Spatial transformation linear fusion tracking method for Doppler radar

Abstract

The invention provides a spatial transformation linear fusion tracking method for a Doppler radar, and the method comprises the steps: firstly constructing a state space of a to-be-tracked target based on the distance of the target relative to the radar, the Doppler speed, the angle and a target speed module; at a preset initial moment, using Doppler radar measurement and target prior information to initialize target related parameters to obtain an initial state; then, the posterior state of the state space of the target to be tracked at the current moment is converted into a Cartesian coordinate system, the state model is used for prediction and then is switched back, and a predicted value at the next moment is obtained; then, according to a linear Kalman filtering theory, filtering and updating the predicted value and the radar measurement value to obtain an optimal state estimation value at the next moment; and finally, the steps of initialization, state transition prediction and filtering update are continuously repeated until target tracking is completed, and the method effectively realizes continuous and accurate tracking of the Doppler radar on the target.

Description

Technical Field

[0001] The invention relates to the technical field of radar target tracking, and in particular provides a spatial transformation linear fusion tracking method for Doppler radar. Background Art

[0002] Radar target tracking technology achieves target positioning, tracking and identification by rationally processing electromagnetic wave detection information. It not only has important applications in national defense and security fields such as surveillance, early warning, tracking and missile guidance, but is also an important basic technology in civilian fields such as autonomous driving and low-altitude economy.

[0003] Since Doppler radar can denoise in the frequency domain, its anti-interference ability is stronger than that of ordinary radar. In tracking applications, Doppler radar can obtain the target's Doppler measurement, namely radial velocity, in addition to the target's distance and azimuth. Existing studies have shown that making full use of Doppler velocity can not only effectively improve tracking accuracy, but also enhance the system's ability to identify targets. However, in radar tracking systems, physical quantities in the Cartesian coordinate system are usually used to characterize the target's motion state, while the distance, azimuth and radial velocity measurements provided by Doppler radar are all values ​​in the polar coordinate system. The coordinate system transformation introduces nonlinearities that are difficult to resolve between the target's motion state and the radar measurement. Therefore, using these measurements to track in the Cartesian coordinate system is a nonlinear state estimation problem. Among them, Doppler measurement is a composite function of multiple Cartesian coordinate system state quantities and has strong nonlinearity, which makes it difficult to efficiently use Doppler measurement. Therefore, seeking reasonable methods to resolve the nonlinearity between the target's motion state and measurement, and avoiding the influence of the correlation between distance and radial velocity on filtering to maintain tracking accuracy are the main research contents of Doppler radar target tracking.

[0004] The optimal Bayesian solution to the nonlinear problem in radar tracking requires the propagation of the full probability density function, but since the form of the probability density is unrestricted, it cannot usually be described using a finite number of parameters. Therefore, any practical estimation must use some kind of approximation. Many suboptimal methods have been developed, such as extended Kalman filtering, unscented Kalman filtering, measurement conversion Kalman filtering, particle filtering and other technologies, which can be roughly divided into analytical approximation, numerical approximation and Monte Carlo methods. However, the above approximation methods based on mixed coordinate systems will cause serious non-Gaussian distortion when converting the Gaussian distribution in the measurement space to the state space during the update process. This phenomenon is often encountered in broadband radar systems with high range accuracy, making it difficult to ensure filtering accuracy and consistency. Further, the technical means for targeted processing of nonlinear Doppler measurements mainly include sequential processing, Doppler measurement conversion and measurement matrix transformation. The sequential processing methods include sequential extended Kalman filtering and sequential unscented Kalman filtering. The significance of sequential processing is to first use distance and angle filtering, and then fuse high-precision state filter values ​​and Doppler measurements, which can reduce the errors caused by strong nonlinearity. In order to reduce the nonlinearity of range-rate measurement, the Doppler measurement conversion method constructs the so-called "pseudo-measurement" by multiplying the range and range-rate measurement results. However, the errors of range and range-rate are statistically correlated, and replacing the range-rate measurement with pseudo-measurement essentially amplifies the error of range-rate. The decoupled unbiased conversion measurement Kalman filter with Doppler measurement is a representative of the measurement matrix transformation technology. It filters the distance and angle through the decoupled and debiased measurement conversion Kalman, and then constructs the time-varying angle measurement equation through the geometric relationship between the Doppler measurement and the Cartesian velocity component, and expands the dimension of the measurement matrix to complete the filtering. However, the performance of this method is greatly affected by the accuracy of the angle measurement. In general, the above methods attempt to use Doppler information more effectively, but they have not been able to resolve the nonlinear problem in the state update process, and the tracking accuracy still has room for improvement. On the other hand, considering the universality of Doppler radar tracking scenarios, general methods make special assumptions on the form of prior information, and these idealized assumptions cannot be met in practice. For example, the initial state of the target is the position and velocity in the Cartesian coordinate system, and the probability density obeys the Gaussian distribution. This form of prior information, especially the velocity information in the Cartesian coordinate system, does not exist a priori in actual scenarios. Summary of the invention

