A coordinate system transformation fusion filtering tracking method and system for dual-base station radars

Abstract

The application discloses a coordinate system transformation fusion filtering tracking method and system for a dual-base station radar, and relates to the technical field of radar target tracking. The method comprises the following steps: firstly, establishing state and observation equations, and determining an initial state of a target based on prior information in a Cartesian coordinate system. Then, a target motion state is obtained through one-step prediction, sigma points are generated by using U transformation, and a mean value and a covariance of state space prediction are calculated and constructed. Next, measurement data and prediction data are fused by using a Kalman filter to obtain optimal state estimation and a covariance matrix. Finally, the updated state estimation is converted back to the Cartesian coordinate system based on U transformation, and the process is repeated until the tracking is completed. The application can avoid the nonlinear filtering problem in the updating process, and improves the robustness and precision of tracking.

Description

Technical Field

[0001] This invention relates to the field of radar target tracking technology, and in particular to a coordinate system transformation fusion filtering tracking method and system for dual-base station radar. Background Technology

[0002] In modern aerospace defense systems, continuous surveillance of stealth aircraft is a crucial issue for national security. With the iterative upgrades in stealth technology, the radar cross-section (RCS) of aircraft has significantly decreased, leading to a continuous attenuation of secondary reflected signals. Faced with this challenge, traditional monostatic radar systems (including pulse-Doppler radar and bistatic / multistatic radar) are increasingly showing limitations in anti-stealth operations. Active radar, due to the need to continuously emit detection electromagnetic waves, exposes its own radiation source characteristics while searching for targets, making it vulnerable to targeting and attack by anti-radiation weapons. Purely passive radar, relying on receiving electromagnetic leakage signals from targets, is increasingly limited in detection efficiency due to the advancements in electromagnetic silence technology for stealth platforms. Furthermore, the high false alarm rate in complex electromagnetic environments makes it difficult to build a reliable air situation monitoring system. Dual-base station radar, through a spatially separated transmitter and receiver architecture, organically integrates the technological advantages of active and passive radar. Its working principle is as follows: several radiating nodes are responsible for electromagnetic illumination of the warning airspace, while covertly deployed receiver nodes constitute the monitoring station. Due to the spatial decoupling between the radiation source and the receiving unit, targets find it difficult to implement effective electromagnetic evasion strategies. This new radar system exhibits highly flexible deployment characteristics, utilizing existing radar facilities' physical platforms and embedding new sensor nodes to construct multi-base detection arrays adapted to different battlefield environments. The system's comprehensive advantages are mainly reflected in three aspects: significantly improving the battlefield survivability of the radiation source, enabling dynamic reconfiguration of sensor resources, and effectively enhancing the collaborative combat effectiveness of regional air defense and anti-missile systems.

[0003] A dual-base station radar is a unified radar system consisting of one or more transmitters and one or more receivers. It uses only one transmitter / receiver unit and is a fundamental component of multi-station radar. Dual-base station radar can detect, locate, measure velocity, and track targets. Compared to single-base station radar, dual-base station radar offers the following advantages: it can detect targets from multiple directions, facilitating target identification and anti-stealth detection; it improves the probability of target detection and the continuity of target position and trajectory; transmitters operating in different frequency bands can work alternately, improving the system's anti-interference capabilities and reliability; and it enhances system survivability, preventing system collapse due to malfunctions in local transmitters or receivers.

[0004] Since its inception in the 1960s, the Kalman filter algorithm has been widely used in communications, power, aerospace, and industrial control due to its ability to predict system states using state equations and update them with minimum mean square error estimates based on observation data. While Kalman filtering performs well in linear Gaussian systems, its direct application in nonlinear systems is limited. In dual-base station radar target tracking, the target information acquired by the radar includes range, angle, and Doppler velocity. This observation data not only contains errors but also exhibits a nonlinear relationship with the target's state in Cartesian coordinates. To achieve continuous target tracking, nonlinear filtering techniques based on Kalman filtering have emerged. The Extended Kalman Filter (EKF) is a commonly used method, which linearizes the nonlinear equations through Taylor series expansion, facilitating engineering implementation. However, EKF has lower accuracy when handling high-dimensional and strongly nonlinear systems, and the calculation of the Jacobian matrix is ​​complex. The Unscented Kalman Filter (UKF) and the Sigma-Point Transform Kalman Filter (SPTKF) are representative deterministic sampling methods. UKF predicts data through unscented transformation, while SPTKF approximates the posterior probability distribution by measuring data through unscented transformation, thus avoiding the local linearization problem of EKF. Nevertheless, these methods still have shortcomings in terms of accuracy, time complexity, and consistency. Although nonlinear filtering techniques such as EKF and UKF have made some progress in radar target tracking, their performance remains poor in high-dimensional, strongly nonlinear scenarios. Summary of the Invention

