Air maneuvering multi-target three-dimensional tracking method based on volume-mean-square Kalman filtering

Abstract

The invention provides an air maneuvering multi-target three-dimensional tracking method based on volume mean square Kalman filtering, and relates to the technical field of radar signal processing, and the method comprises the following steps: building an air maneuvering multi-target three-dimensional cooperative turning motion model and a three-coordinate radar measurement model; performing prediction filtering on a Gaussian item in the multi-target probability hypothesis density function through a volume mean square Kalman filter; updating a mean value and a covariance matrix of Gaussian items through a volume-mean-square Kalman filter based on the measurement position and Doppler information, and obtaining a multi-target track Gaussian component estimation set; performing pruning and merging operation on the Gaussian component to reduce the complexity of the system; and performing multi-target number estimation and state extraction according to the pruned and merged Gaussian components. According to the method disclosed by the invention, the high-precision advantage of the volume mean square Kalman filter and the multi-target tracking capability of the probability hypothesis density filter are utilized, so that the air maneuvering multi-target tracking and multi-target number estimation performance superior to that of a traditional method is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and in particular to a mean square volume Kalman filter three-dimensional tracking method for aerial maneuverable multi-targets. Background Art

[0002] With the gradual development of radar technology, three-dimensional tracking technology of maneuvering targets has been widely used in various civil and military fields, such as intelligent transportation systems, aerial reconnaissance and early warning, battlefield target monitoring, etc.

[0003] Compared to traditional single-target tracking, multi-target tracking often faces more daunting challenges, such as false alarms, clutter interference, and an unknown and time-varying number of targets. Furthermore, existing multi-target tracking technologies struggle to address the large model errors and high nonlinearity of aerial maneuvering target tracking systems, resulting in poor multi-target tracking accuracy and target number estimation.

[0004] Therefore, a high-precision and efficient three-dimensional tracking algorithm for aerial maneuvering multi-targets is urgently needed. Summary of the Invention

[0005] In order to solve the technical problems in the related art, the present invention provides a mean square volume Kalman filter aerial maneuvering multi-target three-dimensional tracking method.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: A three-dimensional tracking method for aerial maneuvering multiple targets using mean square volumetric Kalman filtering includes the following steps: Step S1: Establish a three-dimensional coordinated turning motion model of multiple aerial maneuvering targets and a three-coordinate radar measurement model including range, azimuth, pitch, and Doppler information; Step S2: Predictive filtering is performed on the Gaussian terms in the multi-target probability hypothesis density function by using a mean square cubature Kalman filter; Step S3: Based on the measured position and Doppler information, the mean and covariance matrix of the Gaussian term are updated through the mean square cubature Kalman filter to obtain a set of Gaussian component estimates of the multi-target track; Step S4: performing pruning and merging operations on the Gaussian components to reduce system complexity; Step S5: perform multi-target number estimation and state extraction based on the pruned and merged Gaussian components.

[0007] Optionally, in step S1, the motion model adopts a cooperative turning model, and the state equation of the cooperative turning model is: Where, For the goal The state variables at time ,in, 、 and Respectively represent the target coordinate position in the Cartesian coordinate system, 、 and Respectively 、 and Speed ​​in direction, When turning to the target, it is perpendicular to The angular velocity of the axis, is the state transition matrix, For the goal The state variables at time , is the process distribution matrix, is the process noise vector.

[0008] Optionally, in step S1, the target The nonlinear measurement equation of time is: , where Indicates the target is The measured variable at time, and ,in, Indicates The radial distance from the target to the radar at any moment, Indicates The azimuth angle of the target relative to the radar at any moment, Indicates The target's pitch angle relative to the radar at any moment, Indicates The time is measured by the radial Doppler between the radar and the maneuvering target, Indicates Random measurement error at time, represents a nonlinear measurement relationship, and, exist A random finite set of moments, measurements for: Where, represents the finite state set of the target at time k, Indicates the radar's target status A random finite set after observation, is a random finite set of clutter.

[0009] Optionally, in step S2, the predictive filtering includes: initialization , is the volume point set, is the number of volume points, , Representation matrix No. Column, matrix for: The volume points are propagated through the state transfer equation to calculate the state prediction value and covariance prediction value.