[0005] In order to overcome the above defects, the present invention is proposed to provide a solution or at least partially solve the problem of strong nonlinearity in Doppler radar tracking, which in turn leads to the problem of low tracking performance of Doppler radar.

[0006] The present invention provides a spatial transformation linear fusion tracking method for Doppler radar, comprising: S1, constructing a state space of a target to be tracked based on the distance, Doppler velocity, angle and target velocity modulus of the target relative to the radar; wherein the target velocity modulus is a synthetic velocity of the target relative to a stationary coordinate system, which is obtained by target prior information; S2, at a preset initial time, initializing the distance, Doppler velocity and angle of the target to be tracked relative to the radar by Doppler radar measurement, initializing the target velocity modulus by target prior information, and obtaining the initial state of the target to be tracked; S3, initializing the target to be tracked by the target prior information; S4, initializing the target to be tracked by the target prior information; S5, initializing the target to be tracked by the target prior information; S6, initializing the target to be tracked by the target prior information; S7, initializing the target to be tracked by the target prior information; S8, initializing the target to be tracked by the target prior information The posterior state of the current moment in the state space of the target to be tracked is converted to the Cartesian coordinate system, and the predicted value of the next moment in the Cartesian coordinate system is obtained through the state model prediction, and then the predicted value of the next moment in the Cartesian coordinate system is converted back to the state space of the target to be tracked to obtain the predicted value of the state space of the target to be tracked at the next moment; S4, based on the linear Kalman filter theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated to obtain the optimal state estimate value at the next moment; S5, S2-S4 are repeated continuously until the tracking is completed.

[0007] In a technical solution of the above-mentioned spatial transformation linear fusion tracking method for Doppler radar, based on the linear Kalman filtering theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated, and after obtaining the optimal state estimate value at the next moment, it also includes: unbiased conversion of the optimal state estimate value at the next moment and the state variance at the next moment to a Cartesian coordinate system.

[0008] In a technical solution of the above-mentioned spatial transformation linear fusion tracking method for Doppler radar, the state space of the target to be tracked is expressed as: (1), where are the distance, Doppler velocity, angle and target velocity modulus of the target relative to the radar at the kth moment.

[0009] In a technical solution of the spatial transformation linear fusion tracking method for Doppler radar, S2, at a preset initial time, initialize the distance, Doppler velocity, and angle of the state space of the target to be tracked by Doppler radar measurement, initialize the velocity modulus by target prior information, and obtain the initial state of the target to be tracked, specifically including: when k=1 in formula (1), it represents the initial state of the target to be tracked.

