CN116224320B - A radar target tracking method that processes Doppler measurements in polar coordinates - Google Patents

Abstract

The invention discloses a method for realizing target tracking by Doppler measurement under a polar coordinate system, and relates to the field of Doppler radar target tracking. The motion equation in the Cartesian coordinate system is converted into a polar coordinate system, doppler measurement is introduced, and the Doppler measurement is combined with the radial distance and azimuth angle equivalent value to form a state vector, so that the state and observation are in a linear relation, and the posterior estimation of the target state at each moment is obtained through the least square error linear fusion in the fusion stage, so that the influence of nonlinear filtering on estimation precision is avoided, and the target tracking performance is effectively improved.

Description

A radar target tracking method for processing Doppler measurements in polar coordinates

Technical Field

The invention relates to the field of Doppler radar target tracking, and in particular to a radar target tracking method for processing Doppler measurements in a polar coordinate system.

Background Art

Doppler radar is a common method for detecting target movement. It can detect and track moving targets using the Doppler effect. Due to the particularity of its working system and system environment, it can obtain information such as the distance from the target to the observation point, azimuth, and Doppler measurement (radial velocity). At present, Doppler radar has been widely used in the fields of airborne fire control, air defense warning, and command systems.

In actual target tracking applications, the target motion equation is usually modeled in a Cartesian coordinate system, while radar measurements are usually obtained in polar coordinates. Therefore, solving the target state and measurement nonlinearity is the main problem in target tracking. Due to the strong nonlinearity of Doppler measurement, when this measurement information is added to target tracking, the problem becomes more complicated. In an environment containing clutter, clutter will generate a lot of false information. The nonlinearity of measurement will undoubtedly increase the complexity of the tracking system and lead to a decrease in the algorithm estimation performance. At present, most tracking systems only consider the radar position measurement (distance and angle) and do not make full use of Doppler measurement. In fact, Doppler measurement containing target velocity information also has the potential to improve tracking performance. Doppler measurement is usually the only measurement that contains target velocity information. From the perspective of information, more observation information helps to improve accuracy, and research has shown that making full use of Doppler measurement can effectively improve the tracking accuracy of the target.

To solve the problem of radar target tracking with Doppler measurement, the following nonlinear filtering is usually used:

(1) Sequential Extended Kalman Filter (SEKF): This method first performs a linear debiasing measurement conversion filter on the position measurement, and then directly processes the Doppler measurement using the extended Kalman filter. The disadvantage is that the extended Kalman filter discards higher-order terms above the second order during the linearization process. When encountering strong nonlinearities such as Doppler measurements, the error caused is large, and even filter divergence may occur.

(2) Sequential Unscented Kalman Filter (SUKF): This method processes the position measurement and Doppler measurement sequentially based on the unscented Kalman filter. The disadvantage is that the problem of selecting the parameters of the unscented Kalman filter has not been completely solved, and its filtering effect is also affected by the initial value of the filter like the extended Kalman filter.

(3) Static fusion based on predicted value measurement conversion (SFPRE): In order to weaken the strong nonlinear relationship between Doppler measurement and target state, this method constructs Doppler pseudo-measurement by multiplying the distance measurement and Doppler measurement. Position measurement and Doppler pseudo-measurement are processed by unbiased measurement conversion and debiased measurement conversion, respectively. The disadvantage is that the constructed pseudo-measurement is not the real Doppler measurement, and there will be deviations in the measurement conversion process, which will lead to the degradation of Kalman filter performance.

In the above filtering, for nonlinear observation models, some methods such as Taylor expansion and sigma point delinearization are adopted, which leads to partial information loss. In addition, due to the additional method of approximating nonlinear relationships to linear relationships, the computational complexity is also higher than that of standard Kalman filtering. Although the conversion measurement Kalman filter can use standard Kalman processing after conversion, the conversion state always contains noise during its conversion process, which affects the accuracy of target positioning.

Therefore, how to eliminate the influence of the strong nonlinearity of Doppler measurement on tracking accuracy is an urgent problem to be solved by those skilled in the art.

