Adaptive Tracking Method for Maneuvering Targets under Non-Gaussian Noise Conditions Based on IMM-VB

Abstract

The present invention discloses an adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB, including: obtaining the measurement values of the maneuvering targets; constructing a model set including multiple motion models, and respectively performing interactive mixing on the state estimation values, precision matrices, and conjugate prior distribution parameters of the maneuvering targets; using the variational Bayesian algorithm to filter the mixed state input values, mixed precision matrices, and mixed parameters of the conjugate prior distribution of each motion model to update the state estimation values and precision matrices of each motion model; updating the probabilities corresponding to each motion model in the model set; and updating the state estimation values and precision matrices of the maneuvering targets at the current moment. The method provided by the present invention can achieve real-time and accurate tracking of maneuvering targets under time-varying non-Gaussian noise conditions.

Description

Technical Field

[0001] The present invention belongs to the technical field of target tracking, and particularly relates to an adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB. Background Art

[0002] In the research of maneuvering target tracking technology, the research on process noise and measurement noise is an important part. At present, most of the maneuvering target tracking algorithms are carried out under the assumption that the noise follows a Gaussian distribution. However, in the actual detection process of radar, factors such as environmental disturbances, instantaneous sensor failures, sudden high maneuvers of flying targets, and different scattering intensities at different positions of flying targets will make the process noise or measurement noise have heavy-tailed characteristics, and the occurrence of these factors is uncertain. In this way, the non-Gaussian noise is time-varying during the tracking process. If the traditional maneuvering target tracking algorithm assuming Gaussian white noise is still used, the tracking performance of the algorithm will be reduced or even the problem of tracking loss will occur.

[0003] Shenzhen University disclosed a method for tracking multiple targets under non-Gaussian noise by combining the variational Bayesian method and the labeled multi-Bernoulli filter in its patent document "A Method and System for Tracking Multiple Targets under Glint Noise" (application publication number: CN110390684A). The steps of this method are as follows: First, combine the predicted distribution function and the labeled multi-Bernoulli filter density of the existing and newly born targets at the current moment, then process them to obtain the distribution function and the labeled multi-Bernoulli filter density of each target at the current moment, and finally accurately extract the state estimation values of each target at the current moment in non-Gaussian noise, so as to realize the tracking of multiple targets. The disadvantage of this method is that it does not consider the maneuverability of the target. When the target maneuvers, the established motion model no longer matches the true motion state of the target, which will cause the tracking accuracy of the target to decrease or the problem of tracking loss to occur.

[0004] Shenzhen University discloses a technique for tracking maneuvering targets under non-Gaussian measurement noise by combining the variational Bayesian method and the JMS-PHD filter in its patent document "A Multi-Maneuvering Target Tracking Method and System Applicable to Flicker Noise" (Publication No.: CN107462882A). The steps of this method are as follows: First, use the t-distribution to model the flicker noise, that is, non-Gaussian noise, then apply the variational Bayesian method to approximately obtain the joint probability density under different models, and finally combine the JMS-PHD filter to estimate the state of the target, so as to realize the tracking of multiple maneuvering targets. The deficiency of this method is that in this method, it is only assumed that the measurement noise in the measurement equation is non-Gaussian noise, and the process noise in the state equation still follows a Gaussian distribution. For maneuvering targets, sudden maneuvers will cause the process noise to also be a non-Gaussian distribution with heavy-tailed characteristics. Then, the assumed process Gaussian noise in this method will have a certain deviation from the actual movement of the target, resulting in a decrease in the tracking accuracy of maneuvering targets. Summary of the Invention

[0005] To solve the above problems existing in the prior art, the present invention provides a method for adaptively tracking maneuvering targets under non-Gaussian noise conditions based on IMM-VB (Interactive Multiple Model - Variational Bayesian), aiming to solve the problem of tracking maneuvering targets under time-varying non-Gaussian noise conditions caused by instantaneous sensor failures and sudden maneuvers of flying targets.

[0006] The idea of realizing the object of the present invention is as follows: Use the student t-distribution to model the process noise and measurement noise. For the convenience of applying the variational Bayesian method later, write the student t-distribution in the form of hierarchical Gaussian, and use the conjugate prior distribution to represent the distributions in the hierarchical Gaussian. Next, through the variational Bayesian method, learn the degrees of freedom and precision matrix parameters in the student t-distribution followed by the time-varying non-Gaussian process and measurement noise, so that the KL divergence between the approximate joint posterior probability density and the true joint posterior probability density is minimized. In this way, the student t-distribution corresponding to the estimated parameters is closer to the true noise distribution at each moment, so the obtained state estimation value is also more accurate. Then, calculate the likelihood function and the corresponding probability of each model according to the state estimation values output by each model in the model set, and perform weighted summation on the state estimation values and precision matrices of each filter according to the obtained model probabilities to obtain the final state estimation value and precision matrix at the current moment, thereby realizing the adaptive tracking of maneuvering targets under time-varying non-Gaussian noise conditions.