[0010] In a technical solution of the spatial transformation linear fusion tracking method for Doppler radar, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the next moment in the Cartesian coordinate system through state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, and obtaining the predicted value of the next moment in the state space of the target to be tracked specifically includes: obtaining a number of sigma points generated around the state vector at the current moment: (2) Among them, for The covariance of , is a unit vector with n elements, the elements are 1, and the rest are 0; Indicates points; n is the state The dimension of is the posterior state based on time k The generated central sigma point represents the posterior state at time k itself; and Respectively based on 2n sigma points expanded symmetrically on the left and right; calculate the weight of each sigma point: (3), where , They are the weights of the calculated mean and covariance of the central sigma point respectively; , Calculate the mean and covariance weights for the 2n sigma points that are symmetrical on the left and right; is the sampling parameter, is a scaling parameter that controls the distribution of sigma points. Used to reduce high-order errors in the transformation process and ensure that the matrix The semi-positive definiteness of Represents the non-negative weight coefficients used to combine high-order moment terms, set , superscript Indicates the mean calculation weight, superscript Represents the covariance calculation weight; transfers the sample points in the state space of the target to be tracked to the Cartesian coordinate system: (4), where It represents the sigma sample point of the state space of the target to be tracked converted to the state in the Cartesian coordinate system at time k. Represents the posterior state based on time k The sigma sample point, The nonlinear mathematical relationship for converting the state in the state space of the target to be tracked to the state in the Cartesian coordinate system is: (5), where are the position and velocity on the X-axis and the position and velocity on the Y-axis in the Cartesian coordinate system at time k respectively; the predicted value of each sample point in the form of a 4-dimensional vector in the Cartesian coordinate system is obtained by formula (6): (6), where is the sigma sample point based on each Cartesian state at time k, is the state transfer matrix, The sigma sample points of the Cartesian state prediction at time k+1 based on time k are combined with the weight given by formula (3), and the predicted mean value at time k+1 in the Cartesian coordinate system is calculated using formulas (7) and (8). and the covariance of the Cartesian coordinate system at time k+1 : (7), (8).

[0011] In a technical solution of the spatial transformation linear fusion tracking method for Doppler radar, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the next moment in the Cartesian coordinate system through state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, and obtaining the predicted value of the next moment in the state space of the target to be tracked also includes: first determining the value in formula (5): Is it negative? If it is negative, The calculation result is directly set to 0.

[0012] In a technical solution of the spatial transformation linear fusion tracking method for Doppler radar, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the next moment in the Cartesian coordinate system through state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value of the state space of the target to be tracked at the next moment also includes: based on the process noise covariance at the current moment, the covariance of the noise driving matrix at the current moment to the Cartesian coordinate system at the k+1 moment to update.

[0013] In a technical solution of the spatial transformation linear fusion tracking method for Doppler radar, based on the linear Kalman filtering theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated to obtain the optimal state estimate value at the next moment, which specifically includes: calculating the Kalman gain at the next moment based on the measurement matrix, the covariance of the state space of the target to be tracked at the next moment, and the measurement covariance of the Doppler radar at the next moment; calculating the optimal state estimate at the next moment based on the Kalman gain at the next moment, the measurement matrix, the Doppler radar measurement value at the next moment, and the predicted value of the state space of the target to be tracked at the next moment; calculating the state covariance at the next moment based on the covariance of the state space of the target to be tracked at the next moment, the Kalman gain at the next moment, and the measurement matrix.

[0014] In a technical solution of the above-mentioned spatial transformation linear fusion tracking method for Doppler radar, unbiased conversion of the optimal state estimate value at the next moment and the state variance at the next moment into the Cartesian coordinate system specifically includes: assuming , , , ,but: , , , , where (1,1) is the state vector The element in row 1 and column 1, and so on for other numbers. , , , The optimal estimated distance, Doppler velocity, angle and target velocity modulus at time k+1 are: is the posterior estimate variance of the angle, They are the estimated position and velocity in the X and Y directions in the Cartesian coordinate system at time k+1 respectively.

[0015] The beneficial effects of the spatial transformation linear fusion tracking method for Doppler radar provided by the present invention are as follows: the target state constructed by fusing the observed quantity and the prior velocity model in the method ensures the completeness of the state space, and all necessary information of the target motion system can be provided through the constructed state, thereby improving the accuracy and effectiveness of target tracking; the constructed state space avoids the cross-coordinate system fusion of the observed quantity and the velocity model prior information to the greatest extent. Then, the prediction space is transformed into the Cartesian coordinate system through static nonlinear transformation, and the state is transformed back to the constructed state space after linear prediction, so as to realize the motion law driving the state quantity evolution and provide the measurement prediction value of the Doppler radar, and the two positive and negative space transformations do not change the distribution form of the state, thereby ensuring the integrity of the prediction information; finally, the fusion of the linear measurement is completed in the constructed state space. Compared with the existing methods, the reasonable construction of the state quantity makes the method proposed in the present invention easier to apply in practice. The two coordinate transformations in the state prediction process realize one-step prediction of the constructed state while ensuring the completeness of the information. The filtering in the constructed state space ensures the linearization of the measurement equation and the Gaussian shape of the measurement distribution, solves the strong nonlinear problem in Doppler radar tracking, and improves the tracking performance of the Doppler radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The disclosure of the present invention will become more easily understood with reference to the accompanying drawings. It is easy for those skilled in the art to understand that these drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present invention. In addition, similar numbers in the figures are used to represent similar components, among which: Figure 1 is a schematic flow chart of main steps of a spatial transformation linear fusion tracking method for Doppler radar according to an embodiment of the present invention; Figure 2 It is a comparison diagram of the position root mean square error RMSEs of the present invention, the sequential unscented Kalman filter SUKF and the decoupled unbiased transfer measurement Kalman filter DUCMKF-R with Doppler measurement; Figure 3 It is a comparison diagram of velocity root mean square error RMSEs between the present invention and the sequential unscented Kalman filter SUKF and the decoupled unbiased transfer measurement Kalman filter DUCMKF-R with Doppler measurement. DETAILED DESCRIPTION