[0010] Optionally, the predictive filtering specifically includes: Step S2-1: Calculate the target motion noise covariance matrix and the measurement noise covariance matrix The Cholesky decomposition of and ; Step S2-2: When When , calculate the Cholesky decomposition of the covariance matrix and get its root mean square matrix and predicted values ,in, and are the initial values ​​of the mean vector and covariance matrix respectively; when Calculate and propagate volume points when : Where, represents the mth volume point of the i-th target at time k-1, represents the mean square covariance matrix of the i-th target at time k-1, represents the mean of the Gaussian component of the i-th target at time k-1, represents the volume point after propagation, represents the state transition matrix; Step S2-3: Calculate the predicted value of the state quantity: Where, represents the state prediction value of the i-th target, Step S2-4: Calculate the covariance matrix prediction value: Where, represents the covariance matrix predicted value, Perform QR decomposition on the matrix in the brackets, represents the weighted centralization matrix and, Step S2-5: Calculate the survival weight: Where, represents the survival weight of the i-th target, represents the Gaussian component weight of the i-th target, is the target survival probability; Probability hypothesis density function of the prediction for: Where, , , express The number of new Gaussian components at each moment, represents the number of surviving Gaussian components, Represents the Gaussian distribution function.

[0011] Optionally, in step S3, updating the mean and covariance matrix of the Gaussian term by using the mean square cubature Kalman filter includes: Based on measurement data and Doppler information, and perform mean square volumetric Kalman updates on the mean and covariance of each Gaussian component.

[0012] Optionally, in step S3, updating the mean and covariance matrix of the Gaussian term by using the mean square cubature Kalman filter specifically includes: Step S3-1: Recalculate volume points: Where, represents the mth volume point of the i-th target in the update phase, represents the Gaussian component mean square covariance matrix of the i-th target, represents the volume point set, represents the state prediction value of the i-th target; Step S3-2: Update the measurement and calculate the measurement prediction value: Where, represents the updated measurement, represents the measured predicted mean, represents a nonlinear measurement relationship, Indicates the number of volume points; Step S3-3: Calculate the square root of the measurement error covariance matrix: Where, represents the square root of the measurement error covariance matrix, Perform QR decomposition on the matrix in the brackets, is the measurement noise covariance matrix The Cholesky decomposition of represents an intermediate variable, and Step S3-4: Calculate the cross-covariance matrix: Where, represents the cross-covariance matrix, represents an intermediate variable, and Where, represents the state prediction value of the i-th target, Step S3-5: Calculate the Kalman gain: Where, represents the Kalman gain, represents the measurement error covariance matrix, and ; Step S3-6: Update the mean vector and mean square covariance matrix: Where, represents the updated mean vector of the i-th target at time k, represents the state prediction value of the i-th target, Indicates the target is The measured variables at the time, represents the updated mean square covariance matrix of the i-th target at time k; Step S3-7: Update weights: Where, represents the weight of the i-th target at the updated k-th moment, represents the target detection probability, represents the survival weight of the i-th target, represents the spatial clutter intensity, and , represents the clutter intensity coefficient, and Represent the clutter average and radar detection range respectively, same , where l represents the traversal from the lth Gaussian component to the Jk|k-1th, Represents the likelihood ratio function of the i-th target measurement and satisfies: Where, represents the Gaussian distribution function, represents the dimension of the vector, represents the determinant of the matrix, represents the natural exponential function, Finally, the probability hypothesis density function of the target update is for: Where, , , express The number of new Gaussian components at each moment, Indicates the number of surviving Gaussian components.

[0013] Optionally, in step S4, the pruning and merging operations specifically include: Step S4-1: Setting the pruning threshold , Merge Threshold and the maximum number of Gaussian components ; Step S4-2: Discard update weights less than the pruning threshold Gaussian component of Step S4-3: From the maximum weight The corresponding Gaussian mean Start searching and calculate the satisfaction , All index collections , and merge its Gaussian terms according to the following rules: Where, represents the weight after pruning and merging of Gaussian components, represents the weight of the i-th target at the updated k-th moment, represents the mean of the Gaussian components after pruning and merging, Represents the covariance matrix after pruning and merging of Gaussian components; Output Gaussian term after pruning and merging of Gaussian components .