[0007] The technical problems to be solved by the present invention are realized through the following technical solutions:

[0008] An adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB, including:

[0009] Step 1: Obtain the measurement values of the maneuvering target;

[0010] Step 2: Construct a model set including multiple motion models, and perform interactive mixing on the state estimate value, precision matrix, and conjugate prior distribution parameters of the maneuvering target, respectively, to obtain the mixed state input value, mixed precision matrix, and mixed parameters of the conjugate prior distribution corresponding to each motion model;

[0011] Step 3: Based on the measurement values, use the variational Bayesian algorithm to perform filtering processing on the mixed state input value, mixed precision matrix, and mixed parameters of the conjugate prior distribution of each motion model to update the state estimate value and precision matrix of each motion model;

[0012] Step 4: Update the probability corresponding to each motion model in the model set;

[0013] Step 5: Update the state estimate value and precision matrix of the maneuvering target at the current moment based on the probability corresponding to each motion model and the state estimate value and precision matrix of each motion model.

[0014] In an embodiment of the present invention, in Step 2, performing interactive mixing on the state estimate value, precision matrix, and conjugate prior distribution parameters of the maneuvering target respectively includes:

[0015] Calculate the mixed state input value of each motion model in the model set using the state mixing formula; the state mixing formula is:

[0016]

[0017] Where, represents the mixed state input value of the th motion model in the model set at time represents the total number of motion model types in the model set, represents the summation operation, represents the state estimate value of the th motion model in the model set at time represents the probability that the th motion model in the model set at time converts to the

[0018] th motion model;

[0019] Calculate the mixed precision matrix of each motion model in the model set using the precision matrix mixing formula; the precision matrix mixing formula is:

[0019]

[0020] Among them, represents the mixed-precision matrix of the input of the th motion model in the moment model set, represents the precision matrix of the th motion model in the moment model set, represents the transpose operation;

[0021] Calculate the mixing parameters of the conjugate prior distribution based on each motion model in the model set by using the parameter mixing formula. The calculation formula is:

[0022]

[0023] Among them, and represent the mixing shape parameters of the conjugate parameter distribution gamma distribution of the motion model , and represent the mixing scale parameters of the conjugate parameter distribution gamma distribution of the motion model , and represent the mixing degrees of freedom in the conjugate parameter distribution inverse Wishart distribution of the motion model , and represent the mixing inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution of the motion model , and represent the -th moment shape parameter of the conjugate parameter distribution gamma distribution of the motion model , and represent the -th moment scale parameter of the conjugate parameter distribution gamma distribution of the motion model , and represent the degrees of freedom in the conjugate parameter distribution inverse Wishart distribution of the motion model at the -th moment, and represent the inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution of the motion model at the -th moment.

[0024] In an embodiment of the present invention, step 3 includes:

[0025] 3a) Calculate the predicted values of the state, precision matrix, and conjugate prior distribution parameters of each motion model in the set of computational models, as well as the joint predicted posterior probability density function;

[0026] 3b) Use the variational Bayesian method to learn the conjugate prior distribution parameters, minimizing the KL divergence between the approximate posterior probability density function and the true posterior probability density function, so as to update the state estimate and precision matrix of each motion model.

[0027] In one embodiment of the present invention, the calculation formula in step 3a) is:

[0028]

[0029] where, denotes the predicted value of the state of the th motion model in the model set at time denotes the state transition matrix of the th motion model in the model set, T denotes the transpose, denotes the predicted value of the precision matrix of the th motion model in the model set at time denotes the process noise matrix based on the th motion model in the model set, denotes the dimension of the state vector, denotes the dimension of the measurement, denotes the transfer factor, and denote the predicted values of the shape parameters of the conjugate parameter distribution gamma distribution, and denote the predicted values of the scale parameters of the conjugate parameter distribution gamma distribution, and denote the predicted values of the degrees of freedom in the conjugate parameter distribution inverse Wishart distribution, and denote the predicted values of the inverse precision matrices in the conjugate parameter distribution inverse Wishart distribution.

[0030] In one embodiment of the present invention, step 3b) includes:

[0031] Construct the true posterior probability density function and represent it as an approximate PDF in the form of a free factor;

[0032] Minimize the KL divergence between the approximate posterior probability density function and the true posterior probability density function, thereby obtaining the optimal approximate posterior probability density function to update the state estimate and precision matrix of each motion model.