Summary of the invention

In view of this, the present invention provides a method for realizing target tracking by using Doppler measurement in a polar coordinate system, so as to solve the technical problems existing in the prior art.

In order to achieve the above object, the present invention adopts the following technical solution:

A method for realizing target tracking by using Doppler measurement in a polar coordinate system comprises the following steps:

Step 1, determine the state equations of the uniform linear motion model and the uniform accelerated linear motion model containing radial velocity in polar coordinates and having a linear relationship with Doppler radar measurement;

Step 2: Convert the process noise in the Cartesian coordinate system of the uniform linear motion model and the uniformly accelerated linear motion model to polar coordinates, and use the Unscented transformation to calculate the mean and covariance of the process noise;

Step 3: Based on the prior information in Cartesian coordinates, the state equations of the uniform linear motion model and the uniform accelerated linear motion model are initialized, and the target state and covariance of the target in polar coordinates are initialized using the Monte Carlo method;

Step 4: At the current moment, a motion model is selected according to the prior information of the acceleration of the moving target, and the state transfer matrix of the state equation in polar coordinates, the process noise driving matrix and the statistical characteristics of the process noise are calculated;

Step 5: One-step prediction of the target state and covariance in polar coordinates;

Step 6: Combine the Doppler radar measurement value and complete the update of the target tracking state and covariance at the current moment through minimum variance linear fusion;

Step 7: Loop through steps 4-6 until target tracking is complete.

Optionally, the specific process of determining the state equation of the uniform linear motion model in polar coordinates is: converting the state equation in the Cartesian coordinate system to the polar coordinate system, and the state equation of the uniform linear motion model containing radial velocity in the polar coordinate system is expressed as:

η _RV-CV (k+1)=Φ _RV-CV (k) η _RV-CV (k) + Γ _RV-CV (k) ω _RV-CV (k);

In the formula, represents the state of the target at time k, θ(k) and r(k) are the true values of azimuth and distance respectively. are the angular velocity and radial velocity respectively; represents r(k), The covariance between Var[r(k)] represents where Φ _{RV-CV (k) is the variance of r(k), Φ RV} -CV (k) is the state transfer matrix, Γ _RV-CV (k) is the process noise driving matrix, and ω _RV-CV (k) is the process noise.

Optionally, the specific process of determining the state equation of the uniformly accelerated linear motion model in polar coordinates is: converting the state equation in the Cartesian coordinate system to the polar coordinate system, and the state equation of the uniformly accelerated linear motion model containing radial velocity in the polar coordinate system is expressed as:

η _RV-CA (k+1)=Φ _RV-CA (k)n RV _-CA (k)+Γ _RV-CA (k)ω _RV-CA (k);

In the formula, represents the state of the target at time k, T is the sampling time interval of the Doppler radar, θ(k) and r(k) are the true values of azimuth measurement and distance measurement, respectively. are the angular velocity and radial velocity respectively, are angular acceleration and radial acceleration respectively; represents r(k), The covariance between represent , Φ _RV-CA (k) is the state transfer matrix, Γ _RV-CA (k) is the process noise driving matrix, and ω _RV-CA (k) is the process noise.

Optionally, the Doppler radar position is located at the origin of the polar coordinate system, and the Doppler radar measurement equation is specifically expressed as:

Z _m (k) = f (X (k)) + V _m (k);

θ(k)=arctan(y(k)/x(k));

Where θ _m (k), r _m (k) and are azimuth measurement, distance measurement and Doppler measurement respectively; θ(k), r(k) and They are the true value of azimuth measurement, the true value of distance measurement and the true value of Doppler measurement respectively; and They are azimuth measurement noise, distance measurement noise and Doppler measurement noise, all of which are zero-mean Gaussian white noise, with variances of and (σ _θ , σ _r and is its corresponding standard deviation), and and Not relevant, and Not relevant, and The correlation coefficient is ρ, that is,

Optionally, step 2 specifically includes:

The mean and variance of the three-dimensional random vector are known. After sampling at the sigma point, it is inserted into the nonlinear function f(·), and then the process noise in polar coordinates is obtained by weighted summation. and Statistical properties of

The specific steps for obtaining the mean and covariance of the uniform linear motion model and the uniformly accelerated linear motion model are as follows:

(1) According to the sigma point sampling rule, 2n+1 3D sample points are generated from the mean and variance of the 3D random vector;

(2) Calculate the sample points generated by the nonlinear function transformation in (1);

(3) Determine the weights of the mean and covariance of each three-dimensional sample point;

(4) Based on the weights obtained in (3), determine the mean and variance matrix of the mapping.