[0014] Optionally, in step S5, the target estimated number is specifically: Select weight greater than threshold The number of Gaussian components of is used as the target estimation number .

[0015] Optionally, the state extraction specifically includes: Estimated number based on target , extract the one with the largest weight Gaussian component means as multi-objective state estimation.

[0016] Beneficial effects: 1. Through the above technical solution, the method of the present invention can first achieve high-precision three-dimensional tracking. Specifically, the motion model (step S1) of the present invention and the mean square cubature Kalman filter (steps S2 and S3) work together to process nonlinear maneuvers, effectively reducing position estimation errors and thus achieving high-precision three-dimensional tracking.

[0017] Second, the solution of the present invention can achieve robust multi-target management. Specifically, the present invention can effectively suppress false alarms caused by clutter through Gaussian term propagation combined with pruning and merging (step S4), thereby achieving robust multi-target management.

[0018] Third, the present invention adapts to the original output (range / azimuth / elevation / Doppler) of the three-coordinate radar throughout the entire process without the need for pre-conversion processing, and has good engineering practicality.

[0019] In summary, the method of the present invention can effectively achieve high-precision tracking of maneuvering targets and reliable estimation of the number of multiple targets through the synergistic effect of the above five steps.

[0020] 2. Other beneficial effects or advantages of the present invention will be described in detail in the specific implementation manner. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without paying any creative labor.

[0022] in: Figure 1 1. It is a schematic flow chart of the steps of a method for three-dimensional tracking of multiple targets in aerial maneuvering using a mean square volumetric Kalman filter provided by an exemplary embodiment of the present invention; Figure 2 is a flowchart of a method for three-dimensional tracking of multiple targets in aerial maneuvers provided by an exemplary embodiment of the present invention; Figure 3 is a multi-target tracking simulation parameter table used in an exemplary embodiment of the present invention; Figure 4 is a schematic diagram of original trajectories of multiple targets used in an exemplary embodiment of the present invention; Figure 5 is a multi-target three-dimensional tracking result diagram provided by an exemplary embodiment of the present invention; Figure 6 is a multi-target three-dimensional tracking result diagram provided by an exemplary embodiment of the present invention; Figure 7 It is a schematic diagram of the 3D tracking performance evaluation results of different methods; Figure 8 This is a schematic diagram of the multi-target number estimation results of the traditional method; Figure 9 It is a schematic diagram of a multi-target number estimation result provided by an exemplary embodiment of the present invention. DETAILED DESCRIPTION

[0023] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings 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.

[0024] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but rather merely represents selected embodiments of the present invention. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without creative effort are intended to fall within the scope of protection of the present invention.

[0025] In addition, the terms "including" and "having" and any variations thereof mentioned in the description of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but may optionally include other steps or units that are not listed, or may optionally include other steps or units that are inherent to these processes, methods, products or devices. It should also be noted that in the embodiments of the present invention, words such as "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of the present invention should not be interpreted as being more preferred or more advantageous than other embodiments or design schemes. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a concrete way.

[0026] In order to facilitate relevant technical personnel to have a clearer and more accurate understanding of the technical solution of the present invention, the existing related technologies and the technical problems existing therein are first described in more detail below.

[0027] At present, with the gradual development of radar technology, three-dimensional tracking technology of maneuvering targets has been widely used in various civil and military fields, such as intelligent transportation systems, aerial reconnaissance and early warning, battlefield target monitoring, etc.

[0028] In three-dimensional tracking, multi-target tracking often faces more daunting challenges than traditional single-target tracking, such as false alarms, clutter interference, and an unknown and time-varying number of targets. Furthermore, existing multi-target tracking technologies struggle to address the large model errors and high nonlinearity inherent in aerial maneuvering target tracking systems, resulting in poor multi-target tracking accuracy and target count estimation.