[0033] In one embodiment of the present invention, an approximate PDF in the form of a free factor of the approximation of the true posterior density function is:

[0034]

[0035] wherein, represents the true posterior density function of the th motion model in the model set at time under the condition of obtaining the measurement ; represents the state variable of the th motion model in the model set at time ; represents the probability density function of the auxiliary random variable ; represents the probability density function of the auxiliary random variable ; represents the probability density function of the precision matrix of the th motion model in the model set at time ; represents the probability density function of the measurement matrix of the th motion model in the model set at time ; represents the probability density function of the degree of freedom in the one-step prediction probability density function of the th motion model in the model set at time ; represents the probability density function of the degree of freedom in the one-step prediction probability density function of the

[0036] In one embodiment of the present invention, the optimal approximate posterior probability density function is expressed as:

[0037]

[0038] wherein, represents the value of the variable when the KL divergence reaches the minimum.

[0039] In one embodiment of the present invention, step 4 includes:

[0040] 4a) Calculate the likelihood function of each model in the model, and the calculation formula is as follows:

[0041]

[0042] Among them, represents the likelihood function of the th motion model in the moment model set, represents the evidence lower bound of the marginal log-likelihood, represents the approximate joint posterior probability density function;

[0043] 4b) Update the probabilities of each model in the model set based on the likelihood function obtained in step 4a), and the calculation formula is:

[0044]

[0045] Among them, represents the probability of the th motion model in the moment model set, represents the predicted probability of the th motion model in the model set.

[0046] In an embodiment of the present invention, step 5 includes:

[0047] Calculate the state estimate value of the maneuvering target at the current moment by using the state weighted summation formula; the state weighted summation formula is:

[0048]

[0049] Among them, represents the state estimate value of the maneuvering target at the

[0050] Calculate the precision matrix of the maneuvering target at the current moment by using the precision matrix weighted summation formula; the precision matrix weighted summation formula is:

[0051]

[0052] Among them, represents the precision matrix of the maneuvering target at the represents the precision matrix at the moment based on the motion model

[0053] Advantages of the present invention:

[0054] 1. The present invention introduces an interactive multi-model algorithm. First, a set of multiple motion models is selected, and then the state estimation values of the multiple motion models are weighted and summed using the probabilities of the respective motion models to obtain the final state estimation value of the maneuvering target. This method can achieve accurate tracking of the maneuvering target through the interaction of multiple models under the condition that the motion state of the maneuvering target is uncertain and changes in real time.

[0055] 2. The present invention models the process noise and measurement noise as Student's t-distribution, and uses the variational Bayesian method to learn the parameters of the Student's t-distribution to make the approximate posterior probability density closer to the true posterior probability density, so that the noise represented by the Student's t-distribution is less different from the real noise during tracking. In this way, the problem that factors such as sudden maneuvers of the target and instantaneous failures of the detector can cause the process noise and measurement noise to have heavy-tailed characteristics is overcome, enabling the present invention to track maneuvering targets under time-varying non-Gaussian noise conditions.

[0056] The following will further elaborate on the present invention in conjunction with the accompanying drawings and embodiments. Description of the Drawings

[0057] Figure 1 is a schematic flowchart of a method for adaptively tracking maneuvering targets under non-Gaussian noise conditions based on IMM-VB provided by an embodiment of the present invention;

[0058] Figure 2 is a graph of the true trajectories of an airborne radar and a maneuvering target in a simulation scenario;

[0059] Figure 3 is a comparison graph of the measurement trajectories and the tracking trajectory curves of an airborne radar tracking two maneuvering targets under non-Gaussian noise conditions;

[0060] Figure 4 is a curve graph of the distance error varying with the distance between the airborne radar and maneuvering target 1 during the tracking of maneuvering target 1;

[0061] Figure 5 is a curve graph of the azimuth angle error varying with the distance between the airborne radar and maneuvering target 1 during the tracking of maneuvering target 1;

[0062] Figure 6 is a curve graph of the pitch angle error varying with the distance between the airborne radar and maneuvering target 1 during the tracking of maneuvering target 1;

[0063] Figure 7 is a curve graph of the distance error varying with the distance between the airborne radar and maneuvering target 2 during the tracking of maneuvering target 2;

[0064] Figure 8It is a curve graph of the change in the distance between the azimuth error random carrier radar and the maneuvering target 2 during the tracking process of the maneuvering target 2;

[0065] Figure 9 It is a curve graph of the change in the distance between the pitch angle error random carrier radar and the maneuvering target 2 during the tracking process of the maneuvering target 2. Specific implementation manners

[0066] The following further describes the present invention in detail with reference to specific embodiments, but the implementation manners of the present invention are not limited thereto.

[0067] Embodiment 1

[0068] Please refer to Figure 1 , Figure 1 which is a schematic flowchart of an adaptive tracking method for maneuvering targets under non-Gaussian noise conditions based on IMM-VB provided by an embodiment of the present invention, and includes:

[0069] Step 1: Obtain the measurement values of the maneuvering target.