[0005] The purpose of this invention is to provide a coordinate system transformation fusion filtering tracking method and system for dual-base station radar, which can avoid nonlinear filtering problems in the update process and improve the robustness and accuracy of tracking.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A coordinate system transformation fusion filtering tracking method for dual-base station radar includes:

[0008] Based on the kinematic characteristics of the target, the state equation and observation equation of the dual-base station radar tracking system for the moving target are established, and the initial motion state and initial covariance of the target are determined based on the prior information of the target in Cartesian coordinates.

[0009] Based on the target's motion state and covariance in the Cartesian state space at time k, a one-step prediction is performed to obtain the target's motion state at time k+1; the target's motion state at time k+1 includes the target's predicted state and the predicted covariance matrix.

[0010] Based on the U-transformation, a set of sigma points are generated for the target's predicted state and prediction covariance matrix, and 2n+1 sigma points are generated for the target's n-dimensional motion state in the Cartesian coordinate system. The mean and covariance of the constructed state space prediction are then calculated by weighting.

[0011] The measurement data and prediction data are fused using a Kalman filter to obtain the optimal state estimate and covariance matrix at time k+1 after fusion; the measurement data is obtained by radar measurement; the prediction data is the mean and covariance of the state space prediction.

[0012] Based on the U-transformation, 2n+1 sigma points are generated according to the updated optimal state estimate and the updated covariance matrix at time k+1. Each sigma point in the constructed state space is transformed to the Cartesian coordinate system using the transformation formula, and the mean of the optimal state estimate and the covariance matrix in the Cartesian coordinate system are calculated by weighting.

[0013] Repeat the steps until the tracing is complete.

[0014] Optionally, the establishment of state equations and observation equations for the moving target in the dual-base station radar tracking system based on the target's kinematic characteristics, and the determination of the target's initial motion state and initial covariance based on the target's prior information in Cartesian coordinates, specifically includes:

[0015] Based on the kinematic characteristics of the target, the state equation and observation equation for the moving target of the dual-base station radar tracking system are established, and the formulas are as follows:

[0016] X(k)=F(k)·X(k-1)+G(k)·w(k)

[0017] Z(k)=h(X(k))+v(k)

[0018] Among them, X z (k)=[x(k)x′(k)y(k)y′(k)] is a state vector directly constructed from the received radar observations. This vector represents the target's motion state at time k, i.e., the state at time k in the target's state equation, namely X(k), is substituted into this vector. x(k), x′(k), y(k), and y′(k) are the target's x-direction distance, x-direction velocity, y-direction distance, and y-direction velocity relative to the receiving radar at time k, respectively. F(k), G(k), w(k), and h are the state transition matrix, noise figure matrix, process noise, and observation function, respectively, where w(k)=[w x (k)w y (k)] T w x (k) and w y (k) represents the process noise in the x and y directions, respectively, Zz (k)=[R(k)θ(k)] T Let be the observation vector of the receiving radar at time k, affected by noise interference. This vector represents the target state observed at time k, i.e., the state at time k, Z(k), is substituted into the target observation equation. Here, R(k) is the sum of the distances between the transmitting and receiving radars and the moving target at time k, θ(k) is the angle between the receiving radar and the moving target at time k, and v(k) = [v...]. r (k)v α (k)] Τ For the radar observation noise received at time k, v r (k) represents the measurement distance noise at time k, v α (k) The measurement angle noise at time k is all zero-mean Gaussian white noise, v r (k) and v α (k) are uncorrelated, and the noise covariance matrix is: The specific formula for the observation function h is:

[0019]

[0020] Among them, Z true (k) represents the actual observation state without noise at time k, and L is the distance between the receiving radar and the transmitting radar;

[0021] For a moving target, the initial motion state X(1) and initial covariance P(1) of the target are obtained based on the prior information of the target in Cartesian coordinates.