Optionally, the nonlinear function f(·) in the uniform linear motion model and the uniformly accelerated linear motion model is:

in, and are the tangential process noise and radial process noise of the uniform linear motion model; and are the tangential process noise and radial process noise of the uniformly accelerated linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniformly accelerated linear motion model; θ(k) is a random variable that obeys the normal distribution.

Optionally, the specific process of state initialization is:

(1) When the model is in uniform linear motion, N four-dimensional sample points are randomly generated according to the mean s(0) and covariance S(0) of the initial target state in the Cartesian coordinate system. j＝1,2,3…N; when the model is uniformly accelerated linear motion, N six-dimensional sample points are randomly generated according to the mean b(0) and covariance B(0) of the initial target state in the Cartesian coordinate system. _xj and _yj are the locations of random sample points, and is the velocity of the random sample point, and is the acceleration of the random sample point;

(2) Calculate the value η _j of each state point in polar coordinates;

(3) Calculate the mean and covariance of the state points in polar coordinates;

Optionally, the formula for calculating the value of each state point in polar coordinates under the uniform linear motion model is:

θ _j =arctan(y _j /x _j );

The formula for calculating the value of each state point in polar coordinates under the uniformly accelerated linear motion model is:

θ _j =arctan(y _j /x _j );

Optionally, the specific formula for one-step prediction of the target state and covariance is:

η(k+1,k)=Φ(k)η(k,k)+Γ(k)ω(k);

P(k+1,k)=Φ(k)P(k,k)Φ(k) ^T +Γ(k)Q(k)Γ(K) ^T ;

Where η(k+1,k) and P(k+1,k) are the target state and covariance predicted at time k, respectively, and Q(k) is the process noise covariance matrix.

Optionally, the specific steps of completing the target tracking state and covariance update at the current moment through minimum variance linear fusion are:

η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) ^-1 η(k+1,k)+P _z (k+1,k+ 1) ^-1 η _z (k+1,k)];

P(k+1,k+1)＝[P(k+1,k) ^-1 +P _z (k+1,k+1) ^-1 ] ^-1 ;

In the calculation, the observation vector and its covariance are expanded and the missing elements are set to zero to be suitable for matrix operations;

Among them, when the model is in uniform linear motion,

When the model is in uniformly accelerated linear motion,

Through the above technical solution, it can be known that compared with the prior art, the present invention discloses a method for realizing target tracking by using Doppler measurement in a polar coordinate system, which is different from all the nonlinear filtering algorithms with Doppler measurement in the prior art. It adopts a technical idea that is completely different from the previous algorithms, directly constructs the target state equation in polar coordinates, converts the strong nonlinear problem of Doppler measurement into a linear filtering problem, and then combines with the standard Kalman filter to complete the tracking, thus overcoming the strong nonlinearity between Doppler measurement and target state, being able to track the target with a smaller amount of calculation, and being able to greatly improve the target tracking accuracy.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

Figure 1 is a simplified flow chart of the method of the present invention;

FIG. 2a is a graph showing the error curves of different position tracking algorithms under a uniform linear motion model;

FIG2b is a graph showing the error curves of different tracking speed algorithms under a uniform linear motion model;

FIG3a is a graph showing the error curves of different position tracking algorithms under a uniformly accelerated linear motion model;

FIG3 b is a graph showing error curves of different tracking speed algorithms under a uniformly accelerated linear motion model.