[0070] In this embodiment, the measurement values mainly include the distance between each highly maneuvering target and the airborne radar, the azimuth angle and the pitch angle of each highly maneuvering target relative to the airborne radar.

[0071] Specifically, in this embodiment, the measurement values of each highly maneuvering target can be detected once every 50 milliseconds from the echo signals received by the airborne radar, so as to perform real-time target state estimation according to the measurement values at the current moment.

[0072] Step 2: Construct a model set including multiple motion models, and perform interactive mixing on the state estimation value, precision matrix, and conjugate prior distribution parameters of the maneuvering target, respectively, to correspondingly obtain the mixed state input value, mixed precision matrix, and mixed parameters of the conjugate prior distribution of each motion model.

[0073] First, in this embodiment, multiple appropriate motion models can be selected from existing motion models to form a model set by analyzing the motion characteristics of the maneuvering target.

[0074] Then, perform interactive mixing on the state estimation value, precision matrix, and conjugate prior distribution parameters of each maneuvering target, specifically as follows:

[0075] Use the state mixing formula to calculate the mixed state input value of each motion model in the model set, and the calculation formula is:

[0076]

[0077] Among them, represents at time The mixed state input value of a motion model, represents the total number of motion model types in the model set, represents the summation operation, represents At time, the state estimate value of the th motion model in the model set, represents At time, the th motion model in the model set transitions to the th motion model. The probability is

[0078] Use the precision matrix mixing formula to calculate the mixed precision matrix of each motion model in the model set. The calculation formula is:

[0079]

[0080] where, represents At time, the mixed precision matrix input by the rd motion model in the model set, represents At time, the precision matrix of the th motion model in the model set, represents the transpose operation.

[0081] Use the parameter mixing formula to calculate the mixing parameters of the conjugate prior distribution based on each motion model in the model set. The calculation formula is:

[0082]

[0083] where, and represent the mixing shape parameters of the conjugate parameter distribution gamma distribution of the motion model , and represent the mixing scale parameters of the conjugate parameter distribution gamma distribution of the motion model , and represent the mixing degrees of freedom in the conjugate parameter distribution inverse Wishart distribution of the motion model , and represent the mixing inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution of the motion model , and represent the th motion model's At time, the shape parameter of the conjugate parameter distribution gamma distribution, and represent the motion model of the scale parameter of the moment conjugate parameter distribution gamma distribution, and represents the motion model of the degrees of freedom in the moment conjugate parameter distribution inverse Wishart distribution, and represents the motion model of the inverse precision matrix in the moment conjugate parameter distribution inverse Wishart distribution.

[0084] Step 3: Based on the measurement values, use the variational Bayesian algorithm to filter the mixed state input values, mixed precision matrices, and mixed parameters of the conjugate prior distribution for each motion model to update the state estimation values and precision matrices of each motion model.

[0085] 3a) Calculate the predicted values of the states, precision matrices, and conjugate prior distribution parameters of each motion model in the model set and the joint predicted posterior probability density function. The calculation formula is:

[0086]

[0087] where, represents the predicted value of the state of the th motion model in the model set at time represents the state transition matrix of the th motion model in the model set, represents the transpose, represents the predicted value of the precision matrix of the th motion model in the model set at time represents the process noise matrix based on the th motion model in the model set, represents the dimension of the state vector, represents the dimension of the measurement, represents the transfer factor, and represents the predicted value of the shape parameter of the conjugate parameter distribution gamma distribution, and represents the predicted value of the scale parameter of the conjugate parameter distribution gamma distribution, and represents the predicted value of the degrees of freedom in the conjugate parameter distribution inverse Wishart distribution, and represents the predicted value of the inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution.

[0088] 3b) Use the variational Bayesian method to learn the parameters of the conjugate prior distribution, minimizing the KL divergence between the approximate posterior probability density function and the true posterior probability density function to update the state estimate and precision matrix of each motion model.

[0089] First, construct the true posterior probability density function, which is expressed as

[0090]

[0091] where represents the equivalence symbol, represents all the measurements up to time, represents the auxiliary random variable introduced when writing the one-step state prediction probability density function of the -th motion model in the model set at time as an infinite mixture of Gaussian probability density functions, represents the degrees of freedom parameter in the one-step state prediction probability density function of the -th motion model in the model set at represents the predicted measurement, represents the auxiliary random variable introduced when writing the likelihood function of the -th motion model in the model set at time as an infinite mixture of Gaussian probability density functions, represents the degrees of freedom parameter in the likelihood function of the -th motion model in the model set at and represent the predicted value of the degrees of freedom in the inverse Wishart distribution of the conjugate parameter distribution, and represent the predicted inverse precision matrix in the inverse Wishart distribution of the conjugate parameter distribution, and represent the predicted shape parameter of the gamma distribution of the conjugate parameter distribution, and represent the predicted scale parameter of the gamma distribution of the conjugate parameter distribution, represents the Gaussian distribution, represents the gamma distribution, represents the inverse Wishart distribution.

