A radar target tracking method based on a whirling electromagnetic wave radiation field

Abstract

The application discloses a radar target tracking method based on a vortex electromagnetic wave radiation field, and is applied to the vortex electromagnetic wave radiation field and comprises the following steps: step 100, determining predicted state transition information according to received state information of a target and first process noise; step 200, determining a measurement equation of the target according to the predicted state transition information and second process noise; step 300, determining a predicted measurement equation of the target according to the measurement equation and the predicted state transition information; and step 400, updating the predicted state transition information according to the predicted measurement equation to obtain target predicted state transition information. The application utilizes a mode domain of orbital angular momentum, adds a target azimuth as an observation variable on the basis of a plane wave, realizes accurate estimation of a motion parameter of the target, and improves target tracking precision.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a radar target tracking method based on vortex electromagnetic wave radiation field. Background Technology

[0002] Vortex electromagnetic waves and related concepts are important discoveries in electromagnetism in recent years. In addition to spin angular momentum (i.e., polarization), electromagnetic waves can also possess orbital angular momentum (OAM). Electromagnetic waves carrying OAM are called vortex electromagnetic waves. Compared to plane waves, vortex waves exhibit modal-dependent azimuth modulation phase. Where l is the mode number, representing the magnitude of the orbital angular momentum. The azimuth angle is the angle around the propagation axis. The echo signal's representation in the modal domain and azimuth domain forms a Fourier transform pair. Therefore, by performing a Fast Fourier Transform on the modal domain echo, the azimuth angle of the target can be directly extracted. Even if two targets are within the same range cell, they will exhibit phase differences in the echoes of different modes, thus allowing for resolution in the azimuth dimension. Therefore, vortex radar has a natural azimuth resolution capability.

[0003] Target tracking aims to obtain the target's motion parameters, enabling us to estimate the target's motion state. Target tracking typically uses sensors such as radar to observe the target, establish a motion state model, estimate the target's motion parameters, and finally combine the sensor observation data to achieve target tracking. The target tracking process includes point processing, correlation processing between points and tracks, prediction, and filtering. Among these, prediction and filtering are two crucial parts of target tracking. Prediction mainly addresses the problem of predicting the target's state information in the next tracking cycle, primarily including the prediction of motion state and the prediction of motion state covariance.

[0004] In plane wave radar systems, most methods for achieving azimuth resolution are based on the range-Doppler principle. Under this theory, the range resolution depends on the bandwidth of the transmitted radar signal, while the azimuth resolution depends on the radar's observation angle range. By increasing the transmitted signal bandwidth, the range resolution can meet the needs of most applications. However, in certain specific scenarios, such as active radar seeker terminal guidance and vehicle-mounted forward-looking scenarios, the target is located in the forward-looking area of ​​the observation platform, and the relative angle between the radar and the target is very small, making it virtually impossible to achieve high azimuth resolution. Therefore, during target tracking, the target azimuth angle cannot be used as a radar observation parameter, limiting tracking accuracy. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a radar target tracking method based on vortex electromagnetic wave radiation fields. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] A radar target tracking method based on vortex electromagnetic wave radiation field, applied under vortex electromagnetic wave radiation field, includes the following steps:

[0007] Step 100: Determine the predicted state transition information based on the received target state information and the first process noise;

[0008] Step 200: Determine the target's measurement equation based on the predicted state transition information and the second process noise;

[0009] Step 300: Determine the target's predictive measurement equation based on the measurement equation and the predicted state transition information;

[0010] Step 400: Update the predicted state transition information according to the predicted measurement equation to obtain the target predicted state transition information.

[0011] In one embodiment of the present invention, step 200 includes:

[0012] Step 210: Determine the target measurement vector of the nonlinear system based on the predicted state transition information and the second process noise;

[0013] Step 220: Determine the target measurement equation based on the nonlinear system target measurement vector and the second process noise.

[0014] In one embodiment of the present invention, step 400 includes:

[0015] Step 410: Determine the state information based on the predicted measurement equation and the nonlinear system target measurement vector;

[0016] Step 420: Update the predicted state transition information based on the state information covariance and the state information to obtain the target predicted state transition information.