[0022] Optionally, the motion state of the target at time k+1 is specifically represented as follows:

[0023] X k+1|k =F(k)X(k)

[0024] P k+1|k =F(k)P(k)F(k) Τ +G(k)Q(k)G(k) Τ

[0025] Among them, X k+1|k P k+1|k Let Q(k) be the predicted state and the predicted covariance matrix at time k, respectively, and let Q(k) be the covariance matrix of the process noise.

[0026] Optionally, the step of generating a set of sigma points based on the U-transform for the target's predicted state and prediction covariance matrix, and generating 2n+1 sigma points for the target's n-dimensional motion state in the Cartesian coordinate system, and weighting them to calculate the mean and covariance of the constructed state space prediction, specifically includes:

[0027] Based on the U-transform, predict the target state X at the current time k. k+1|k And the predicted covariance matrix P k+1|k Generate a set of sigma points. For its n-dimensional motion state in the Cartesian coordinate system, generate 2n+1 sigma points. The specific formula is as follows:

[0028] x k (0) =X k+1|k

[0029]

[0030] Where i = 1, 2, ..., n, λ = α 2 (n+κ)-n, where α and κ are scaling parameters used to adjust the distribution of σ points; x k This represents the sigma point generated in the Cartesian coordinate system, while x... k (i) Let represent the i-th sigma point. The formula for the weight of each sigma point is as follows:

[0031]

[0032] Where β is a parameter used to fuse observation noise, W m and W c These are the weights of the mean and covariance, respectively, both being vectors of 2n+1.

[0033] Each sigma point in the Cartesian coordinate system is transformed into a constructed state space using a transformation formula. Specifically, the constructed state space is based on the target's position and velocity states in a two-dimensional polar coordinate system, including the distance r1 between the target and the receiving radar, and the target's tangential velocity v. r1 1. Distance r2 between the target and the transmitting radar; 2. Normal velocity v of the target t The angle θ formed by the target and the receiving radar is used as a vector to describe the target's state, denoted as:

[0034] The mean and covariance of the constructed state-space prediction are calculated using a weighted average. The specific formula for the calculation is as follows:

[0035]

[0036] Among them, W m (i) W represents the mean weight of the i-th sigma point. c (i) Let f represent the covariance weight of the i-th sigma point, and f be the nonlinear transformation function from the Cartesian coordinate system to the constructed state space. The specific transformation method is shown in the following formula:

[0037]

[0038] v t =-v x sinθ+v y cosθ

[0039] Where L is the distance between the receiving radar and the transmitting radar, x is the distance of the target relative to the receiving radar in the x-direction, and v x Let x be the target's velocity relative to the receiving radar, y be the target's distance relative to the receiving radar, and v be the distance in the x-direction. y Let y be the target's velocity relative to the receiving radar.

[0040] Optionally, the optimal state estimate and covariance matrix at time k+1 are expressed as:

[0041] K k+1 = pol P k+1|k T H T (H pol P k+1|k H T +R k ) -1

[0042]

[0043] pol P k+1|k+1 =(IK k+1 H) pol P k+1|k

[0044] Among them, K k+1 It is the Kalman gain at time k+1. This is the optimal state estimate after the update at time k+1. pol P k+1|k+1 This is the updated covariance matrix, where I is the identity matrix, H is the observation matrix of the target observed by the received radar, and z k+1 Let be the observation vector received by the radar at time k+1.