[0017] Some embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood by those skilled in the art that these embodiments are only used to explain the technical principles of the present invention and are not intended to limit the protection scope of the present invention.

[0018] Embodiment 1 like Figure 1As shown, a spatial transformation linear fusion tracking method for Doppler radar in an embodiment of the present invention mainly includes the following steps S1 to S5.

[0019] Step S1, constructing a state space of a target to be tracked based on the distance, Doppler velocity, angle, and target velocity modulus of the target relative to the radar; wherein the target velocity modulus is a synthetic velocity of the target relative to a stationary coordinate system, obtained from target prior information.

[0020] In this embodiment, the distance of the target relative to the radar refers to the spatial interval between the target and the radar. Doppler velocity refers to the radial velocity of the target relative to the radar based on the Doppler effect. Angle refers to the azimuth and elevation of the target relative to the radar. The target velocity modulus indicates the magnitude of the overall motion velocity of the target. Unlike the Doppler velocity, it takes into account the synthetic effect of the motion of the target in all directions and can more comprehensively describe the motion velocity characteristics of the target.

[0021] Step S2: At a preset initial time, the distance, Doppler velocity and angle of the target to be tracked relative to the radar are initialized by Doppler radar measurement, and the target velocity module is initialized by target prior information to obtain the initial state of the target to be tracked.

[0022] In one embodiment, the state space of the target to be tracked is expressed as: (1) in, are the distance, Doppler velocity, angle and target velocity modulus of the target relative to the radar at the kth moment.

[0023] In particular, k=1 indicates that the initial state of the target of this algorithm is obtained by the radar observation value corresponding to the time k=1. is the initial target velocity modulus, which refers to the synthetic velocity of the target relative to the stationary coordinate system and is obtained from the target prior information.

[0024] Covariance of initial target state for: (2) in, They represent the distance variance, angle variance, and Doppler velocity variance of the target in the initial state, respectively, and their values ​​are given by the Doppler radar measurement parameters. is the variance of the initial velocity modulus, and its value is obtained from the target prior information; there is a correlation between the distance and Doppler measurement errors, and the correlation coefficient is .

[0025] Step S3, converting the posterior state of the current moment in the state space of the target to be tracked to the Cartesian coordinate system, obtaining the predicted value of the next moment in the Cartesian coordinate system through the state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value of the next moment in the state space of the target to be tracked.

[0026] In this embodiment, the result obtained after estimating the target state at the current moment is the posterior state, which is in the state space of the target to be tracked. Since the target motion model is easier to analyze and calculate in the Cartesian coordinate system, for example, the U transformation technology can be used to convert the posterior state of the current moment in the state space of the target to be tracked to the Cartesian coordinate system. The purpose of this is to prepare for the subsequent use of the motion model in the Cartesian coordinate system for state prediction. After the state is converted to the Cartesian coordinate system, the mature motion model in the Cartesian coordinate system (such as the approximate uniform motion CV model) can be applied to predict the target state. These motion models are based on physical laws and the motion characteristics of the target, combined with the state information at the current moment (already converted to the Cartesian coordinate system), and the state that the target may be in at the next moment is calculated, thereby obtaining the predicted value of the Cartesian coordinate system at the next moment. The state at the next moment predicted by the motion model in the Cartesian coordinate system is expressed in the Cartesian coordinate system. However, the entire tracking process is constructed based on the state space of the target to be tracked, and subsequent processing and fusion operations also need to be performed in this space. Therefore, it is necessary to convert the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, so that the predicted value of the next moment in the state space of the target to be tracked can be obtained, so as to carry out subsequent measurement fusion and other operations, continuously update the estimate of the target state, and realize accurate tracking of the target.