[0017] In one embodiment of the present invention, step 420 includes:

[0018] Step 421: Determine the prediction covariance based on the state information covariance, the nonlinear system function, and the noise of the third process;

[0019] Step 422: Determine the innovation covariance based on the predicted covariance, the nonlinear system function, and the fourth process noise;

[0020] Step 423: Determine the Kalman filter gain based on the predicted covariance, the measurement equation, and the innovation covariance;

[0021] Step 424: Determine the predicted state transition information for the next time step based on the predicted state transition information, the state information, and the Kalman filter gain;

[0022] Step 425: Update the state information covariance based on the Kalman filter gain, the nonlinear system function, and the predicted covariance;

[0023] Step 426: Repeat steps 421-425 until the preset conditions are met to obtain the target predicted state transition information.

[0024] In one embodiment of the present invention, the expression for the state information of the target is:

[0025]

[0026] Where, x k and y k Indicates the target in discrete time t k The location at any given moment.

[0027] In one embodiment of the present invention, the expression for the predicted state transition information is:

[0028]

[0029] in, Let T represent the state transition matrix, T represent the sampling period, and W(k) represent the noise of the first process.

[0030] In one embodiment of the present invention, the expression for the target measurement vector of the nonlinear system is:

[0031]

[0032] Where h(·) represents the nonlinear system function, and V(k+1) represents the noise of the second process.

[0033] In one embodiment of the present invention, the expression of the measurement equation is:

[0034]

[0035] Where V(k+1) represents the noise of the second process, The azimuth of the target is represented by r(k+1), and the distance to the target is represented by r(k+1).

[0036] In one embodiment of the present invention, the predictive measurement equation is:

[0037]

[0038] In one embodiment of the present invention, the expression for the state information is:

[0039]

[0040] The beneficial effects of this invention are:

[0041] This invention utilizes the modal domain of orbital angular momentum to add the target azimuth angle as an observation on top of plane wave radar. The vortex electromagnetic wave carrying orbital angular momentum has a spatial helical structure around the beam axis in its phase wavefront. This spatial difference in phase distribution allows the radar to maintain azimuth resolution even with a small relative rotation angle between the radar and the target, providing a new dimension of observational information for target tracking. Compared to traditional plane wave radar, it can more accurately estimate target motion parameters, achieving accurate estimation of target motion parameters and improving target tracking accuracy.

[0042] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0043] Figure 1 A flowchart illustrating steps 300 and 400 provided in an embodiment of the present invention;

[0044] Figure 2 A comparison diagram of CRLB curves under vortex wave and plane wave modes provided in an embodiment of the present invention;

[0045] Figure 3a This is the result of estimating the position parameters of a moving target under the vortex electromagnetic wave system provided in the embodiments of the present invention;

[0046] Figure 3b This is the velocity parameter estimation result of a moving target under the vortex electromagnetic wave system provided in the embodiments of the present invention;

[0047] Figure 4a This is the result of estimating the position parameters of a moving target under a plane wave system in an embodiment of the present invention;

[0048] Figure 4b This is the estimation result of the velocity parameters of the moving target under the plane wave system in the embodiment of the present invention;

[0049] Figure 5a This is a comparison diagram of the position coordinate estimation errors of vortex waves and plane waves in an embodiment of the present invention;

[0050] Figure 5b This is a comparison diagram of the target velocity estimation errors of vortex waves and plane waves in an embodiment of the present invention. Detailed Implementation

[0051] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0052] A radar target tracking method based on vortex electromagnetic wave radiation field, applied to the radiation field formed by vortex electromagnetic waves emitted by radar, includes the following steps:

[0053] Step 100: Determine the predicted state transition information based on the received target state information and the first process noise.

[0054] A detection model under the vortex electromagnetic wave radiation field is established. The information received by the radar and the target motion state are represented by state transition equations and measurement equations, respectively, reflecting the input-output relationship of the system. The input is represented by the state transition equation, which consists of a certain time function and noise representing random fluctuations. The output is represented by the measurement equation, which is a function of the state vector and is usually subject to disturbances by random measurement errors.

[0055] Specifically, firstly, the target's state information received by the radar is represented by a state transition equation. The target's state information includes its position and velocity.

[0056] Assuming a target moves at a constant velocity in a two-dimensional plane, then the moving target in discrete time t k Time and location information (x) k ,y k This can be represented as:

[0057]

[0058] In the above formula, (x0, y0) is the initial position of the target, and v x With v y These represent the target's velocity along the horizontal and vertical axes, respectively, and T is the sampling period. The above equation can be expressed recursively as follows:

[0059]

[0060] in, They represent x respectively k ,y k The result of taking the first derivative with respect to time.