[0045] Optionally, the step of generating 2n+1 sigma points based on the U-transformation, according to the updated optimal state estimate and the updated covariance matrix at time k+1, transforming each sigma point in the constructed state space to the Cartesian coordinate system using a transformation formula, and then weighted and calculating the mean of the optimal state estimate and the covariance matrix in the Cartesian coordinate system, specifically includes:

[0046] Based on the U-transform, the optimal state is estimated after the update at time k+1. With the updated covariance matrix pol P k+1|k+1 The formula for generating 2n+1 sigma points is as follows:

[0047]

[0048] in, pol X k+1 To construct the sigma points generated in the construction space, pol X k+1 (i) Let i be the i-th sigma point;

[0049] Each sigma point in the constructed state space is transformed to Cartesian coordinates using a transformation formula, and the mean and covariance matrix of the optimal state estimate in Cartesian coordinates are calculated using weighted summations. The specific formulas are as follows:

[0050]

[0051] Where g is the nonlinear transformation function from the state space to the Cartesian coordinate system, and the specific transformation method is shown in the following formula:

[0052] R = r1 + r2

[0053]

[0054] Where L is the distance between the receiving radar and the transmitting radar, and R is the sum of the distances of the moving target from the transmitting radar and the receiving radar.

[0055] Optionally, the target motion state in the constructed state space is represented as:

[0056]

[0057] Where r1(k) represents the distance between the receiving radar and the moving target at time k. Let rk represent the radial velocity of the moving target relative to the receiving radar at time k, and let r2(k) represent the distance between the transmitting radar and the moving target at time k. t θ(k) represents the tangential velocity of the moving target relative to the receiving radar at time k, and θ(k) represents the angle of the moving target relative to the receiving radar at time k.

[0058] The present invention also provides a coordinate system transformation fusion filtering tracking system for dual-base station radar, comprising:

[0059] The initial state construction module is used to establish the state equation and observation equation of the dual-base station radar tracking system for moving targets based on the kinematic characteristics of the targets, and to determine the initial motion state and initial covariance of the targets based on the prior information of the targets in Cartesian coordinates.

[0060] A one-step prediction module is used to make a one-step prediction based on the motion state and covariance of the target at time k in the Cartesian state space, so as to obtain the motion state of the target at time k+1; the motion state of the target at time k+1 includes the target predicted state and the predicted covariance matrix.

[0061] The first U-transform module is used to generate a set of sigma points for the target's predicted state and prediction covariance matrix based on the U-transform, and to generate 2n+1 sigma points for the target's n-dimensional motion state in the Cartesian coordinate system, and to calculate the mean and covariance of the constructed state space prediction by weighting.

[0062] The fusion module is used to fuse measurement data and prediction data using a Kalman filter to obtain the optimal state estimate and covariance matrix at time k+1 after fusion; the measurement data is obtained by radar measurement; the prediction data is the mean and covariance of the state space prediction.

[0063] The second U-transformation module is used to generate 2n+1 sigma points based on the U-transformation, according to the updated optimal state estimate and the updated covariance matrix at time k+1. It then uses the transformation formula to transform each sigma point in the constructed state space to the Cartesian coordinate system and calculates the mean of the optimal state estimate and the covariance matrix in the Cartesian coordinate system using weighted calculation.

[0064] The loop module is used to loop through the steps until the tracing ends.

[0065] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0066] This invention discloses a coordinate system transformation fusion filtering tracking method and system for dual-base station radar. The method includes first establishing state and observation equations and determining the initial state of the target based on prior information in Cartesian coordinates. Then, the target motion state is obtained through one-step prediction, and sigma points are generated using U-transform to calculate the mean and covariance of the constructed state space prediction. Next, the measurement data and prediction data are fused using a Kalman filter to obtain the optimal state estimate and covariance matrix. Finally, the updated state estimate is transformed back to the Cartesian coordinate system based on U-transform, and this process is repeated until tracking ends. This invention avoids nonlinear filtering problems in the update process, improving the robustness and accuracy of tracking. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is a flowchart of the coordinate system transformation fusion filtering tracking method used for dual-base station radar in this embodiment;

[0069] Figure 2 This is a schematic diagram of the state space constructed based on dual-base station radar observations and target motion state in this embodiment;

[0070] Figure 3 This is a schematic diagram of the RMSE results for target location estimation using various methods in this embodiment;

[0071] Figure 4 This is a schematic diagram of the RMSE results for target velocity estimation using various methods in this embodiment. Detailed Implementation

[0072] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0073] The purpose of this invention is to provide a coordinate system transformation fusion filtering tracking method and system for dual-base station radar, which can avoid nonlinear filtering problems in the update process and improve the robustness and accuracy of tracking.