DETAILED DESCRIPTION

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

The embodiment of the present invention discloses a method for implementing target tracking by using Doppler measurement in a polar coordinate system, as shown in FIG1 , comprising the following steps:

Step 1, determine the state equations of the uniform linear motion model and the uniform accelerated linear motion model containing radial velocity in polar coordinates and having a linear relationship with Doppler radar measurement;

Step 2: Convert the process noise in the Cartesian coordinate system of the uniform linear motion model and the uniformly accelerated linear motion model to polar coordinates, and use the Unscented transformation to calculate the mean and covariance of the process noise;

Step 3: Based on the prior information in Cartesian coordinates, the state equations of the uniform linear motion model and the uniform accelerated linear motion model are initialized, and the target state and covariance of the target in polar coordinates are initialized using the Monte Carlo method;

Step 4: At the current moment, a motion model is selected according to the prior information of the acceleration of the moving target, and the state transfer matrix of the state equation in polar coordinates, the process noise driving matrix and the statistical characteristics of the process noise are calculated;

Step 5: One-step prediction of the target state and covariance in polar coordinates;

Step 6: Combine the Doppler radar measurement value and complete the update of the target tracking state and covariance at the current moment through minimum variance linear fusion;

Step 7: Loop through steps 4-6 until target tracking is complete.

In a specific embodiment, the specific process of determining the state equation of the uniform linear motion model in polar coordinates is: converting the state equation in the Cartesian coordinate system to the polar coordinate system, and the state equation of the uniform linear motion model containing radial velocity in the polar coordinate system is expressed as:

η _RV-CV (k+1)=Φ _RV-CV (k) η _RV-CV (k) + Γ _RV-CV (k) ω _RV-CV (k);

In the formula, represents the state of the target at time k, θ(k) and r(k) are the true values of azimuth and distance respectively. are the angular velocity and radial velocity respectively; represents r(k), The covariance between Var[r(k)] represents where Φ _{RV-CV (k) is the variance of r(k), Φ RV} -CV (k) is the state transfer matrix, Γ _RV-CV (k) is the process noise driving matrix, and ω _RV-CV (k) is the process noise.

In a specific embodiment, the specific process of determining the state equation of the uniformly accelerated linear motion model in polar coordinates is: converting the state equation in the Cartesian coordinate system to the polar coordinate system, and the state equation of the uniformly accelerated linear motion model containing radial velocity in the polar coordinate system is expressed as:

η _RV-CA (k+1)=Φ _RV-CA (k)n RV _-CA (k)+Γ _RV-CA (k)ω _RV-CA (k);

In the formula, represents the state of the target at time k, T is the sampling time interval of the Doppler radar, θ(k) and r(k) are the true values of azimuth measurement and distance measurement, respectively. are the angular velocity and radial velocity respectively, are angular acceleration and radial acceleration respectively; represents r(k), The covariance between represent , Φ _RV-CA (k) is the state transfer matrix, Γ _RV-CA (k) is the process noise driving matrix, and ω _RV-CA (k) is the process noise.

In a specific embodiment, the Doppler radar position is located at the origin of the polar coordinate system, and the Doppler radar measurement equation is specifically expressed as:

Z _m (k) = f (X (k)) + V _m (k);

θ(k)=arctan(y(k)/x(k));

Where θ _m (k), r _m (k) and are azimuth measurement, distance measurement and Doppler measurement respectively; θ(k), r(k) and They are the true value of azimuth measurement, the true value of distance measurement and the true value of Doppler measurement respectively; and They are azimuth measurement noise, distance measurement noise and Doppler measurement noise, all of which are zero-mean Gaussian white noise, with variances of and (σ _θ , σ _r and is its corresponding standard deviation), and and Not relevant, and Not relevant, and The correlation coefficient is ρ, that is,

In a specific embodiment, step 2 specifically includes:

Given a three-dimensional random vector and The mean and variance of the sigma point are sampled and then input into the nonlinear function f(·), and then the process noise in polar coordinates is obtained by weighted summation. and Statistical properties of

Taking the uniform linear motion model as an example, find and The specific steps of the process are:

(1) According to the sigma point sampling rule, and Generate 2n+1 3D sample points;

Wherein, n=3; Representation Matrix The i-th column of the square root of the lower triangular decomposition of ; λ＝α ² (n+k)-n; α is a positive number, 10 ^-4 ≤α≤1; k＝3-n;