[0027] In one embodiment, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the Cartesian coordinate system at the next moment through state model prediction, and then converting the predicted value of the Cartesian coordinate system at the next moment back to the state space of the target to be tracked, and obtaining the predicted value of the state space of the target to be tracked at the next moment specifically includes: Get several sigma points generated around the state vector at the current moment: (2) in, for The covariance of , is a unit vector with n elements, the elements are 1, and the rest are 0; Indicates points; n is the state The dimension of is the posterior state based on time k The generated central sigma point represents the posterior state at time k itself; and Respectively based on 2n sigma points expanded symmetrically on both sides; Calculate the weight of each sigma point: (3) in, , They are the weights of the calculated mean and covariance of the central sigma point respectively; , Calculate the mean and covariance weights for the 2n sigma points that are symmetrical on the left and right; is the sampling parameter, is a scaling parameter that controls the distribution of sigma points. Used to reduce high-order errors in the transformation process and ensure that the matrix The semi-positive definiteness of Represents the non-negative weight coefficients used to combine high-order moment terms, set , superscript Indicates the mean calculation weight, superscript Represents the covariance calculation weight; Transfer the sample points in the state space of the target to be tracked to the Cartesian coordinate system: (4) in, It represents the sigma sample point of the state space of the target to be tracked converted to the state in the Cartesian coordinate system at time k. Represents the posterior state based on time k The sigma sample point, The nonlinear mathematical relationship for converting the state in the state space of the target to be tracked to the state in the Cartesian coordinate system is: (5) in, are the position and velocity on the X-axis and the position and velocity on the Y-axis in the Cartesian coordinate system at time k respectively; The sample in the Cartesian coordinate system is denoted as ,in They are the sigma sample points of the position and velocity on the X-axis and the sigma sample points of the position and velocity on the Y-axis after conversion;

[0028] Next, based on the CV model, the predicted value of each sample point in the form of a 4-dimensional vector in the Cartesian coordinate system is obtained through formula (6): (6) in, is the sigma sample point based on each Cartesian state at time k, is the state transfer matrix, The sigma sample points of the Cartesian state prediction at time k+1 based on time k are combined with the weights given by formula (3), and the predicted mean value at time k+1 in the Cartesian coordinate system is calculated using formulas (7) and (8). and the covariance of the Cartesian coordinate system at time k+1 : (7) (8) in, One-step predicted state for the target.

[0029] In one embodiment, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the next moment in the Cartesian coordinate system through state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, and obtaining the predicted value of the next moment in the state space of the target to be tracked also includes: based on the process noise covariance at the current moment, the covariance of the noise driving matrix at the current moment to the Cartesian coordinate system at the k+1 moment to update.

[0030] Considering the influence of process noise in the CV model, the covariance of k+1 time To update: (9) In formula (9), and They are The process noise covariance at time t and the noise driving matrix.

[0031] Since the process noise in the prediction increases the covariance, it is necessary to sample the state again, and the predicted mean at time k+1 in the Cartesian coordinate system is and the updated covariance , use formula (10) again to sample and get the sample points , and is passed back to the state space of the target to be tracked via (12). Specifically expressed as: (10) (11)

[0032] In the above formula, is the one-step prediction mean based on time k+1 The generated central sigma point represents the one-step prediction mean at time k+1 itself; and Respectively based on 2n sigma points expanded symmetrically on both sides, is the predicted mean at time k+1 through the Cartesian coordinate system Return to each state sigma sampling point of the constructed target state space to be tracked.

[0033] The specific relationship of the nonlinear mathematical transformation from the Cartesian coordinate system state to the constructed target state space state described in the above formula is: (12) In formula (12), are respectively the predicted values ​​of each state at time k+1 in the target state space to be tracked.

[0034] For the above calculation results, the predicted value of the state space of the target to be tracked at the next moment is obtained by calculating equations (13) and (14): and the covariance of the next moment of the state space of the target to be tracked : (13) (14) In one embodiment, S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the next moment in the Cartesian coordinate system through a state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, and obtaining the predicted value of the next moment in the state space of the target to be tracked also includes: first determining the value in formula (5) Is it negative? If it is negative, The calculation result is directly set to 0.