[0061] In reality, a target's motion is almost never perfectly uniform linear; its velocity will inevitably fluctuate to varying degrees due to human or environmental factors. These minute changes can be considered process noise. After introducing process noise, the target's equation of motion becomes:

[0062]

[0063] Among them, v x With v y These represent the target's velocity along the horizontal and vertical axes, respectively. Additionally, the target's velocity can be expressed as:

[0064]

[0065] In the uniform velocity model, the state vector is used. To describe the dynamic characteristics of the system (the state information of the target), the predicted state transition information (state transition equation) in matrix form is as follows:

[0066]

[0067] Wherein, W(k) represents the noise of the first process, which has a mean of 0 and a variance of σ. 2 Gaussian white noise. The above equation can be rewritten as:

[0068]

[0069] in, Let be the state transition matrix.

[0070] Step 200: Determine the target's measurement equation based on the predicted state transition information and the second process noise. Specifically, express the target's motion state using measurement equations. Step 200 includes steps 210-220:

[0071] Step 210: Determine the target measurement vector of the nonlinear system based on the predicted state transition information and the second process noise.

[0072] To represent the measurement process of sensors such as radar, the measurement equation in a plane wave system typically uses the target distance measured by radar as the observation. However, because vortex electromagnetic waves have inherent azimuth resolution, the observation in a vortex electromagnetic wave system includes the target's azimuth angle, which is the positional information. The measurement equation (target measurement vector in a nonlinear system) is as follows:

[0073]

[0074] h(·) represents the nonlinear system function (the nonlinear radar system function), and V(k+1) represents the noise of the second process, which has a mean of 0 and a variance of σ. 2 Gaussian white noise.

[0075] Step 220: Determine the target measurement equation based on the nonlinear system target measurement vector and the second process noise. The measurement equation under the vortex electromagnetic wave system is expressed as:

[0076]

[0077] Let r(k+1) represent the azimuth of the target and r(k+1) represent the distance to the target. Expanding the above formula, we can obtain:

[0078]

[0079] A single snapshot of a vortex electromagnetic wave can obtain the target's range and azimuth information. Under the same snapshot conditions, plane waves can only use range information as a measurement, while the vortex electromagnetic wave system can use both azimuth and range as measurements simultaneously, thus increasing the amount of information obtained from the observation.

[0080] Step 300: Determine the target's predictive measurement equation based on the measurement equation and the predicted state transition information. For example... Figure 1 As shown, the Extended Kalman Filter (EKF) is an extension of the standard Kalman filter for nonlinear cases. The EKF performs a Taylor expansion of the nonlinear function, omitting higher-order terms and retaining only the first-order terms to linearize the nonlinear function. Finally, it uses the Kalman filter algorithm to approximate the system's state and variance estimates, thus filtering the signal.

[0081] In this step, Taylor expansion is used to linearize the nonlinear function, and a one-step prediction of the state is performed. The predicted measurement equation is obtained based on the measurement equation:

[0082]

[0083] Step 400: Update the predicted state transition information according to the predicted measurement equation to obtain the target predicted state transition information. Step 400 includes steps 410-420:

[0084] Step 410: Determine the state innovation based on the predictive measurement equation and the nonlinear system target measurement vector. Specifically, in this step, the state innovation expression is obtained by subtracting the predictive measurement equation from the nonlinear system target measurement vector:

[0085]

[0086] Step 420: Update the predicted state transition information based on the state information covariance and state innovation to obtain the target predicted state transition information. Step 420 includes steps 421-426:

[0087] Step 421: Determine the prediction covariance based on the state information covariance, the nonlinear system function, and the third process noise. In this step, the state information covariance is predicted, where the state information covariance is: in, Z represents the error value of the state information. k ={Z(j),j=1,2,...,k}.

[0088] The predicted covariance is: P(k+1|k)=h X (k)P(k|k)h X '(k)+Q(k);

[0089] Among them, h X (k) represents the Jacobian matrix of the nonlinear system function, h X '(k) denotes the transpose of the Jacobian matrix.

[0090] Step 422: Determine the innovation covariance based on the prediction covariance, the nonlinear system function, and the fourth process noise. The formula for calculating the innovation covariance is:

[0091] S(k+1)=h X (k+1)P(k+1|k)h X '(k+1)+R(k+1);

[0092] Where R(k+1) represents the measurement noise covariance.

