A Spatial Transformation Linear Fusion Tracking Method for Doppler Radar

Abstract

The present invention provides a spatial transformation linear fusion tracking method for a Doppler radar, including: First, based on the distance, Doppler velocity, angle of the target relative to the radar, and the target velocity modulus, construct the state space of the target to be tracked; at a preset initial moment, use the Doppler radar measurement and the target prior information to initialize the target-related parameters to obtain the initial state; then, convert the posterior state of the state space of the target to be tracked at the current moment to the Cartesian coordinate system, and then convert it back after state model prediction to obtain the predicted value at the next moment; then, according to the linear Kalman filtering theory, filter and update the predicted value and the radar measurement value to obtain the optimal state estimate value at the next moment; finally, continuously repeat the initialization, state transformation prediction, and filtering update steps until the target tracking is completed. This method effectively realizes the continuous and accurate tracking of the target by the Doppler radar.

Description

Technical Field

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

[0002] Radar target tracking technology realizes target positioning, tracking and recognition by reasonably processing electromagnetic wave detection information. It not only has important applications in national defense security fields such as surveillance, early warning, tracking and missile guidance, but also is 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 not only the distance and azimuth angle of the target, but also the Doppler measurement of the target, i.e., the radial velocity. Existing research shows that making full use of the Doppler velocity can not only effectively improve the tracking accuracy, but also enhance the system's ability to identify targets. However, in a radar tracking system, the motion state of a target is usually described by physical quantities in a Cartesian coordinate system, while the distance, azimuth angle and radial velocity measurements provided by Doppler radar are all values in a polar coordinate system. The coordinate transformation introduces intractable nonlinearity between the target motion state and the radar measurements. Therefore, tracking in the Cartesian coordinate system using these measurement values is a nonlinear state estimation problem. Among them, the Doppler measurement is a composite function of multiple Cartesian coordinate state variables and has strong nonlinearity, which makes it difficult to efficiently utilize the Doppler measurement. Therefore, seeking a reasonable method to resolve the nonlinearity between the target motion state and the measurements, and avoiding the influence of the correlation between the distance and the radial velocity on filtering to maintain the tracking accuracy is the main research content of Doppler radar target tracking.

[0004] The optimal Bayesian solution to the nonlinear problem in radar tracking requires propagating the full probability density function. However, since the form of the probability density is unrestricted, it usually cannot be described using a finite number of parameters. Therefore, any practical estimation must use some approximation. Many suboptimal methods have been developed, such as extended Kalman filtering, unscented Kalman filtering, measurement conversion Kalman filtering, particle filtering, etc. These techniques can be roughly divided into analytical approximation, numerical approximation, and Monte Carlo methods. However, when the above approximation methods based on the hybrid coordinate system convert the Gaussian distribution in the measurement space to the state space during the update process, serious non-Gaussian distortions will occur, which is often encountered in wideband radar systems with high range accuracy, resulting in difficulties in ensuring filtering accuracy and consistency. Further, the main technical means for dealing with the nonlinearity of Doppler measurements are sequential processing, Doppler measurement conversion, and measurement matrix transformation. The methods of sequential processing include sequential extended Kalman filtering and sequential unscented Kalman filtering. The significance of sequential processing is to first use range and angle filtering, and then fuse the state filtering value with high accuracy and Doppler measurement, which can reduce the error caused by strong nonlinearity. The Doppler measurement conversion method constructs a so-called "pseudo-measurement" by multiplying the range and range rate measurement results to reduce the nonlinearity of range rate measurement. However, the range and range rate errors are statistically correlated, and replacing the range rate measurement with the pseudo-measurement essentially amplifies the range rate error. The decoupled unbiased conversion measurement Kalman filter with Doppler measurement is a representative of the measurement matrix transformation technology. It filters the range and angle through the decoupled debiased measurement conversion Kalman, and then completes the filtering through the time-varying angle measurement equation constructed by the geometric relationship between the Doppler measurement and the Cartesian velocity components, and expanding the measurement matrix. However, the performance of this method is greatly affected by the accuracy of the angle measurement. Generally speaking, the above methods attempt to make more effective use of Doppler information, but they have not been able to solve the nonlinear problem in the state update process, and there is still room for improvement in tracking accuracy. On the other hand, considering the universality of the Doppler radar tracking scenario, general methods make special assumptions about the form of the prior information, and these idealized assumptions cannot be satisfied in practice. For example, the initial state of the target is the position and velocity in the Cartesian coordinate system, and the probability density follows a Gaussian distribution. This form of prior information, especially the velocity information in the Cartesian coordinate system, does not exist a priori in the actual scenario. Summary of the Invention