[0074] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0075] This invention provides a coordinate system transformation fusion filtering tracking method for dual-base station radar, comprising:

[0076] S1: Based on the kinematic characteristics of the target, the state equation and observation equation of the dual-base station radar tracking system for the moving target are established, and their formulas are as follows:

[0077] X(k)=F(k)·X(k-1)+G(k)·w(k) (1)

[0078] Z(k)=h(X(k))+v(k) (2)

[0079] Among them, X z (k)=[x(k) x′(k) y(k) y′(k)] is a state vector directly constructed from the received radar observations. This vector represents the target's motion state at time k, i.e., the state at time k in the target's state equation, i.e., X(k), x(k), y(k), y′(k) are substituted into the target's state equation. x(k), x′(k), y(k), y′(k) are the target's x-direction distance, x-direction velocity, y-direction distance, and y-direction velocity relative to the receiving radar at time k, respectively. F(k), G(k), w(k), and h are the state transition matrix, noise figure matrix, process noise, and observation function, respectively, where w(k)=[w x (k) w y (k)] T w x (k) and w y (k) represents the process noise in the x and y directions. Z z (k)=[R(k)θ(k)] T Let be the observation vector of the receiving radar at time k, affected by noise interference. This vector represents the target state observed at time k, i.e., the state at time k, Z(k), is substituted into the target observation equation. Here, R(k) is the sum of the distances between the transmitting and receiving radars and the moving target at time k, θ(k) is the angle between the receiving radar and the moving target at time k, and v(k) = [v...]. r (k)v α (k)] Τ For the radar observation noise received at time k, v r (k) represents the measurement distance noise at time k, v α (k) The measurement angle noise at time k is all zero-mean Gaussian white noise, v r (k) and v α (k) are uncorrelated, and the noise covariance matrix is: The specific formula for the observation function h is:

[0080]

[0081] Z true (k) represents the actual observation state without noise at time k, and L is the distance between the receiving radar and the transmitting radar.

[0082] For the moving target, the initial motion state X(1) and initial covariance P(1) of the target are obtained based on the prior information of the target in Cartesian coordinates;

[0083] S2: Based on the target motion state and covariance in the Cartesian state space at time k, a one-step prediction is performed to obtain the motion state at time k+1. The specific formula is as follows:

[0084] X k+1|k =F(k)X(k)(4)

[0085] P k+1|k =F(k)P(k)F(k) Τ +G(k)Q(k)G(k) Τ (5)

[0086] Where X k+1|k P k+1|k Let Q(k) be the predicted state and the predicted covariance matrix at time k, respectively, and let Q(k) be the covariance matrix of the process noise.

[0087] S3: Predicted target state X at current time k based on U-transform k+1|k And the predicted covariance matrix P k+1|k Generate a set of sigma points. For its n-dimensional motion state in the Cartesian coordinate system, generate 2n+1 sigma points. The specific formula is as follows:

[0088] x k (0) =X k+1|k (6)

[0089]

[0090] Where i = 1, 2, ..., n, λ = α 2 (n+κ)-n, where α and κ are scaling parameters used to adjust the distribution of σ points. k This represents the sigma point generated in the Cartesian coordinate system, while x... k (i) Let represent the i-th sigma point. The formula for the weight of each sigma point is as follows:

[0091]

[0092] Where β is a parameter used to fuse observation noise, W m and W c These are the weights of the mean and covariance, respectively, both being 2n+1 vectors.