[0093] Step 423: Determine the Kalman filter gain based on the prediction covariance, measurement equation, and innovation covariance. The formula for calculating the Kalman filter gain is:

[0094] K(k+1)=P(k+1|k)H'(k+1)S -1 (k+1).

[0095] Step 424: Determine the predicted state transition information for the next time step based on the predicted state transition information, the state innovation, and the Kalman filter gain.

[0096]

[0097] Step 425: Update the state information covariance based on the Kalman filter gain, nonlinear system function, and predicted covariance. The update equation is:

[0098] P(k+1|k+1)=[IK(k+1)h X (k+1)]P(k+1|k)[I+K(k+1)h X (k+1)]'-K(k+1)R(k+1)K'(k+1). Where I is the identity matrix.

[0099] Step 426: Repeat steps 421-425 until the preset conditions are met to obtain the target predicted state transition information. In this step, based on the updated state information covariance, the above steps can be returned to continue covariance prediction. Then, based on the new predicted covariance, the updated innovation covariance is calculated. Next, the updated Kalman filter gain is calculated, and the predicted state transition information is updated based on the updated Kalman filter gain. This process is repeated until the preset conditions are met. Finally, after multiple iterations, the updated predicted state transition information is obtained, which is the motion parameter to be estimated, i.e., the target's predicted state transition information (target predicted state transition information). The preset condition for iteration is the maximum number of iterations.

[0100] In this embodiment, the Cramer-Rao lower bound (CRLB) for parameter estimation under plane wave and vortex wave modes can be calculated respectively to evaluate the tracking accuracy of the present invention.

[0101] First, CRLB is calculated under the vortex electromagnetic wave system.

[0102] The measurement equations under the vortex electromagnetic wave system can be written in the following form:

[0103] H[n]=f(X)+w1[n]n=0,1...N-1;

[0104] Where w1[n] is a variable with a mean of 0 and a variance of σ. 2 The noise is Gaussian white noise, N is the number of samples, and X is the state vector. Since w1[n] follows a Gaussian distribution, the likelihood function can be obtained as follows:

[0105]

[0106] Where θ=[x,y,v] x ,v y Let ] be the state vector. Taking the logarithm of the likelihood function, we can express it as:

[0107]

[0108] The final inverse of the Fisher information matrix is:

[0109]

[0110] Then, the CRLB is calculated under the plane wave system:

[0111] The measurement equation under a plane wave system can be written in the following form:

[0112]

[0113] Where w2[n] is a variable with a mean of 0 and a variance of σ. 2 Gaussian white noise, where N is the number of samples.

[0114] Similar to the calculation steps for vortex waves, the likelihood function is first obtained based on the measurement equations for plane waves. Then, the logarithm of the likelihood function is taken, and finally, the inverse of the Fisher information matrix under the plane wave regime can be obtained based on the log-likelihood function.

[0115]

[0116] The diagonal elements of the inverse Fisher information matrix are lower bounds on the variances of the estimates of the four motion state parameters of the target. The difference between the diagonal elements yields the following expression:

[0117]

[0118] As can be seen from the above formula, the lower bound of the estimated variance of each motion parameter under the vortex electromagnetic wave system is significantly smaller than that under the plane wave system. Figure 2 The CRLB curves for vortex wave and plane wave systems are presented. The figures show that the CRLB decreases slowly with increasing observation period, and the CRLB of the vortex electromagnetic wave estimation variance is significantly smaller than that of the plane wave estimation variance. Therefore, from the perspective of deriving the Cramero lower bound, the tracking accuracy under the vortex electromagnetic wave system is significantly superior to that under the plane wave system.

[0119] In this embodiment, by utilizing the modal domain of orbital angular momentum, the target azimuth angle is added as an observation on top of the plane wave. The vortex electromagnetic wave carrying orbital angular momentum has a spatial helical structure around the beam axis in its phase wavefront. This spatial difference in phase distribution allows the radar to maintain azimuth resolution even with a small relative rotation angle between the radar and the target, providing a new dimension of observation information for target tracking. Compared to traditional plane wave radar, it can more accurately estimate target motion parameters, achieving accurate estimation of target motion parameters and improving target tracking accuracy.

[0120] The following simulation data processing results further illustrate the correctness and effectiveness of the present invention.