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

[0006] The present invention provides a spatial transformation linear fusion tracking method for a Doppler radar, including: S1. Construct 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 the composite velocity of the target relative to the stationary coordinate system and is obtained from the target prior information; S2. At a preset initial moment, initialize the distance, Doppler velocity, and angle of the target to be tracked relative to the radar through Doppler radar measurement, and initialize the target velocity modulus through the target prior information to obtain the initial state of the target to be tracked; S3. Convert the posterior state at the current moment in the state space of the target to be tracked to the Cartesian coordinate system, predict the predicted value at the next moment in the Cartesian coordinate system through the state model, and then convert the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked; S4. Based on the linear Kalman filter theory, filter and update the predicted value at the next moment in the state space of the target to be tracked and the measurement value of the Doppler radar at the next moment to obtain the optimal state estimation value at the next moment; S5. Continuously repeat S2 - S4 until the tracking ends.

[0007] In a technical solution of the above-mentioned spatial transformation linear fusion tracking method for a Doppler radar, after filtering and updating the predicted value at the next moment in the state space of the target to be tracked and the measurement value of the Doppler radar at the next moment based on the linear Kalman filter theory to obtain the optimal state estimation value at the next moment, it further includes: unbiasedly converting the optimal state estimation value at the next moment and the state variance at the next moment to the Cartesian coordinate system.

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

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

[0010] In a technical solution of the above spatial transformation linear fusion tracking method for Doppler radar, S3, converting the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked specifically includes: obtaining a plurality of sigma points generated around the state vector at the current moment: (2) where is the covariance of , is a unit vector with n elements, the -th element is 1, and the remaining elements are 0; the superscript represents the -th point; n is the dimension of the state , is the central sigma point generated based on the posterior state at time k, representing the posterior state at time k itself; and respectively represent 2n sigma points symmetrically expanded based on ; calculating the weight of each sigma point: (3), where , are the weights for calculating the mean and covariance of the central sigma point respectively; , are the weights for calculating the mean and covariance of the 2n sigma points symmetrically on the left and right respectively; is the sampling parameter, is the scaling parameter, controlling the distribution of sigma points, and the parameter is used to reduce the high-order error during the transformation process and ensure the positive semi-definiteness of the matrix , represents a non-negative weighting coefficient for combining high-order moment terms, set , the superscript represents the weight for mean calculation, and the superscript represents the weight for covariance calculation; transferring the sample points in the state space of the target to be tracked to the Cartesian coordinate system: (4), where represents the sigma sample point of the state converted from the state space of the target to be tracked to the Cartesian coordinate system at time k, represents the sigma sample point based on the posterior state at time k, The non - linear mathematical relationship for converting the state in the state space of the target to be tracked into the state in the Cartesian coordinate system is: (5), where are respectively 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; the predicted values of the sample points in the form of 4 - dimensional vectors in each Cartesian coordinate system are obtained through Equation (6): (6), where is the sigma sample point based on the Cartesian states at time k, is the state transition matrix, is the sigma sample point predicted for the Cartesian states at time k + 1 based on the Cartesian states at time k. Combining with the weights given by Equation (3), using Equations (7) and (8), calculate the predicted mean at time k + 1 in the Cartesian coordinate system and the covariance at time k + 1 in the Cartesian coordinate system : (7), (8).

[0011] In a technical solution of the above - mentioned spatial transformation linear fusion tracking method for Doppler radar, in S3, the posterior state at the current moment in the state space of the target to be tracked is converted into the Cartesian coordinate system, the predicted value at the next moment in the Cartesian coordinate system is obtained through state - model prediction, and then the predicted value at 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 at the next moment in the state space of the target to be tracked. It further includes: first, judge whether in Equation (5) is negative. If it is negative, then directly set the calculation result of to 0.

[0012] In a technical solution of the above - mentioned spatial transformation linear fusion tracking method for Doppler radar, in S3, the posterior state at the current moment in the state space of the target to be tracked is converted into the Cartesian coordinate system, the predicted value at the next moment in the Cartesian coordinate system is obtained through state - model prediction, and then the predicted value at 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 at the next moment in the state space of the target to be tracked. It further includes: updating the covariance at time k + 1 in the Cartesian coordinate system based on the process - noise covariance at the current moment and the noise - driving matrix at the current moment.