[0093] Each sigma point in the Cartesian coordinate system is transformed into a constructed state space using a transformation formula. This constructed state space is specifically based on the target's position and velocity states in a two-dimensional polar coordinate system, i.e., the distance r1 between the target and the receiving radar, and the target's tangential velocity v... r1 The distance r2 between the target and the transmitting radar, and the normal velocity v of the target. t The angle θ formed by the target and the receiving radar is used as a vector to describe the target's state, which is [r1v r1 r2vt θ] Τ The mean and covariance of the constructed state-space prediction are calculated using a weighted average. The specific formula for the calculation is as follows:

[0094]

[0095] Among them W m (i) W represents the mean weight of the i-th sigma point. c (i) Let f represent the covariance weight of the i-th sigma point, and f be the nonlinear transformation function from the Cartesian coordinate system to the constructed state space. The specific transformation method is shown in the following formula:

[0096]

[0097]

[0098] v t =-v x sinθ+v y cosθ (17)

[0099] In the above formula, L is the distance between the receiving radar and the transmitting radar, x is the distance of the target relative to the receiving radar in the x-direction, and v is the distance of the target relative to the receiving radar in the x-direction. x Let x be the target's velocity relative to the receiving radar, y be the target's distance relative to the receiving radar, and v be the distance in the x-direction. y The target's velocity relative to the receiving radar in the y-direction;

[0100] S4: Obtain the measurement data z at time k+1 obtained from the received radar measurement. k+1 =[R k+1 θ k+1 ] T , where R k+1 Let θ be the sum of the distances of the moving target from the transmitting radar and the receiving radar at time k+1. k+1 Let be the angle between the moving target and the receiving radar at time k+1. The measured and predicted data are fused using a Kalman filter to obtain the optimal state estimate and covariance matrix at time k+1 after fusion. The specific formula is as follows:

[0101] K k+1 = pol P k+1|k T H T (H pol P k+1|k H T +R k ) -1 (18)

[0102]

[0103] pol P k+1|k+1 =(IK k+1 H) pol P k+1|k (20)

[0104] Where K k+1 It is the Kalman gain at time k+1. This is the optimal state estimate after the update at time k+1. pol P k+1|k+1 It is the updated covariance matrix, and I is the identity matrix;

[0105] S5: Based on the U-transform, the optimal state is estimated using the update at time k+1. With the updated covariance matrix pol P k+1|k+1 The formula for generating 2n+1 sigma points is as follows:

[0106]

[0107] in pol X k+1 This represents the sigma point generated within the construction space, while pol X k+1 (i) This represents the i-th sigma point.

[0108] Each sigma point in the constructed state space is transformed to Cartesian coordinates using a transformation formula, and the mean and covariance matrix of the optimal state estimate in Cartesian coordinates are calculated using weighted summations. The specific formulas are as follows:

[0109]

[0110]

[0111] Where g is the nonlinear transformation function from the state space to the Cartesian coordinate system, and the specific transformation method is shown in the following formula:

[0112] R = r1 + r2 (26)

[0113]

[0114] In the above formula, L is the distance between the receiving radar and the transmitting radar, and R is the sum of the distances of the moving target from the transmitting radar and the receiving radar.

[0115] S6: Repeat steps S2 to S5 until the tracing ends.

[0116] Furthermore, in this invention, the target motion state based on the constructed state space in steps S3 to S5 is as follows:

[0117]

[0118] Where r1(k) represents the distance between the receiving radar and the moving target at time k. Let rk represent the radial velocity of the moving target relative to the receiving radar at time k, and let r2(k) represent the distance between the transmitting radar and the moving target at time k. t θ(k) represents the tangential velocity of the moving target relative to the receiving radar at time k, and θ(k) represents the angle of the moving target relative to the receiving radar at time k. These values ​​represent the motion state of the target in the constructed state space.

[0119] As a specific implementation method, such as... Figures 1-4 The example shown.

[0120] Figure 1 This is a flowchart of a coordinate system transformation fusion filtering tracking method for dual-base station radar according to the present invention.