(2) Calculate the sample points generated by the nonlinear function transformation;

Y ⁽ⁱ⁾ = f[χ ⁽ⁱ⁾ ], i = 0~2n

(3) Determine the weights of the mean and covariance of each three-dimensional sample point;

Among them, the superscript m is the mean, c is the covariance; the subscript is the sampling point; for the normal distribution, β = 2 is the optimal value;

(4) Based on the weights obtained in (3), determine the mean and variance matrix of the mapping;

Here we take the uniform linear motion model as an example, and The process of obtaining , when it is a uniformly accelerated linear motion model, and The process of obtaining is the same as the above solution process.

In a specific embodiment, the nonlinear function f(·) in the uniform linear motion model and the uniform accelerated linear motion model is:

in, and are the tangential process noise and radial process noise of the uniform linear motion model; and are the tangential process noise and radial process noise of the uniformly accelerated linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniformly accelerated linear motion model; θ(k) is a random variable that obeys the normal distribution.

In a specific embodiment, the specific process of initializing the state is:

(1) When the model is in uniform linear motion, N four-dimensional sample points are randomly generated according to the mean s(0) and covariance S(0) of the initial target state in the Cartesian coordinate system. j＝1,2,3…N; when the model is uniformly accelerated linear motion, N six-dimensional sample points are randomly generated according to the mean b(0) and covariance B(0) of the initial target state in the Cartesian coordinate system. _xj and _yj are the locations of random sample points, and is the velocity of the random sample point, and is the acceleration of the random sample point;

(2) Calculate the value η _j of each state point in polar coordinates;

(3) Calculate the mean and covariance of the state points in polar coordinates;

In a specific embodiment, the formula for calculating the value of each state point in polar coordinates under the uniform linear motion model is:

θ _j =arctan(y _j /x _j );

The formula for calculating the value of each state point in polar coordinates under the uniformly accelerated linear motion model is:

θ _j =arctan(y _j /x _j );

In a specific embodiment, the specific formula for one-step prediction of the target state and covariance is:

η(k+1,k)=Φ(k)η(k,k)+Γ(k)ω(k);

P(k+1,k)=Φ(k)P(k,k)Φ(k) ^T +Γ(k)Q(k)Γ(K) ^T ;

Where η(k+1,k) and P(k+1,k) are the target state and covariance predicted at time k, respectively, and Q(k) is the process noise covariance matrix.

In a specific embodiment, the specific steps of completing the target tracking state and covariance update at the current moment through minimum variance linear fusion are:

η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) ^-1 η(k+1,k)+P _z (k+1,k+ 1) ^-1 η _z (k+1,k)];

P(k+1,k+1)＝[P(k+1,k) ^-1 +P _z (k+1,k+1) ^-1 ] ^-1 ;

In the calculation, the observation vector and its covariance are expanded and the missing elements are set to zero to be suitable for matrix operations; when the model is uniform linear motion,

When the model is in uniformly accelerated linear motion,

In a specific embodiment, the radar target tracking method of the present invention is used to track a target moving in a uniform linear motion in a two-dimensional space. The initial position of the target is (10km, 10km), the initial velocity is (8m/s, 10m/s), and the Doppler radar located at the origin of the coordinates provides the distance, azimuth and Doppler measurement of the target with a sampling period of 1s. The method proposed in this patent is compared with the SEKF, SUKF and SFPRE algorithms with Doppler measurement. The standard deviations of the measurement noise are σ _r = 100m, σ _θ = 1°, The correlation coefficient ρ = 0.5, and the simulation results of the root mean square error of position and velocity of different algorithms are shown in Figure 2a and Figure 2b.

In a specific embodiment, the radar target tracking method of the present invention is used to track a target moving in a uniformly accelerated linear motion in a two-dimensional space. The target initial position is (10km, 10km), the initial velocity is (8m/s, 10m/s), and the initial acceleration is (2m/s ² , 2m/s ² ). The Doppler radar located at the origin of the coordinate system provides the distance, azimuth, and Doppler measurements of the target with a sampling period of 1s. The method proposed in this patent is compared with the SEKF, SUKF, and SFPRE algorithms with Doppler measurement. The standard deviations of the measurement noise are σ _r = 100m, σ _θ = 1°, The correlation coefficient ρ = 0.5, and the simulation results of the root mean square error of position and velocity of different algorithms are shown in Figure 3a and Figure 3b.