[0013] In a technical solution of the above-mentioned spatial transformation linear fusion tracking method for Doppler radar, based on the linear Kalman filtering theory, filtering and updating are performed on the predicted value of the state space of the target to be tracked at the next moment and the measured value of the Doppler radar at the next moment 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 measured value of the Doppler radar 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, unbiasedly transforming the optimal state estimate value and the state variance at the next moment to the Cartesian coordinate system specifically includes: Let 、 、 、 ,then:

[0015] ,

[0016] ,

[0017] ,

[0018] ,where (1,1) is the element in the 1st row and 1st column of the state vector ,and so on for other numbers. 、 、 、 are respectively the distance, Doppler velocity, angle, and target velocity modulus of the optimal estimate at the (k + 1)th moment. is the posterior estimate variance of the angle. are respectively the position and velocity estimates in the X and Y directions in the Cartesian coordinate system at the (k + 1)th moment.

[0019] The beneficial effects of a spatial transformation linear fusion tracking method for Doppler radar provided by the present invention are as follows: In this method, the target state constructed by fusing the observation quantity and the prior velocity modulus ensures the completeness of the state space, and all necessary information of the target motion system can be provided by the constructed state, improving the accuracy and effectiveness of target tracking; the constructed state space maximally avoids the cross-coordinate system fusion of the observation quantity and the prior information of the velocity modulus. Then, the prediction space is transformed into the Cartesian coordinate system through a static non-linear transformation, and after linear prediction, the state is transformed back into the constructed state space to realize the evolution of the state quantity driven by the motion law and provide the measurement prediction value of the Doppler radar. The two forward and reverse space transformations do not change the distribution form of the state, ensuring the integrity of the prediction information; finally, the fusion of linear measurements is completed in the constructed state space. Compared with the existing methods, the reasonable construction of the state quantity makes the method proposed by the present invention easier to be applied in practice. The two coordinate transformations in the state prediction process realize the one-step prediction of the constructed state while ensuring the integrity of the information, and filtering in the constructed state space ensures the linearization of the measurement equation and the Gaussian form of the measurement distribution, solving the strong non-linear problem in Doppler radar tracking and improving the tracking performance of the Doppler radar. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Referring to the accompanying drawings, the disclosure of the present invention will become more readily understood. It is easily understood by those skilled in the art that these drawings are only for illustrative purposes and are not intended to limit the protection scope of the present invention. In addition, similar numbers in the drawings are used to represent similar components, where:

[0021] Figure 1 is a schematic diagram of the main step flow of a spatial transformation linear fusion tracking method for Doppler radar according to an embodiment of the present invention;

[0022] Figure 2 is a comparison diagram of the present invention with the sequential unscented Kalman filter SUKF and the decoupled unbiased transformed measurement Kalman filter DUCMKF-R with Doppler measurement regarding the root mean square error RMSEs of position;

[0023] Figure 3 is a comparison diagram of the present invention with the sequential unscented Kalman filter SUKF and the decoupled unbiased transformed measurement Kalman filter DUCMKF-R with Doppler measurement regarding the root mean square error RMSEs of velocity. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0024] Some embodiments of the present invention will be 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 principle of the present invention and are not intended to limit the protection scope of the present invention.

[0025] Embodiment 1

[0026] As Figure 1 shown, a spatial transformation linear fusion tracking method for a Doppler radar in an embodiment of the present invention mainly includes the following steps S1 to S5.

[0027] Step S1: Construct a 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 composite velocity of the target relative to the stationary coordinate system and is obtained from the target prior information.

[0028] 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: the radial velocity of the target relative to the radar obtained based on the Doppler effect. Angle: usually refers to the azimuth angle and elevation angle of the target relative to the radar. The target velocity modulus represents the magnitude of the overall motion velocity of the target. Different from the Doppler velocity, it considers the motion synthesis effect of the target in all directions and can more comprehensively describe the motion velocity characteristics of the target.

[0029] Step S2: At a preset initial moment, measure and initialize the distance, Doppler velocity, and angle of the target to be tracked relative to the radar through the Doppler radar, and initialize the target velocity modulus through the target prior information to obtain the initial state of the target to be tracked.

[0030] In one embodiment, the state space of the target to be tracked is expressed as:

[0031] (1)

[0032] Wherein, are respectively the distance, Doppler velocity, angle, and target velocity modulus of the target relative to the radar at the kth moment.