[0035] S4. Based on the linear Kalman filter theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated to obtain the optimal state estimation value at the next moment.

[0036] The specific calculation method is as follows: , , , in, is the Kalman gain at time k+1, is the measurement matrix, specifically the observation matrix connecting the state space of the target to be tracked (range, Doppler velocity, angle, velocity modulus) and the Doppler radar observation, is the Doppler radar measurement value at time k+1, are the distance, angle, and Doppler velocity measurements at time k+1, is the measurement covariance of the Doppler radar at time k+1.

[0037] In one embodiment, based on the linear Kalman filtering theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated to obtain the optimal state estimate value at the next moment, and it also includes: unbiased conversion of the optimal state estimate value at the next moment and the state variance at the next moment to a Cartesian coordinate system.

[0038] Specifically, , , , ,but: , , , , Among them, (1,1) is the state vector The element in row 1 and column 1, and so on for other numbers. , , , The optimal estimated distance, Doppler velocity, angle and target velocity modulus at time k+1 are respectively is the posterior estimate variance of the angle, They are the estimated position and velocity in the X and Y directions in the Cartesian coordinate system at time k+1 respectively.

[0039] S5. Repeat S2-S4 until the tracking is completed.

[0040] Consider a typical Doppler detection radar tracking system fixed at the origin. The radar can obtain the distance, angle and Doppler velocity of the tracked object at each sampling moment, and measure the noise distance error. , angle error , Doppler velocity error , correlation coefficient between distance and Doppler velocity measurement Consider a scenario where the radar tracks a moving target. The initial position of the target is (20km, 10km), the radar sampling period is T=1s, and the initial velocity of the target is (-12m / s, 16m / s). Assume that the process noise is zero-mean Gaussian white noise with a standard deviation of 0.01m / s. The standard deviation of the initial velocity modulus is .

[0041] Figure 2 The RMSEs of target position estimates for various methods are shown. Figure 3 The RMSEs of target speed estimation of various methods are shown. From the comparison in the figure, it can be seen that the method proposed in this patent has fast convergence speed and high accuracy. Because the state constructed by it fits the actual application scenario in form, no special assumptions and transformations are required for the prior information, which ensures the integrity of the prior information. In addition, during the filtering process, the state is linearly related to the measurement, and no nonlinear approximation is required, thus ensuring the convergence and accuracy of the state update.

[0042] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A spatial transformation linear fusion tracking method for Doppler radar, characterized in that: include: S1. Constructing the state space of the target to be tracked based on the distance, Doppler velocity, angle, and target velocity modulus of the target relative to the radar; wherein the target velocity modulus is the synthetic velocity of the target relative to the stationary coordinate system, which is obtained from the target prior information; S2. At a preset initial time, the distance, Doppler velocity and angle of the target to be tracked relative to the radar are initialized by Doppler radar measurement, and the target velocity modulus is initialized by target prior information to obtain the initial state of the target to be tracked; S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the Cartesian coordinate system at the next moment through state model prediction, and then converting the predicted value of the Cartesian coordinate system at the next moment back to the state space of the target to be tracked to obtain a predicted value of the state space of the target to be tracked at the next moment; S4, based on the linear Kalman filter theory, filtering and updating the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment to obtain the optimal state estimation value at the next moment; S5. Repeat S2-S4 until the tracking is completed.

2. The method according to claim 1, characterized in that: Based on the linear Kalman filtering theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated, and after obtaining the optimal state estimation value at the next moment, the method also includes: unbiasedly converting the optimal state estimation value at the next moment and the state variance at the next moment into a Cartesian coordinate system.

3. The method according to claim 1, characterized in that The state space of the target to be tracked is expressed as: （1） in, are the distance, Doppler velocity, angle and target velocity modulus of the target relative to the radar at the kth moment.

4. The method according to claim 3, characterized in that S2. At a preset initial time, the distance, Doppler velocity, and angle of the state space of the target to be tracked are initialized by Doppler radar measurement, and the velocity module is initialized by target prior information to obtain the initial state of the target to be tracked. Specifically, when k=1 in formula (1), it represents the initial state of the target to be tracked.