[0121] The simulation experiments of this invention were implemented using Matlab simulation software.

[0122] Suppose there is a tracking radar used to detect a moving target in a plane. The moving target's motion is a typical uniform linear motion. The target's initial state is known, with an initial position of (50m, 25m), an x-axis velocity of 5m / s, a y-axis velocity of 10m / s, and a radar scan cycle of 200. The system's observation noise is represented by a Gaussian white noise.

[0123] Figure 3a , Figure 3b , Figure 4a and Figure 4b The parameter estimation results for moving targets under vortex electromagnetic wave and plane wave modes are presented respectively. The figures show that under the vortex electromagnetic wave mode, both the estimated velocity and coordinate values ​​are basically consistent with the actual values. However, under the plane wave mode, as the observation period increases, the predicted position coordinates gradually deviate from the actual values, while the predicted velocity, although trending in the same direction, shows a significant error.

[0124] from Figure 5a It can be seen that as the number of observation periods increases, the coordinate estimation error of the plane wave gradually increases, while the coordinate estimation error of the vortex electromagnetic wave basically oscillates around the zero line. Furthermore, the coordinate estimation error of the plane wave is consistently greater than that of the vortex electromagnetic wave. From... Figure 5b It can be seen that the velocity estimation error of the plane wave is always greater than that of the vortex electromagnetic wave. From the perspective of comparing estimation errors, the target tracking accuracy under the vortex electromagnetic wave system is greater than that under the plane wave system. Therefore, this simulation verifies the correctness and effectiveness of the present invention.

[0125] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media that can store program code, such as ROM, RAM, magnetic disk, or optical disk.

[0126] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0127] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0128] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A radar target tracking method based on vortex electromagnetic wave radiation field, characterized in that, Applied to vortex electromagnetic wave radiation fields, the following steps are included: Step 100: Determine the predicted state transition information based on the received target state information and the first process noise; the expression for the predicted state transition information is: ； in, Represents the state transition matrix. Indicates the sampling period. This indicates noise in the first process; ; and Indicates the target in discrete time The position at that moment; They represent The result of taking the first derivative with respect to time; Step 200, determining the target's measurement equation based on the predicted state transition information and the second process noise, includes: Step 210: Determine the target measurement vector of the nonlinear system based on the predicted state transition information and the second process noise; the target measurement vector of the nonlinear system is expressed as: ； Represents a nonlinear system function. This represents the noise in the second process, which has a mean of 0 and a variance of... Gaussian white noise; Step 220: Determine the target measurement equation based on the nonlinear system target measurement vector and the second process noise; Step 300: Determine the target's predictive measurement equation based on the measurement equation and the predicted state transition information; Step 400: Update the predicted state transition information according to the predicted measurement equation to obtain the target predicted state transition information.

2. The radar target tracking method based on vortex electromagnetic wave radiation field according to claim 1, characterized in that, Step 400 includes: Step 410: Determine the state information based on the predicted measurement equation and the nonlinear system target measurement vector; Step 420: Update the predicted state transition information based on the state information covariance and the state information to obtain the target predicted state transition information.

3. The radar target tracking method based on vortex electromagnetic wave radiation field according to claim 2, characterized in that, Step 420 includes: Step 421: Determine the prediction covariance based on the state information covariance, the nonlinear system function, and the noise of the third process; Step 422: Determine the innovation covariance based on the predicted covariance, the nonlinear system function, and the fourth process noise; Step 423: Determine the Kalman filter gain based on the predicted covariance, the measurement equation, and the innovation covariance; Step 424: Determine the predicted state transition information for the next time step based on the predicted state transition information, the state information, and the Kalman filter gain; Step 425: Update the state information covariance based on the Kalman filter gain, the nonlinear system function, and the predicted covariance; Step 426: Repeat steps 421-425 until the preset conditions are met to obtain the target predicted state transition information.

4. The radar target tracking method based on vortex electromagnetic wave radiation field according to claim 1, characterized in that, The expression for the measurement equation is: ； in, This indicates noise in the second process. Indicates the azimuth of the target. Indicates the distance to the target.

5. A radar target tracking method based on vortex electromagnetic wave radiation field according to claim 4, characterized in that, The prediction measurement equation is: 。 6. The radar target tracking method based on vortex electromagnetic wave radiation field according to claim 5, characterized in that, The expression for the status information is: 。

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