[0092] Since it has no closed analytical solution, it is written as an approximate PDF (Probability Density Function) in the form of an approximate free factor:

[0093]

[0094] wherein, represents the true posterior density function of the th motion model in the model set at the time of obtaining the measurement ; represents the probability density function of the state variable of the th motion model in the model set at the time of ; represents the probability density function of the auxiliary random variable ; represents the probability density function of the auxiliary random variable ; represents the probability density function of the precision matrix of the th motion model in the model set at the time of ; represents the probability density function of the measurement matrix of the th motion model in the model set at the time of ; represents the probability density function of the degree of freedom in the one-step prediction probability density function of the

[0095] th

[0096]

[0097] motion model in the model set at the time of

[0098] Minimize the KL divergence between the approximate posterior probability density function and the true posterior probability density function, so as to obtain the optimal approximate posterior probability density function to update the state estimate value and the precision matrix of each motion model. Among them, the optimal approximate posterior probability density function is expressed as:

[0099]

[0100] Solve the optimal approximate posterior probability density function, and substitute the optimal solution into the formula in step 3a) to calculate the state estimate value and the precision matrix of each motion model. and and , , , , Substitute them into the above formula respectively, and the approximate posterior PDF of each variable can be obtained.

[0101] Step 4: Update the probability corresponding to each motion model in the model set.

[0102] 4a) Calculate the likelihood function of each model in the model, and the calculation formula is as follows:

[0103]

[0104] where denotes the likelihood function of the th motion model in the model set at time denotes the evidence lower bound of the marginal log-likelihood, denotes the approximate joint posterior probability density function.

[0105] , denotes taking the logarithm, denotes the prior probability density function of the measurement corresponding to the th motion model in the model set at time denotes the measurement obtained at time denotes the measurements obtained from 1 to time.

[0106] 4b) Update the probability of each model in the model set based on the likelihood function obtained in step 4a), and the calculation formula is:

[0107]

[0108] where denotes the probability of the th motion model in the model set at time denotes the prediction probability of the th motion model in the model set.

[0109] Step 5: Update the state estimate value and precision matrix of the maneuvering target at the current moment based on the probability corresponding to each motion model, the state estimate value of each motion model, and the precision matrix.

[0110] Calculate the state estimate value of the maneuvering target at the current moment using the state weighted summation formula; the state weighted summation formula is:

[0111]

[0112] Among them, represents the state estimation value of the maneuvering target at time

[0113] The precision matrix of the maneuvering target at the current time is calculated using the weighted summation formula of the precision matrix; the weighted summation formula of the precision matrix is:

[0114]

[0115] Among them, represents the precision matrix of the maneuvering target at time represents the precision matrix at time based on the motion model

[0116] The present invention introduces an interactive multiple model algorithm. First, a set of multiple motion models is selected, and then the state estimation values of the multiple motion models are weighted and summed using the probabilities of each motion model to obtain the final state estimation value of the maneuvering target; this method can achieve precise tracking of the maneuvering target through the interaction of multiple models when the motion state of the maneuvering target is uncertain and changes in real time.

[0117] In addition, the present invention models the process noise and measurement noise as a Student's t-distribution, and uses the variational Bayesian method to learn the parameters of the Student's t-distribution to make the approximate posterior probability density closer to the true posterior probability density, so that the noise represented by the Student's t-distribution is closer to the real noise during tracking, thus overcoming the problem that factors such as sudden maneuvers of the target and instantaneous failures of the detector will cause the process noise and measurement noise to have heavy-tailed characteristics, enabling the present invention to track maneuvering targets under time-varying non-Gaussian noise conditions.

[0118] Embodiment 2

[0119] Next, in combination with simulation experiments, the beneficial effects of the present invention will be further described.

[0120] 1. Conditions of the simulation experiment.

[0121] In this embodiment, the simulation is completed using MATLAB R2019a software on a computer with an Intel(R) Core(TM) i7-9700K CPU 3.60 GHz processor.

[0122] Simulation scenario setup: The carrier aircraft where the radar is located moves in a uniform straight line. Two highly maneuverable targets attack the carrier aircraft based on the proportional navigation law, with a speed of about Mach 4. Taking the flight direction of the carrier aircraft as the reference, maneuvering target 1 appears at a right-side azimuth angle of 30°, elevation angle of 20°, and a distance of 15 km. Maneuvering target 2 appears at a left-side azimuth angle of 30°, elevation angle of 20°, and a distance of 14.5 km, and conducts guidance attacks on the carrier aircraft.

[0123] 2. Simulation content and result analysis.