5. The method according to claim 4, characterized in that S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the Cartesian coordinate system at the next moment through state model prediction, and then converting the predicted value of the Cartesian coordinate system at the next moment back to the state space of the target to be tracked, and obtaining the predicted value of the state space of the target to be tracked at the next moment specifically includes: Get several sigma points generated around the state vector at the current moment: （2） in, for The covariance of , is a unit vector with n elements, the elements are 1, and the rest are 0; Indicates points; n is the state The dimension of is the posterior state based on time k The generated central sigma point represents the posterior state at time k itself; and Respectively based on 2n sigma points expanded symmetrically on both sides; Calculate the weight of each sigma point: （3） in, , They are the weights of the calculated mean and covariance of the central sigma point respectively; , Calculate the mean and covariance weights for the 2n sigma points that are symmetrical on the left and right; is the sampling parameter, is a scaling parameter that controls the distribution of sigma points. Used to reduce high-order errors in the transformation process and ensure that the matrix The semi-positive definiteness of Represents the non-negative weight coefficients used to combine high-order moment terms, set , superscript Indicates the mean calculation weight, superscript Represents the covariance calculation weight; Transfer the sample points in the state space of the target to be tracked to the Cartesian coordinate system: （4） in, It represents the sigma sample point of the state space of the target to be tracked converted to the state in the Cartesian coordinate system at time k. Represents the posterior state based on time k The sigma sample point, The nonlinear mathematical relationship for converting the state in the state space of the target to be tracked to the state in the Cartesian coordinate system is: （5） in, are the position and velocity on the X-axis and the position and velocity on the Y-axis in the Cartesian coordinate system at time k respectively; The predicted value of each sample point in the form of a 4-dimensional vector in the Cartesian coordinate system is obtained by formula (6): （6） in, is the sigma sample point based on each Cartesian state at time k, is the state transfer matrix, The sigma sample points of the Cartesian state prediction at time k+1 based on time k are combined with the weights given by formula (3), and the predicted mean value at time k+1 in the Cartesian coordinate system is calculated using formulas (7) and (8). and the covariance of the Cartesian coordinate system at time k+1 : （7） （8）。 6. The method according to claim 5, characterized in that S3, converting the posterior state of the current moment in the state space of the target to be tracked to a Cartesian coordinate system, obtaining a predicted value of the Cartesian coordinate system at the next moment through state model prediction, and then converting the predicted value of the Cartesian coordinate system at the next moment back to the state space of the target to be tracked, and obtaining the predicted value of the state space of the target to be tracked at the next moment also includes: First determine the Is it negative? If it is negative, The calculation result is directly set to 0.

7. The method according to claim 6, characterized in that S3, converting the posterior state of the current moment in the state space of the target to be tracked to the Cartesian coordinate system, obtaining the predicted value of the next moment in the Cartesian coordinate system through the state model prediction, and then converting the predicted value of the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, and obtaining the predicted value of the state space of the target to be tracked at the next moment also includes: based on the process noise covariance at the current moment, the covariance of the noise driving matrix at the current moment to the Cartesian coordinate system at the k+1 moment to update.

8. The method according to claim 1, characterized in that Based on the linear Kalman filter theory, the predicted value of the state space of the target to be tracked at the next moment and the Doppler radar measurement value at the next moment are filtered and updated to obtain the optimal state estimation value at the next moment, which specifically includes: Calculate the Kalman gain at the next moment based on the measurement matrix, the covariance of the state space of the target to be tracked at the next moment, and the measurement covariance of the Doppler radar at the next moment; Calculate the optimal state estimate at the next moment based on the Kalman gain at the next moment, the measurement matrix, the Doppler radar measurement value at the next moment, and the predicted value of the state space of the target to be tracked at the next moment; Based on the covariance of the state space of the target to be tracked at the next moment, the Kalman gain at the next moment, and the measurement matrix, the state covariance at the next moment is calculated.

9. The method according to claim 2, characterized in that: The unbiased conversion of the optimal state estimate at the next moment and the state variance at the next moment to the Cartesian coordinate system specifically includes: set up , , , ,but: ， ， ， ， Among them, (1,1) is the state vector The element in row 1 and column 1, and so on for other numbers. , , , The optimal estimated distance, Doppler velocity, angle and target velocity modulus at time k+1 are: is the posterior estimate variance of the angle, They are the estimated position and velocity in the X and Y directions in the Cartesian coordinate system at time k+1 respectively.

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