[0033] In particular, k = 1 represents the initial state of the target of this algorithm, and its values are respectively obtained from the radar observation values corresponding to the moment k = 1. is the initial target velocity modulus, which refers to the composite velocity of the target relative to the stationary coordinate system and is obtained from the target prior information.

[0034] The covariance of the initial target state is:

[0035] (2)

[0036] Wherein, respectively represent the distance variance, angle variance, and Doppler velocity variance of the initial state target, and their values are given by the measurement parameters of the Doppler radar. 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 .

[0037] Step S3: Convert the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system, predict the predicted value at the next moment in the Cartesian coordinate system through the state model, and then convert the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked.

[0038] 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 more convenient for analysis and calculation in the Cartesian coordinate system, for example, the U transformation technology can be used to convert the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system. The purpose of this is to prepare for subsequent state prediction using the motion model in the Cartesian coordinate system. After converting the state to the Cartesian coordinate system, a mature motion model in the Cartesian coordinate system (such as the approximate constant velocity 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), to deduce the possible state of the target at the next moment, thereby obtaining the predicted value at the next moment in the Cartesian coordinate system. The state obtained after predicting the next moment through the motion model in the Cartesian coordinate system is represented 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 carried out in this space. Therefore, it is necessary to convert the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked, so as to obtain the predicted value at the next moment in the state space of the target to be tracked for subsequent measurement fusion and other operations, continuously update the estimation of the target state, and achieve accurate tracking of the target.

[0039] In one embodiment, S3: Converting the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked specifically includes:

[0040] Obtain a number of sigma points generated around the state vector at the current moment:

[0041] (2)

[0042] Among them, is the covariance of , is a unit vector with n elements, the th element is 1, and the rest of the elements are 0; the superscript denotes the th point; n is the dimension of the state space, is the central sigma point generated based on the posterior state at time k, representing the posterior state at time k itself; and respectively denote 2n sigma points symmetrically expanded based on ; The 2n sigma points are symmetrically expanded on the left and right;

[0043] Calculate the weights of each sigma point:

[0044] (3)

[0045] where , are the weights for calculating the mean and covariance of the central sigma point respectively; , are the weights for calculating the mean and covariance of the 2n sigma points symmetrically distributed on the left and right respectively; is the sampling parameter, is the scaling parameter that controls the distribution of the sigma points. The parameter is used to reduce the high-order error during the transformation process and ensure the positive semi-definiteness of the matrix ; represents a non-negative weighting coefficient used to combine high-order moment terms. Set , and the superscript represents the weight for mean calculation, and the superscript represents the weight for covariance calculation;

[0046] Transfer the sample points in the state space of the target to be tracked to the Cartesian coordinate system:

[0047] (4)

[0048] where denotes the sigma sample point of the state transferred from the state space of the target to be tracked to the Cartesian coordinate system at time k, denotes the sigma sample point based on the posterior state at time k ; is the non-linear mathematical relationship for transforming the state from the state space of the target to be tracked to the state in the Cartesian coordinate system:

[0049] (5)

[0050] 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;

[0051] Denote the samples in the Cartesian coordinate system as , where 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 transformation, respectively;

[0052] Next, based on the CV model, obtain the predicted values of the sample points in the form of 4D vectors in each Cartesian coordinate system through Equation (6):

[0053] (6)

[0054] where is the sigma sample point of each Cartesian state at time k, is the state transition matrix, is the sigma sample point predicted for each Cartesian state at time k+1 based on the sigma sample points of each Cartesian state at time k. Combining with the weights given by Equation (3), use Equations (7) and (8) to calculate the predicted mean at time k+1 in the Cartesian coordinate system and the covariance at time k+1 in the Cartesian coordinate system :

[0055] (7)

[0056] (8)

[0057] where is the one-step predicted state of the target.

[0058] In one embodiment, S3, converting the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked further includes: updating the covariance at time k+1 in the Cartesian coordinate system based on the process noise covariance at the current moment and the noise driving matrix at the current moment.