[0029] In recent years, in order to solve the problem of multi-target tracking, methods based on random finite set theory have been greatly developed. For example, the paper "Vo BN, Ma W K. The Gaussian mixture probability hypothesis density filter[J]. IEEE Transactions on signal processing, 2006, 54(11):4091-4104." proposed a Gaussian mixture probability hypothesis density filter. This scheme achieves time-varying joint estimation of the number and state of multiple targets by modeling targets and measurements as random finite sets and recursively propagating the posterior density through the probability hypothesis density. However, this scheme is only applicable to two-dimensional multi-target tracking problems with low linear or nonlinear degree, and cannot be applied to three-dimensional tracking of aerial maneuvering multi-targets.

[0030] For example, the paper "Ren Z, Zhang H, Wu H. Measurement-Aided Cubature WeightCorrection GM-PHD algorithm for Muti-target tracking[C] / / 2020 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC). IEEE, 2020: 1-5" proposes a weight-corrected Gaussian mixture probability hypothesis density multi-target tracking method based on cubature Kalman filtering. This scheme improves tracking filter accuracy through weight correction. However, this scheme suffers from poor convergence, and the filtering results are prone to divergence.

[0031] For example, the paper "Bo Juntian, Zhang Jiahao, Wang Guohong, et al. A 3D Multi-Target Tracking-Before-Detection Algorithm with Dual Accumulation and Self-Feedback Optimization [J]. Journal of Electronics & Information Technology, 2022, 44(YU): 1-8" proposes a dual-accumulation-optimized tracking-before-detection algorithm for weak target detection and tracking. This approach alleviates the problems of strong targets drowning out weak targets and crosstalk between formation targets. However, this approach's measurement model fails to consider the target's Doppler information relative to the radar platform, resulting in limited improvement in tracking accuracy.

[0032] Based on the above analysis, it can be seen that existing related technologies have problems such as low average tracking accuracy and low precision in multi-target estimation. Therefore, how to achieve high-precision and efficient three-dimensional tracking of multiple targets in aerial maneuvers has become an urgent problem to be solved.

[0033] The technical solution of the present invention is described in detail below with reference to the accompanying drawings.

[0034] like Figures 1 to 9 As shown, the present invention provides a mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method, comprising the following steps: Step S1: Establish a three-dimensional coordinated turning motion model of multiple aerial maneuvering targets and a three-coordinate radar measurement model including range, azimuth, pitch, and Doppler information; In this embodiment, the motion model of the present invention utilizes a three-dimensional coordinated turning model, which accurately describes the maneuvering characteristics of aerial targets (e.g., turns and climbs), providing a physically consistent state evolution basis for subsequent nonlinear filtering. Furthermore, the measurement model of the present invention directly utilizes raw observation data through three-coordinate radar multi-parameter measurements (range, azimuth, pitch, and Doppler), effectively avoiding information loss and enhancing the observability of state estimation (particularly utilizing Doppler radial velocity information).

[0035] Step S2: Predictive filtering is performed on the Gaussian terms in the multi-target probability hypothesis density function by using a mean square cubature Kalman filter; In this embodiment, the present invention can effectively avoid the truncation error of traditional linearization (eg, EKF) by performing nonlinear propagation on the Gaussian term, thereby effectively improving the prediction accuracy.

[0036] Step S3: Based on the measured position and Doppler information, the mean and covariance matrix of the Gaussian term are updated through the mean square cubature Kalman filter to obtain a set of Gaussian component estimates of the multi-target track; In this embodiment, the present invention simultaneously utilizes position measurement (range / azimuth / elevation) and Doppler measurement to correct the mean and covariance of the Gaussian term, thereby effectively suppressing clutter interference.

[0037] Step S4: performing pruning and merging operations on the Gaussian components to reduce system complexity; In this embodiment, the present invention can effectively constrain the number of Gaussian components through pruning (eliminating low-weight items) and merging (aggregating similar items), effectively maintain real-time performance and reduce computational complexity.

[0038] Step S5: perform multi-target number estimation and state extraction based on the pruned and merged Gaussian components.

[0039] In this embodiment, the present invention directly estimates the number of targets and extracts the states based on the Gaussian component weights (eg, those with greater weights are prioritized), which can effectively avoid false alarms.

