking method according to claim 2, characterized in that: After screening the actual observation value of the target at the current moment according to the adaptive tracking gate, the method further includes changing the size of the adaptive tracking gate back to the size before the enlargement within a preset period.

4. The improved adaptive tracking gate target tracking method according to claim 2, characterized in that: The formula used to amplify the adaptive tracking gate by increasing the unified measurement prediction covariance matrix is ​​expressed as: in, represents the unified measurement prediction covariance matrix after amplification at time k, is the i-th expansion step; S k represents the unified measurement prediction covariance matrix at time k, p is the number of times the adaptive tracking gate is amplified; H is the observation matrix, and the superscript T is the matrix transpose.

5. The improved adaptive tracking gate target tracking method according to claim 4, characterized in that: The i-th expansion step size is determined by the measurement prediction value of the sub-model corresponding to the maximum maneuvering level and the unified measurement prediction covariance matrix. The calculation formula of the sub-model corresponding to the maximum maneuvering level is expressed as: Among them, j" represents the sub-model corresponding to the maximum maneuverability level, represents the unified measurement prediction value from time k-1 to time k, It represents the measured predicted value of sub-model j from time k-1 to time k, the superscript T represents transposition, and N represents the number of sub-models.

6. The improved adaptive tracking gate target tracking method according to claim 1, characterized in that: The improved joint probability data association method is used to perform probability association on the effective observation values ​​of the target at the current moment to obtain the centralized unified observation value of the target at the current moment, including: The approximate posterior probability of the association between the valid observation and the target is calculated based on the probability that the valid observation falls into the adaptive tracking gate, the measurement innovation, the covariance matrix and the clutter density; If the valid observation value at the current moment is only within one wave gate, there is no need to adjust the measurement association probability; If the valid observation value at the current moment is in the intersection gate, the measurement association probability needs to be adjusted; According to the weighted summation of the associated probabilities of each valid observation value, the centralized unified observation value of the target at the current moment is calculated.

7. The improved adaptive tracking gate target tracking method according to claim 6, characterized in that: If the valid observation value at the current moment is in the intersection gate, the calculation formula used to adjust the measurement association probability includes: in, represents the corrected association probability between the valid observation value j' and the target t at the current moment, α is the attenuation coefficient, n represents the total number of targets, It represents the probability of association between the valid observation value j' that falls within only one tracking gate and the target t at the current moment.

8. The improved adaptive tracking gate target tracking method according to claim 1, characterized in that: The updating of the transition probability parameters of each sub-model in the interactive multi-model according to the estimated value of the motion state of the target at the current moment includes: According to the model likelihood function and the transition probability parameter, updating the transition probability of each sub-model in the interactive multi-model at the current moment; Constructing a correction function according to the model likelihood function to adaptively adjust the state transition probability of each sub-model in the interactive multi-model; After adjusting the transition probability matrix using the correction function, comparing the magnitudes of all diagonal elements and the first parameter, and the magnitudes of non-diagonal elements and the second parameter; If the transition probability matrix is ​​greater than the first parameter, the first transition calculation function is used to calculate the transition probability of each sub-model in the interacting multi-model; If the transition probability matrix is ​​less than the second parameter, the second transition calculation function is used to calculate the transition probability of each sub-model in the interacting multi-model.

9. The improved adaptive tracking gate target tracking method according to claim 8, characterized in that: According to the model likelihood function, the calculation formula of the correction function used for adaptively adjusting each sub-model in the interactive multi-model includes: Among them, p ii (k) represents the probability of sub-model i transferring to sub-model i at time k, p ij (k) represents the probability of sub-model i transferring to sub-model j at time k, p in (k) represents the probability of sub-model i transferring to sub-model n at time k, a represents the first parameter, and b represents the second parameter.

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