[0059] Considering the influence of the process noise in the CV model, update the covariance at time k+1:

[0060] (9)

[0061] In Equation (9), and are respectively the process noise covariance and the noise driving matrix at time

[0062] Since the process noise in the prediction increases the covariance, it is necessary to sample the state again. For the predicted mean at time k+1 in the Cartesian coordinate system and the updated covariance , sample again using equation (10) to obtain the sample points , and transfer them back to the state space of the target to be tracked via equation (12). Specifically, it is expressed as:

[0063] (10)

[0064] (11)

[0065] In the above equation, is the one-step predicted mean based on the time k+1 The generated central sigma point represents the one-step predicted mean at time k+1 itself; and respectively represent 2n sigma points symmetrically expanded based on , is the predicted mean at time k+1 in the Cartesian coordinate system The state sigma sampling points transferred back to the constructed state space of the target to be tracked.

[0066] The specific relationship of the nonlinear mathematical transformation described by the above equation from the Cartesian coordinate system state to the state of the constructed state space of the target to be tracked is:

[0067] (12)

[0068] In equation (12), are the predicted values at time k+1 for each state in the state space of the target to be tracked, respectively.

[0069] For the above calculation results, calculate the predicted value at the next time in the state space of the target to be tracked and the covariance at the next time in the state space of the target to be tracked through equations (13) and (14):

[0070] (13)

[0071] (14)

[0072] In one embodiment, S3, converting the posterior state at the current moment in the state space of the target to be tracked into the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked further includes: first determining whether in formula (5) is negative. If it is negative, then the calculation result is directly set to 0.

[0073] S4. Based on the linear Kalman filtering theory, filtering and updating the predicted value at the next moment in the state space of the target to be tracked and the Doppler radar measurement value at the next moment to obtain the optimal state estimation value at the next moment.

[0074] The specific calculation method is as follows:

[0075] ,

[0076] ,

[0077] ,

[0078] where 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 (distance, 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 respectively, is the measurement covariance of the Doppler radar at time k + 1.

[0079] In one embodiment, after filtering and updating the predicted value at the next moment in the state space of the target to be tracked and the Doppler radar measurement value at the next moment based on the linear Kalman filtering theory to obtain the optimal state estimation value at the next moment, it further includes: unbiasedly converting the optimal state estimation value at the next moment and the state variance at the next moment to the Cartesian coordinate system.

[0080] Specifically, let , , , , then:

[0081] ,

[0082] ,

[0083] ,

[0084] ,

[0085] Among them, (1,1) is the state vector The element in the first row and the first column, and so on for other numbers. , , , are respectively the distance, Doppler velocity, angle, and target velocity modulus of the optimal estimate at the (k + 1)-th moment, and is the posterior estimation variance of the angle, are respectively the position and velocity estimates in the X and Y directions in the Cartesian coordinate system at the (k + 1)-th moment.

[0086] S5. Continuously repeat S2 - S4 until the tracking ends.

[0087] Consider a tracking system with a typical Doppler detection radar fixed at the origin. At each sampling moment, the radar can obtain the distance, angle, and Doppler velocity of the object being tracked. The measurement noise distance error , the angle error , the Doppler velocity error , and the correlation coefficient between the distance and Doppler velocity measurements . Consider the scenario where the radar tracks a moving target. The initial position of the target is (20 km, 10 km), the radar sampling period is T = 1 s, the initial velocities of the target are all (-12 m / s, 16 m / s), and assume that the process noise is zero-mean Gaussian white noise with a standard deviation of 0.01 m / s. The standard deviation of the initial velocity modulus .

[0088] Figure 2 Shows the RMSEs of the target position estimates of various methods. Figure 3 Shows the RMSEs of the target velocity estimates of various methods. It can be seen from the comparison in the figure that the method proposed in this patent has a fast convergence speed and high accuracy. Because the constructed state conforms to the actual application scenario in form, there is no need to make special assumptions and transformations on the prior information, which ensures the integrity of the prior information. Moreover, during the filtering process, the state and the measurement are linearly related, and there is no need for nonlinear approximation, thus ensuring the convergence and accuracy of the state update.

[0089] So far, the technical solution of the present invention has been described in combination 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 all fall within the protection scope of the present invention.

Claims

1. A spatial transformation linear fusion tracking method for Doppler radar, characterized in that, Including: S1. Construct a 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 composite velocity of the target relative to the stationary coordinate system and is obtained from the prior information of the target. S2. At a preset initial moment, initialize the distance, Doppler velocity, and angle of the target to be tracked relative to the radar through Doppler radar measurement, and initialize the target velocity modulus through the prior information of the target to obtain the initial state of the target to be tracked. S3. Convert the posterior state at the current moment in the state space of the target to be tracked to the Cartesian coordinate system, predict the predicted value at the next moment in the Cartesian coordinate system through the state model, and then convert the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked. S4. Based on the linear Kalman filtering theory, filter and update the predicted value at the next moment in the state space of the target to be tracked and the measurement value of the Doppler radar at the next moment to obtain the optimal state estimate value at the next moment. S5. Continuously repeat S2 - S4 until the tracking ends.