[0124] The simulation experiment of the present invention is to use the method of the present invention to track the above two highly maneuverable targets guided by the proportional navigation law, and the results are as Figures 2 - 9 shown.

[0125] The motion trajectories of the two maneuvering targets in the present invention are to conduct guidance attacks on the carrier aircraft where the airborne radar is located based on the prior art of the proportional navigation law.

[0126] Figure 2 is the real trajectory diagram of the airborne radar and the maneuvering targets in the simulation scenario. Among them, the curve marked with a plus sign represents the motion trajectory curve of the carrier aircraft where the radar is located, and the curve marked with a solid line represents the trajectory curves of the two maneuvering targets being tracked.

[0127] Figure 3 is a comparison diagram of the measurement trajectory and the tracking trajectory curve of the airborne radar tracking two maneuvering targets under non-Gaussian noise conditions. The tracking trajectory curve is obtained by calculating the state estimation values of the two maneuvering targets every 50 ms using the method of the present invention, and plotting all the state estimation values of the two maneuvering targets after 134 calculations. The abscissa represents the corresponding value of the position coordinates of the two maneuvering targets moving along the x-axis in three-dimensional space, the ordinate represents the corresponding value of the position coordinates of the maneuvering target moving along the y-axis in three-dimensional space, and the vertical coordinate represents the corresponding value of the position coordinates of the maneuvering target moving along the z-axis in three-dimensional space, with the unit being meters (m). Figure 3 In, the curve marked with a dashed line represents the measurement trajectory curve of the two highly maneuverable targets, the curve marked with a solid line represents the trajectory curves of the two highly maneuverable targets being tracked, and the curve marked with a plus sign represents the motion trajectory curve of the carrier aircraft where the radar is located.

[0128] Figure 4 is a curve graph of the distance error changing with the distance between the random carrier radar and maneuvering target 1 during the tracking process of maneuvering target 1. It is mainly obtained by comparing the trajectory curve of maneuvering target 1 tracked by the method of the present invention with the real trajectory curve. Figure 4 In, the abscissa represents the distance between the airborne radar and maneuvering target 1, with the unit being kilometers, and the ordinate represents the distance error of maneuvering target 1, with the unit being meters. Figure 4Among them, the curve marked by dotted lines represents the measurement error curve of the distance of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the distance measurement value of the maneuvering target 1 at each moment and the true value of the azimuth angle. The curve marked by solid lines represents the tracking error curve of the distance of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the distance estimated value of the maneuvering target 1 at each moment and the true distance value.

[0129] Figure 5 It is a curve graph of the change in the azimuth angle error during the tracking process of the maneuvering target 1 with respect to the distance between the random carrier radar and the maneuvering target 1. Figure 5 It is obtained by comparing the trajectory curve of the tracking of the maneuvering target 1 obtained by the method of the present invention with the true trajectory curve. Figure 5 The abscissa in it represents the distance between the airborne radar and the maneuvering target 1, with the unit of kilometer, and the ordinate represents the azimuth angle error of the maneuvering target 1, with the unit of degree. Figure 5 Among them, the curve marked by dotted lines represents the measurement error curve of the azimuth angle of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the azimuth angle measurement value of the maneuvering target 1 at each moment and the true value of the azimuth angle. The curve marked by solid lines represents the tracking error curve of the azimuth angle of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the azimuth angle estimated value of the maneuvering target 1 at each moment and the true value of the azimuth angle.

[0130] Figure 6 It is a curve graph of the change in the pitch angle error during the tracking process of the maneuvering target 1 with respect to the distance between the random carrier radar and the maneuvering target 1. It is obtained by comparing the trajectory curve of the tracking of the maneuvering target 1 obtained by the method of the present invention with the true trajectory curve. Figure 6 The abscissa in it represents the distance between the airborne radar and the maneuvering target 1, with the unit of kilometer, and the ordinate represents the pitch angle error of the maneuvering target 1, with the unit of degree. Figure 6 Among them, the curve marked by dotted lines represents the measurement error curve of the pitch angle of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the pitch angle measurement value of the maneuvering target 1 at each moment and the true value of the pitch angle. The curve marked by solid lines represents the tracking error curve of the pitch angle of the maneuvering target 1. This curve is obtained by taking the absolute value of the difference between the pitch angle estimated value of the maneuvering target 1 at each moment and the true value of the pitch angle.

[0131] Figure 7 It is a curve graph of the change in the distance error during the tracking process of the maneuvering target 2 with respect to the distance between the random carrier radar and the maneuvering target 2. It is obtained by comparing the trajectory curve of the tracking of the maneuvering target 2 obtained by the method of the present invention with the true trajectory curve. Figure 7 The abscissa in it represents the distance between the airborne radar and the maneuvering target 2, with the unit of kilometer, and the ordinate represents the distance error of the maneuvering target 2, with the unit of meter.Figure 7 The curve marked with dotted lines represents the measurement error curve of the distance of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the distance measurement value of the maneuvering target 2 at each moment and the true value of the azimuth angle. The curve marked with solid lines represents the tracking error curve of the distance of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the distance estimated value of the maneuvering target 2 at each moment and the true value of the distance.