[0040] Through the above technical solution, the method of the present invention can first achieve high-precision three-dimensional tracking. Specifically, the motion model (step S1) of the present invention and the mean square cubature Kalman filter (steps S2 and S3) work together to process nonlinear maneuvers, effectively reducing position estimation errors and thus achieving high-precision three-dimensional tracking.

[0041] Second, the solution of the present invention can achieve robust multi-target management. Specifically, the present invention can effectively suppress false alarms caused by clutter through Gaussian term propagation combined with pruning and merging (step S4), thereby achieving robust multi-target management.

[0042] Third, the present invention adapts to the original output (range / azimuth / elevation / Doppler) of the three-coordinate radar throughout the entire process without the need for pre-conversion processing, and has good engineering practicality.

[0043] In summary, the method of the present invention can effectively achieve high-precision tracking of maneuvering targets and reliable estimation of the number of multiple targets through the synergistic effect of the above five steps.

[0044] This method takes advantage of the high precision of the mean square cubature Kalman filter and the multi-target tracking capability of the probability hypothesis density filter, achieving aerial maneuver multi-target tracking and multi-target number estimation capabilities that are superior to traditional methods.

[0045] The following describes the technical solution of the present invention in detail using an exemplary embodiment as an example and in conjunction with the accompanying drawings. (It should be noted that the present invention is primarily verified using simulation experiments, and all steps and conclusions were verified on Matlab 2024a.) In this exemplary embodiment, the flowchart of the method for three-dimensional tracking of multiple targets in aerial maneuvers of the present invention can be found in Figure 2 , the specific process includes: Step 1: Establish a multi-target motion model Consider five aerial maneuvering targets, and their specific parameters are shown in Table 1 below: Table 1 Target number and motion parameters According to the above motion state, the track settings of multiple targets are as follows: Figure 4 The multi-target tracking simulation parameters are shown in Figure 3 The total tracking time is , sampling interval Considering the three-dimensional maneuvering of aerial targets, the cooperative turning model (CT) is adopted. The state equation of the CT model can be written as: ,in, is the state variable, 、 and Respectively represent the target coordinate position in the Cartesian coordinate system, 、 and Represent the speed in the x, y, and z directions respectively, Indicates the angular velocity of the target when turning (perpendicular to the z-axis). is the state variable of the target at time k-1. is the state transfer matrix, which can be recorded as: is the process noise distribution matrix: in, is the model velocity error variance, is the model turning speed error variance. At this moment, the target may survive or disappear, and new targets may be generated. The random finite set of target states can be expressed as: in, is a random finite set of survival targets, is a random finite set of new targets. Represents a merge set operation.

[0046] Step 2: Establish a multi-target measurement model Consider a three-coordinate radar detecting an aerial target, where the radar is located at the origin of the coordinate system. The nonlinear measurement equation of time can be expressed as: ,in, represents the measured variable, where Indicates the radial distance from the target to the radar, The target's azimuth angle relative to the radar, Indicates the target's pitch angle relative to the radar. Represents the radial Doppler measurement between the radar and the maneuvering target. Represents random measurement error, whose value is similar to the ranging error , angle measurement error , , speed measurement error The specific ranging error is 30m, the azimuth angle measurement error is 1.2° / s, the pitch angle measurement error is 1.2° / s, and the speed measurement error is 1m / s.

[0047] Nonlinear measurement relationship It can be recorded as A random finite set of moments, measurements Random finite set of clutter and a random finite set of targets Composition can be written as: Step 3: Mean Square Volume Kalman Probability Hypothesis Density Filter Prediction set up Probability hypothesis density function of the target at the moment for: ,in, represents the total number of Gaussian mixture components, express Obey the mean , the variance is Gaussian distribution, , , Respectively represent The weights, mean vectors, and mean squared covariance matrices of the Gaussian mixture components.

[0048] Perform mean square cubature Kalman predictive filtering on the above three Gaussian mixture components: (1) Initialization: Calculate the volume point set using the following formula: ,in, is the number of volume points, . Represent the following matrix The mth column Calculate the Cholesky decomposition of the target motion noise covariance matrix Q and the measurement noise covariance matrix R, which are respectively denoted as and .