As shown in Figures 2a, 2b, 3a and 3b, the position and velocity estimation accuracy of each method is continuously improved over time. Under different motion models, the method proposed in the present invention can reduce the influence of strong nonlinearity of Doppler measurement, and improve tracking accuracy and convergence speed. For the method proposed in the present invention, a linear Kalman filter can be used to process the state vector and the measurement vector to ensure the convergence of dynamic estimation.

In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A method for tracking a target using Doppler measurement in a polar coordinate system, comprising the following steps: Step 1, determine the state equations of the uniform linear motion model and the uniform accelerated linear motion model containing radial velocity in polar coordinates and having a linear relationship with Doppler radar measurement; Step 2: Convert the process noise in the Cartesian coordinate system of the uniform linear motion model and the uniformly accelerated linear motion model to polar coordinates, and use the Unscented transformation to calculate the mean and covariance of the process noise; Step 3: Based on the prior information in Cartesian coordinates, the state equations of the uniform linear motion model and the uniform accelerated linear motion model are initialized, and the target state and covariance of the target in polar coordinates are initialized using the Monte Carlo method; Step 4: At the current moment, a motion model is selected according to the prior information of the acceleration of the moving target, and the state transfer matrix of the state equation in polar coordinates, the process noise driving matrix and the statistical characteristics of the process noise are calculated; Step 5: One-step prediction of the target state and covariance in polar coordinates; Step 6: Combine the Doppler radar measurement value and complete the update of the target tracking state and covariance at the current moment through minimum variance linear fusion; Step 7: Loop through steps 4-6 until target tracking is complete. 2. The method for realizing target tracking by using Doppler measurement in polar coordinate system according to claim 1 is characterized in that the specific process of determining the state equation of the uniform linear motion model in polar coordinate system is: converting the state equation in Cartesian coordinate system to polar coordinate system, and the state equation of the uniform linear motion model containing radial velocity in polar coordinate system is expressed as: η _RV-CV (k+1)=Φ _RV-CV (k) η _RV-CV (k) + Γ _RV-CV (k) ω _RV-CV (k); In the formula, represents the state of the target at time k, θ(k) and r(k) are the true values of azimuth and distance respectively. are the angular velocity and radial velocity respectively; represents r(k), The covariance between Var[r(k)] represents where Φ _{RV-CV (k) is the variance of r(k), Φ RV} -CV (k) is the state transfer matrix, Γ _RV-CV (k) is the process noise driving matrix, and ω _RV-CV (k) is the process noise. 3. The method for realizing target tracking by using Doppler measurement in polar coordinate system according to claim 1 is characterized in that the specific process of determining the state equation of the uniformly accelerated linear motion model in polar coordinate system is: converting the state equation in Cartesian coordinate system to polar coordinate system, and the state equation of the uniformly accelerated linear motion model containing radial velocity in polar coordinate system is expressed as: η _RV-CA (k+1)=Φ _RV-CA (k)n RV _-CA (k)+Γ _RV-CA (k)ω _RV-CA (k); In the formula, represents the state of the target at time k, T is the sampling time interval of the Doppler radar, θ(k) and r(k) are the true values of azimuth measurement and distance measurement, respectively. are the angular velocity and radial velocity respectively, are angular acceleration and radial acceleration respectively; represents r(k), The covariance between represent , Φ _RV-CA (k) is the state transfer matrix, Γ _RV-CA (k) is the process noise driving matrix, and ω _RV-CA (k) is the process noise. 4. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, wherein the Doppler radar position is located at the origin of the polar coordinate system, and the equation for Doppler radar measurement is specifically expressed as: Z _m (k) = f (X (k)) + V _m (k); θ(k)=arctan(y(k)/x(k)); Where θ _m (k), r _m (k) and are azimuth measurement, distance measurement and Doppler measurement respectively; θ(k), r(k) and They are the true value of azimuth measurement, the true value of distance measurement and the true value of Doppler measurement respectively; and They are azimuth measurement noise, distance measurement noise and Doppler measurement noise, all of which are zero-mean Gaussian white noise, with variances of and _σθ , _σr and is its corresponding standard deviation, and and Not relevant, and Not relevant, and The correlation coefficient is ρ, that is, 5. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, wherein step 2 specifically comprises: The mean and variance of the three-dimensional random vector are known. After sampling at the sigma point, it is input into the nonlinear function f(), and then the process noise in polar coordinates is obtained by weighted sum. and Statistical properties of The specific steps for obtaining the mean and covariance of the uniform linear motion model and the uniformly accelerated linear motion model are as follows: (1) According to the sigma point sampling rule, 2n+1 3D sample points are generated from the mean and variance of the 3D random vector; (2) Calculate the sample points generated by the nonlinear function transformation in (1); (3) Determine the weights of the mean and covariance of each three-dimensional sample point; (4) Based on the weights obtained in (3), determine the mean and variance matrix of the mapping. 6. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 5, characterized in that the nonlinear function f() in the uniform linear motion model and the uniform accelerated linear motion model is: in, and are the tangential process noise and radial process noise of the uniform linear motion model; and are the tangential process noise and radial process noise of the uniformly accelerated linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniform linear motion model; and is the zero-mean Gaussian white noise in the X and Y directions of the uniformly accelerated linear motion model; θ(k) is a random variable that obeys the normal distribution. 7. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, wherein the specific process of performing state initialization is: (1) When the model is in uniform linear motion, N four-dimensional sample points are randomly generated according to the mean s(0) and covariance S(0) of the initial target state in the Cartesian coordinate system. When the model is uniformly accelerated linear motion, N six-dimensional sample points are randomly generated according to the mean b(0) and covariance B(0) of the initial target state in the Cartesian coordinate system. _xj and _yj are the locations of random sample points, and is the velocity of the random sample point, and is the acceleration of the random sample point; (2) Calculate the value η _j of each state point in polar coordinates; (3) Calculate the mean and covariance of the state points in polar coordinates; 8. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, characterized in that the formula for calculating the value of each state point in the polar coordinate system under the uniform linear motion model is: θ _j =arctan(y _j /x _j ); The formula for calculating the value of each state point in polar coordinates under the uniformly accelerated linear motion model is: θ _j =arctan(y _j /x _j ); 9. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, characterized in that the specific formula for one-step prediction of the target state and covariance is: η(k+1,k)=Φ(k)η(k,k)+Γ(k)ω(k); P(k+1,k)=Φ(k)P(k,k)Φ(k) ^T +Γ(k)Q(k)Γ(K) ^T ; Where η(k+1,k) and P(k+1,k) are the target state and covariance predicted at time k, respectively, and Q(k) is the process noise covariance matrix. 10. The method for realizing target tracking by using Doppler measurement in a polar coordinate system according to claim 1, characterized in that the specific steps of completing the target tracking state and covariance update at the current moment by minimum variance linear fusion are: η(k+1,k+1)＝P(k+1,k+1)[P(k+1,k) ^-1 η(k+1,k)+P _z (k+1,k+ 1) ^-1 η _z (k+1,k)]; P(k+1,k+1)＝[P(k+1,k) ^-1 +P _z (k+1,k+1) ^-1 ] ^-1 ; In the calculation, the observation vector and its covariance are expanded and the missing elements are set to zero to be suitable for matrix operations; Among them, when the model is in uniform linear motion, When the model is in uniformly accelerated linear motion, Where θ _m (k), r _m (k) and They are azimuth measurement, distance measurement and Doppler measurement respectively; and They are azimuth measurement noise, distance measurement noise and Doppler measurement noise, all of which are zero-mean Gaussian white noise, with variances of and _σθ , _σr and is its corresponding standard deviation, and and Not relevant, and Not relevant, and The correlation coefficient is ρ, that is,