[0132] Figure 8 It is a curve graph of the change in the azimuth angle error during the tracking of the maneuvering target 2 with respect to the distance between the random carrier radar and the maneuvering target 2. It is obtained by comparing the trajectory curve of the tracking of the maneuvering target 2 obtained by the method of the present invention with the true trajectory curve. Figure 8 The abscissa in it represents the distance between the airborne radar and the maneuvering target 2, with the unit of kilometer, and the ordinate represents the azimuth angle error of the maneuvering target 2, with the unit of degree. Figure 8 The curve marked with dotted lines represents the measurement error curve of the azimuth angle of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the azimuth angle measurement value of the maneuvering target 2 at each moment and the true value of the azimuth angle. The curve marked with solid lines represents the tracking error curve of the azimuth angle of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the azimuth angle estimated value of the maneuvering target 2 at each moment and the true value of the azimuth angle.

[0133] Figure 9 It is a curve graph of the change in the pitch angle error during the tracking of the maneuvering target 2 with respect to the distance between the random carrier radar and the maneuvering target 2. It is obtained by comparing the trajectory curve of the tracking of the maneuvering target 2 obtained by the method of the present invention with the true trajectory curve. Figure 9 The abscissa in it represents the distance between the airborne radar and the maneuvering target 2, with the unit of kilometer, and the ordinate represents the pitch angle error of the maneuvering target 2, with the unit of degree. Figure 9 The curve marked with dotted lines represents the measurement error curve of the pitch angle of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the pitch angle measurement value of the maneuvering target 2 at each moment and the true value of the pitch angle. The curve marked with solid lines represents the tracking error curve of the pitch angle of the maneuvering target 2. This curve is obtained by taking the absolute value of the difference between the pitch angle estimated value of the maneuvering target 2 at each moment and the true value of the pitch angle.

[0134] From Figure 2 and Figure 3 it can be seen that the trajectory curves of the two maneuvering targets obtained by the method of the present invention under non-Gaussian noise conditions almost coincide with the true trajectory curves, indicating that the trajectory curves of the two maneuvering targets tracked by the method of the present invention have high accuracy.

[0135] From Figures 4 - 9It can be seen that during the process of tracking two maneuvering targets under non-Gaussian noise conditions, the measurement errors and tracking errors of the distance, azimuth angle, and elevation angle gradually decrease as the distance between the maneuvering targets and the airborne radar approaches, and the tracking errors of the distance, azimuth angle, and elevation angle are always smaller than the measurement errors, indicating that the method of the present invention can track maneuvering targets under non-Gaussian noise conditions simultaneously.

[0136] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the protection scope of the present invention.

Claims

1. An adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB, characterized in that, Including: Step 1: Obtain the measurement values of the maneuvering target; Step 2: Construct a model set including multiple motion models, and perform interactive mixing on the state estimate value, precision matrix, and conjugate prior distribution parameters of the maneuvering target respectively, and correspondingly obtain the mixed state input value, mixed precision matrix, and mixed parameters of the conjugate prior distribution for each motion model; Step 3: Based on the measurement values, use the variational Bayesian algorithm to perform filtering processing on the mixed state input value, mixed precision matrix, and mixed parameters of the conjugate prior distribution for each motion model to update the state estimate value and precision matrix of each motion model; Step 4: Update the probability corresponding to each motion model in the model set; Step 5: Update the state estimate value and precision matrix of the maneuvering target at the current moment based on the probability corresponding to each motion model and the state estimate value and precision matrix of each motion model.