[0049] (2) When When , calculate the Cholesky decomposition of the covariance matrix and get its root mean square matrix , and the predicted value ,in, and are the initial values ​​of the mean vector and covariance matrix. Calculate and propagate volume points when : Where, represents the mth volume point of the i-th target at time k-1, represents the mean square covariance matrix of the i-th target at time k-1, represents the mean of the Gaussian component of the i-th target at time k-1, represents the volume point after propagation, represents the state transition matrix; (3) Calculate the predicted value of state quantity , where represents the state prediction value of the i-th target; (4) Calculate the covariance matrix prediction value , where represents the covariance matrix predicted value, Perform QR decomposition on the matrix in the brackets, represents the weighted centralization matrix and, (5) Calculate the survival weight , where represents the survival weight of the i-th target, represents the Gaussian component weight of the i-th target, is the target survival probability; therefore, the predicted probability assumes a density function for: , where , , express The number of new Gaussian components at each moment, represents the number of surviving Gaussian components, Represents the Gaussian distribution function.

[0050] Step 4: Mean Square Volume Kalman Probability Hypothesis Density Filter Update Based on the prediction results of step 3 and Measurement data at all times , for The mean of the Gaussian components and mean square covariance Performing the square volume Kalman-probability hypothesis density filter update: (1) Recompute the volume points: (2) Update the measurement and calculate the measurement prediction value: (3) Calculate the square root of the measurement error covariance matrix: where, (4) Calculate the mutual covariance matrix: where, (5) Calculate the Kalman gain where, .

[0051] (6) Update the mean vector and the square covariance matrix (7) Update the weight where, denotes the target detection probability, denotes the spatial clutter intensity, denotes the clutter intensity coefficient, and denotes the clutter mean and radar detection range. is the target measurement likelihood ratio function, which satisfies: where, denotes the dimension of the vector, denotes the determinant of the matrix.

[0052] Finally, the probability hypothesis density function of the target update can be written as where, .

[0053] Step five: Gaussian component pruning and merging Since the number of Gaussian components will gradually increase with the detection process, it is necessary to perform secondary component pruning and similar component merging operations to reduce the total number of Gaussian classifications. , Merge Threshold and the maximum number of Gaussian components .

[0054] (1) Gaussian component pruning: If the updated weight of the Gaussian component is less than the pruning threshold , then the Gaussian component is discarded, otherwise it is retained.

[0055] (2) Gaussian component merging: from the maximum weight The corresponding Gaussian mean Start searching and calculate the satisfaction , All index collections , merge their Gaussian terms according to the following rules Finally, the Gaussian term after pruning and merging the Gaussian components is output .

[0056] Step 6: Target number estimation and state extraction (1) Target number estimation: select the weight greater than the threshold The number of Gaussian components of is used as the target estimation number .

[0057] (2) Multi-target state extraction: based on the estimated number of targets , extract the one with the largest weight Gaussian component means as multi-objective state estimation.

[0058] Based on the filtering process from step 3 to step 6, traverse At this moment, the three-dimensional tracking results of multiple target tracks are finally obtained.

[0059] The results of multi-target three-dimensional tracking using traditional methods are as follows: Figure 5 As shown in the figure, the black solid line represents the true trajectory, the black dots represent the estimated trajectory, and the gray cross represents all radar measurement data (including target measurement and clutter measurement). Figure 5 In the traditional method, the target trajectory tracking accuracy is low, and the estimated trajectory points have a large deviation from the actual trajectory. In addition, it can be seen that there are many false target tracking points in the tracking scene. This is because the traditional probability hypothesis density multi-target tracking method based on the extended Kalman filter cannot be effectively applied to tracking scenes with high nonlinearity and large model errors. The three-dimensional tracking trajectory results of the method proposed in this invention are shown in Figure 2. Figure 6It can be seen that the tracking accuracy of the method proposed in the application is significantly improved, and there are almost no false target tracking points.