2. The method according to claim 1, wherein After obtaining the optimal state estimate value at the next moment by filtering and updating the predicted value at the next moment in the state space of the target to be tracked and the measurement value of the Doppler radar at the next moment based on the linear Kalman filtering theory, it further includes: unbiasedly converting the optimal state estimate value at the next moment and the state variance at the next moment to the Cartesian coordinate system.

3. The method according to claim 1, wherein The state space of the target to be tracked is expressed as: （1） wherein, are respectively the distance, Doppler velocity, angle of the target relative to the radar at the k-th moment, and the magnitude of the target velocity.

4. The method according to claim 3, characterized in that, S2. At a preset initial moment, initializing the distance, Doppler velocity, and angle of the state space of the target to be tracked through Doppler radar measurement, and initializing the velocity modulus through the prior information of the target to obtain the initial state of the target to be tracked specifically includes: when k = 1 in Equation (1), it represents the initial state of the target to be tracked.

5. The method according to claim 4, wherein S3. Converting the posterior state at the current moment in the state space of the target to be tracked to the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked specifically includes: Obtain a number of sigma points generated around the state vector at the current moment: （2） wherein, is the covariance of, , is a unit vector with n elements, the -th element is 1 and the rest are 0; the superscript represents the -th point; n is the dimension of the state ; is the central sigma point generated based on the posterior state at time k, representing the posterior state itself at time k; and respectively represent 2n sigma points symmetrically expanded around ; Calculate the weight of each sigma point: （3） Among them, and are the weights for calculating the mean and covariance of the central sigma point respectively; and are the weights for calculating the mean and covariance of 2n sigma points that are symmetric left and right respectively; is the sampling parameter, is the scaling parameter, which controls the distribution of sigma points. The parameter is used to reduce the high-order error during the transformation process and ensure the positive semi-definiteness of the matrix ; represents a non-negative weighted coefficient used to combine high-order moment terms. Setting , the superscript represents the mean calculation weight, and the 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） Among them, denotes the sigma sample points for converting the state space of the target to be tracked at time k to the state in the Cartesian coordinate system, denotes the sigma sample points based on the posterior state at time k ; The non-linear mathematical relationship for converting the state from the state space of the target to be tracked to the state in the Cartesian coordinate system is: （5） wherein, are respectively 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; Obtain the predicted value of the sample point in the form of a 4D vector in each Cartesian coordinate system through Equation (6): （6） Among them, is the sigma sample point based on the Cartesian states at time k, is the state transition matrix, is the sigma sample point predicted for the Cartesian states at time k+1 based on the states at time k. Then, combining with the weights given by Equation (3) and using Equations (7) and (8), calculate the predicted mean at time k+1 in the Cartesian coordinate system and the covariance at time k+1 in the Cartesian coordinate system : （7） （8）。 6. The method according to claim 5, wherein S3. Converting the posterior state at the current moment in the state space of the target to be tracked to the Cartesian coordinate system, predicting the predicted value at the next moment in the Cartesian coordinate system through the state model, and then converting the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked further includes: First, determine whether in formula (5) is negative. If it is negative, then directly set the calculation result to 0.

7. The method according to claim 6, characterized in that, S3. Convert the posterior state at the current moment in the state space of the target to be tracked to the Cartesian coordinate system, predict the predicted value at the next moment in the Cartesian coordinate system through the state model, and then convert the predicted value at the next moment in the Cartesian coordinate system back to the state space of the target to be tracked to obtain the predicted value at the next moment in the state space of the target to be tracked. It further includes: updating the covariance at the (k + 1)-th moment in the Cartesian coordinate system based on the process noise covariance at the current moment and the noise driving matrix at the current moment. Perform an update.

8. The method according to claim 1, characterized in that, Based on the linear Kalman filtering theory, filtering and updating the predicted value at the next moment in the state space of the target to be tracked and the measurement value of the Doppler radar at the next moment to obtain the optimal state estimate value at the next moment 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 measurement value of the Doppler radar at the next moment, and the predicted value of the state space of the target to be tracked at the next moment; Calculate 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.

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

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