2. The adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB according to claim 1, characterized in that, In step 2, performing interactive mixing on the state estimate value, precision matrix, and conjugate prior distribution parameters of the maneuvering target respectively includes: Calculating the mixed state input value of each motion model in the model set using the state mixing formula; the state mixing formula is: Among them, represents the mixed state input value of the j-th motion model in the model set at time k-1, n represents the total number of motion model types in the model set, and ∑ represents the summation operation. represents the state estimation value of the i-th motion model in the model set at time k-1. represents the probability that the i-th motion model in the model set at time k-1 transitions to the j-th motion model. Calculating the mixed precision matrix of each motion model in the model set using the precision matrix mixing formula; the precision matrix mixing formula is: Among them, represents the mixed-precision matrix of the input of the j-th motion model in the model set at time k-1, represents the precision matrix of the i-th motion model in the model set at time k-1, and T represents the transpose operation; Calculating the mixed parameters of the conjugate prior distribution based on each motion model in the model set using the parameter mixing formula, and the calculation formula is: Among them, and represent the mixing shape parameters of the conjugate parameter distribution gamma distribution of the motion model j, and represent the mixing scale parameters of the conjugate parameter distribution gamma distribution of the motion model j, and represent the mixing degrees of freedom in the conjugate parameter distribution inverse Wishart distribution of the motion model j, and represent the mixing inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution of the motion model j, and represent the shape parameters of the conjugate parameter distribution gamma distribution at the k-1 moment of the motion model i, and represent the scale parameters of the conjugate parameter distribution gamma distribution at the k-1 moment of the motion model i, and represent the degrees of freedom in the conjugate parameter distribution inverse Wishart distribution at the k-1 moment of the motion model i, and represent the inverse precision matrix in the conjugate parameter distribution inverse Wishart distribution at the k-1 moment of the motion model i.

3. The adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB according to claim 2, characterized in that, Step 3 includes: 3a) Calculating the predicted values and joint predicted posterior probability density functions of the state, precision matrix, and conjugate prior distribution parameters of each motion model in the model set; 3b) Using the variational Bayesian method to learn the conjugate prior distribution parameters to minimize the KL divergence between the approximate posterior probability density function and the true posterior probability density function to update the state estimate value and precision matrix of each motion model.

4. The adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB according to claim 3, characterized in that, The calculation formula in step 3a) is: Among them, represents the state prediction value of the j-th motion model in the model set at time k, F j represents the state transition matrix of the j-th motion model in the model set, T represents the transpose, represents the precision matrix prediction value of the j-th motion model in the model set at time k, Q j represents the process noise matrix based on the j-th motion model in the model set, n x represents the dimension of the state vector, n z represents the dimension of the measurement, ρ represents the transfer factor, and represent the predicted shape parameter values of the conjugate parameter distribution gamma distribution, and represent the predicted scale parameter values of the conjugate parameter distribution gamma distribution, and represent the predicted degrees of freedom values in the conjugate parameter distribution inverse Wishart distribution, and represent the predicted inverse precision matrix values in the conjugate parameter distribution inverse Wishart distribution.

5. The adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB according to claim 4, characterized in that, Step 3b) includes: Constructing the true posterior probability density function and expressing it as an approximate PDF in the form of an approximate free factor; the approximate PDF in the form of an approximate free factor of the true posterior probability density function is: where, p(Θ k |Z 1:k ,M k = j) represents the true posterior density function of the j-th motion model in the model set at time k under the condition of obtaining the measurement Z 1:k , represents the state variable of the j-th motion model in the model set at time k 's probability density function, represents the probability density function of the auxiliary random variable , represents the probability density function of the auxiliary random variable , represents the precision matrix of the j-th motion model in the model set at time k 's probability density function, represents the measurement matrix of the j-th motion model in the model set at time k 's probability density function, represents the degree of freedom in the one-step prediction probability density function of the j-th motion model in the model set at time k 's probability density function, represents the degree of freedom in the one-step prediction probability density function of the j-th motion model in the model set at time k 's probability density function; Minimizing the KL divergence between the approximate posterior probability density function and the true posterior probability density function to obtain the optimal approximate posterior probability density function to update the state estimate value and precision matrix of each motion model.

6. The adaptive tracking method for maneuvering targets under non-Gaussian noise based on IMM-VB according to claim 5, characterized in that, The optimal approximate posterior probability density function is expressed as: where argminKL(·||·) represents the value of the variable when the KL divergence reaches the minimum.

7. The maneuvering target adaptive tracking method based on IMM-VB under non-Gaussian noise conditions according to claim 6, wherein, Step 4 includes: 4a) Calculating the likelihood function of each model in the model, and the calculation formula is as follows: Among them, represents the likelihood function of the j-th motion model in the model set at time k, L(Q) represents the evidence lower bound of the marginal log-likelihood, and Q represents the approximate joint posterior probability density function; 4b) Updating the probability of each model in the model set based on the likelihood function obtained in step 4a), and the calculation formula is: Among them, represents the probability of the j-th motion model in the model set at time k, represents the predicted probability of the j-th motion model in the model set.

8. The maneuvering target adaptive tracking method based on IMM-VB under non-Gaussian noise conditions according to claim 7, wherein, Step 5 includes: Calculating the state estimate value of the maneuvering target at the current moment using the state weighted summation formula; the state weighted summation formula is: Among them, represents the state estimation value of the maneuvering target at time k; Calculating the precision matrix of the maneuvering target at the current moment using the precision matrix weighted summation formula; the precision matrix weighted summation formula is: Among them, Σ k represents the accuracy matrix of the maneuvering target at time k, represents the accuracy matrix based on motion model j at time k.

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