[0060] In the application, the most widely used optimal mode assignment (OSPA) evaluation index in multi-target tracking is used to measure the performance of different methods. In the simulation of the application, 200 Monte Carlo test times are used, and the obtained performance indexes are averaged. Figure 7 The quantitative comparison of the tracking performance of the traditional method and the proposed method is given. It can be seen that the OSPA distance and OSPA base of the proposed method are significantly improved compared with the traditional method, with an average improvement of about 39.3% and 78.8%, respectively. Figure 8 and 9 The target number estimation results of the traditional method and the proposed method are given, respectively. The solid line represents the true value, and the dot represents the average target estimation number of the corresponding method. Obviously, with the change of time, due to the false targets, the target number estimation of the traditional method is far more than the true value. On the contrary, the target number estimation accuracy of the proposed method basically keeps consistent with the true value, and the accurate estimation of the number of multi-targets can be realized.

[0061] The core innovation point of the application is to use the estimation accuracy advantage of the mean square volume Kalman filter for nonlinear systems, and combine the multi-target prediction updating ability of the probability hypothesis density filter, to realize the air mobile multi-target number estimation and high-precision three-dimensional tracking better than the traditional method.

[0062] In summary, it can be seen that the method of the application for the three-dimensional tracking problem of air mobile targets, under the condition of large model error and high nonlinear system, realizes the multi-target tracking accuracy and target number estimation accuracy better than the traditional tracking method.

[0063] The above is only a specific embodiment of the application, but the protection scope of the application is not limited thereto, any change or replacement within the technical scope disclosed by the application should be covered in the protection scope of the application. Therefore, the protection scope of the application should be subject to the protection scope of the claims.

Claims

1. A mean square volumetric Kalman filter method for three-dimensional tracking of multiple targets in aerial maneuverability, characterized in that: The steps include: Step S1: Establish a three-dimensional coordinated turning motion model of multiple aerial maneuvering targets and a three-coordinate radar measurement model including range, azimuth, pitch, and Doppler information; Step S2: Predictive filtering is performed on the Gaussian terms in the multi-target probability hypothesis density function by using a mean square cubature Kalman filter; Step S3: Based on the measured position and Doppler information, the mean and covariance matrix of the Gaussian term are updated through the mean square cubature Kalman filter to obtain a set of Gaussian component estimates of the multi-target track; Step S4: performing pruning and merging operations on the Gaussian components to reduce system complexity; Step S5: perform multi-target number estimation and state extraction based on the pruned and merged Gaussian components.

2. The mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 1, characterized in that: In step S1, the motion model adopts a cooperative turning model, and the state equation of the cooperative turning model is: Where, For the goal The state variables at time ,in, 、 and Respectively represent the target coordinate position in the Cartesian coordinate system, 、 and Respectively 、 and Speed ​​in direction, When turning to the target, it is perpendicular to The angular velocity of the axis, is the state transition matrix, For the goal The state variables at time , is the process distribution matrix, is the process noise vector.

3. The mean square volume Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 2, characterized in that: In step S1, the target The nonlinear measurement equation of time is: Where, Indicates the target is The measured variable at time, and ,in, Indicates The radial distance from the target to the radar at any moment, Indicates The azimuth angle of the target relative to the radar at any moment, Indicates The target's pitch angle relative to the radar at any moment, Indicates The time is measured by the radial Doppler between the radar and the maneuvering target, Indicates Random measurement error at time, represents a nonlinear measurement relationship, and, exist A random finite set of moments, measurements for: Where, represents the finite state set of the target at time k, Indicates the radar's target status A random finite set after observation, is a random finite set of clutter.

4. The mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 1, characterized in that: In step S2, the predictive filtering includes: initialization , is the volume point set, is the number of volume points, , Representation matrix No. Column, matrix for: The volume points are propagated through the state transfer equation to calculate the state prediction value and covariance prediction value.

5. The mean square volume Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 4, characterized in that: The predictive filtering specifically includes: Step S2-1: Calculate the target motion noise covariance matrix and the measurement noise covariance matrix The Cholesky decomposition of and ; Step S2-2: When When , calculate the Cholesky decomposition of the covariance matrix and get its root mean square matrix and predicted values ,in, and are the initial values ​​of the mean vector and covariance matrix respectively; when Calculate and propagate volume points when : Where, represents the mth volume point of the i-th target at time k-1, represents the mean square covariance matrix of the i-th target at time k-1, represents the mean of the Gaussian component of the i-th target at time k-1, represents the volume point after propagation, represents the state transition matrix; Step S2-3: Calculate the predicted value of the state quantity: Where, represents the state prediction value of the i-th target, Step S2-4: Calculate the covariance matrix prediction value: Where, represents the covariance matrix predicted value, Perform QR decomposition on the matrix in the brackets, represents the weighted centralization matrix and, Step S2-5: Calculate the survival weight: Where, represents the survival weight of the i-th target, represents the Gaussian component weight of the i-th target, is the target survival probability; Probability hypothesis density function of the prediction for: Where, , , express The number of new Gaussian components at each moment, represents the number of surviving Gaussian components, Represents the Gaussian distribution function.

6. The mean square volume Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 1, characterized in that: In step S3, updating the mean and covariance matrix of the Gaussian term by using the mean square cubature Kalman filter includes: Based on measurement data And Doppler information, the mean and covariance of each Gaussian component are updated by mean square volume Kalman.

7. The mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 6, characterized in that: In step S3, updating the mean and covariance matrix of the Gaussian term by using the mean square cubature Kalman filter specifically includes: Step S3-1: Recalculate volume points: Where, represents the mth volume point of the i-th target in the update phase, represents the Gaussian component mean square covariance matrix of the i-th target, represents the volume point set, represents the state prediction value of the i-th target; Step S3-2: Update the measurement and calculate the measurement prediction value: Where, represents the updated measurement, represents the measured predicted mean, represents a nonlinear measurement relationship, Indicates the number of volume points; Step S3-3: Calculate the square root of the measurement error covariance matrix: Where, represents the square root of the measurement error covariance matrix, Perform QR decomposition on the matrix in the brackets, is the measurement noise covariance matrix The Cholesky decomposition of represents an intermediate variable, and Step S3-4: Calculate the cross-covariance matrix: Where, represents the cross-covariance matrix, represents an intermediate variable, and Where, represents the state prediction value of the i-th target, Step S3-5: Calculate the Kalman gain: Where, represents the Kalman gain, represents the measurement error covariance matrix, and ; Step S3-6: Update the mean vector and mean square covariance matrix: Where, represents the updated mean vector of the i-th target at time k, represents the state prediction value of the i-th target, Indicates the target is The measured variables at the time, represents the updated mean square covariance matrix of the i-th target at time k; Step S3-7: Update weights: Where, represents the weight of the i-th target at the updated k-th moment, represents the target detection probability, represents the survival weight of the i-th target, represents the spatial clutter intensity, and , represents the clutter intensity coefficient, and Represent the clutter average and radar detection range respectively, same ,in l Indicates that from l Gaussian components traverse to the J k|k-1 indivual, Represents the likelihood ratio function of the i-th target measurement and satisfies: Where, represents the Gaussian distribution function, represents the dimension of the vector, represents the determinant of the matrix, represents the natural exponential function, Finally, the probability hypothesis density function of the target update is for: Where, , , express The number of new Gaussian components at each moment, Indicates the number of surviving Gaussian components.

8. The mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 1, characterized in that: In step S4, the pruning and merging operations specifically include: Step S4-1: Setting the pruning threshold , Merge Threshold and the maximum number of Gaussian components ; Step S4-2: Discard update weights less than the pruning threshold Gaussian component of Step S4-3: From the maximum weight The corresponding Gaussian mean Start searching and calculate the satisfaction , All index collections , and merge its Gaussian terms according to the following rules: Where, represents the weight after pruning and merging of Gaussian components, represents the weight of the i-th target at the updated k-th moment, represents the mean of the Gaussian components after pruning and merging, Represents the covariance matrix after pruning and merging of Gaussian components; Output Gaussian term after pruning and merging of Gaussian components .

9. The mean square volumetric Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 1, characterized in that: In step S5, the target estimated number is specifically: Select weight greater than threshold The number of Gaussian components of is used as the target estimate number .

10. The mean square volume Kalman filter aerial maneuvering multi-target three-dimensional tracking method according to claim 9, characterized in that: The state extraction specifically includes: Estimated number based on target , extract the one with the largest weight Gaussian component means as multi-objective state estimation.

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