[0121] Figure 2 This is a schematic diagram illustrating the state space construction based on dual-base station radar observations and target motion states of this invention. The nature of the target's motion is independently determined by its own dynamic characteristics, rather than being constrained by the observation parameters describing the motion state. The definitions of various physical quantities are essentially mathematical representations of motion characteristics through multi-dimensional observation. They can be modeled using state vectors in a Cartesian coordinate system or by constructing observation models in the measurement space, but different modeling dimensions will result in differentiated information structures. For example... Figure 2 As shown, this patent innovatively employs dual-base station radar to integrate ranging and angle measurement information for target localization. By combining tangential and normal velocity components to construct a velocity model, it not only achieves a complete representation of motion characteristics but also transforms the dual-base radar observation equations into linear functional relationships. This linear mapping characteristic allows the filtering process to be completed within an ideal Gaussian linear space, thereby significantly improving tracking accuracy and stability. The core breakthrough of this scheme lies in constructing a universally applicable dual-base radar state-space modeling paradigm, whose tracking performance demonstrates significant advantages over traditional methods, providing a new technical path for state estimation in multi-source heterogeneous observation systems.

[0122] Figure 3The graph shows the RMSE of target position estimation using various methods. The comparison demonstrates that the method proposed in this patent has fast convergence speed and high accuracy. Because other methods perform filtering in Cartesian coordinates, the probability density is distorted during the filtering process, resulting in information loss. In contrast, the prediction and update in this invention are performed in an adaptively constructed state space. Its filtering structure is not only linear but also guarantees the Gaussianity of the state probability density. Finally, Kalman filtering is used to fuse the state vector and observation vector values, thereby ensuring the convergence and stability of the dynamic estimation.

[0123] Figure 4 The figure shows the RMSE of target velocity estimation for various methods. It is clear from the figure that the method proposed in this patent consistently maintains a performance advantage in velocity estimation compared to the other three methods. This is because it constructs a filtering space that is more reasonable than the Cartesian coordinate system.

[0124] Figure 3 and Figure 4 This is a comparison chart of the root mean square error (RMSE) of position and root mean square error (RMSE) of velocity between the present invention and three internationally recognized methods: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Sigma Point Transform Kalman Filter (SPTKF), according to embodiments of the present invention. For convenience, the meanings of symbols and terms not explained in this patent are summarized in Table 1.

[0125] Table 1 Explanation of Nouns and Symbols

[0126]

[0127] Based on the above basic description, consider a typical dual-base station radar tracking system where the receiving radar is fixed at the origin. At each sampling moment, the radar can obtain the distance and angle of the tracked object. The observation noise distance error σ of the dual-base station radar is... r =2m, angular error σ θ =1.5deg. Consider a scenario where radar tracks an aerial target. The target's initial position is (10km, 10km), the radar sampling period is T = 1 second, the simulation duration is 100 seconds, and the target's initial velocity is (10m / s, 18m / s). Assume the process noise is zero-mean Gaussian white noise with a standard deviation of 0.1m / s. The simulation compares the root mean square error (RMSE) of several of the most effective methods with the method proposed in this invention for estimating the target position and velocity. The smaller the RMSE, the higher the tracking accuracy. The following examples all underwent 50 Monte Carlo simulations.

[0128] Therefore, the present invention has the following beneficial effects:

[0129] Its dual-base station radar coordinate system transformation fusion filtering tracking method differs from all existing dual-base station radar tracking fusion algorithms. This theoretical technique differs from the orthogonal decomposition motion description of the Cartesian coordinate system. Its technical approach constructs a state filtering fusion space based on the target's motion state in the Cartesian coordinate system, derives a linear state equation, and finally uses Kalman filtering to complete the tracking. The tracked data is then transformed into the Cartesian coordinate system without traces and output. The technical effect is that it solves the nonlinearity problem in filtering, ensuring that information distortion caused by various errors during radar observation and state information fusion is prevented, allowing for more effective fusion of target state and radar observation information. The technical objective is that, compared with currently recognized and state-of-the-art methods, this patent improves tracking robustness and accuracy without increasing computational complexity.

[0130] Numerous experiments have shown that the position and velocity tracking accuracy achieved by the method provided in this invention is superior to the most effective internationally recognized methods, including Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Sigma Point Transform Kalman Filter (SPTKF). Especially in medium- to long-range tracking scenarios, this technology can significantly improve tracking performance and maintain high stability without requiring substantial investment in hardware upgrades.

[0131] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0132] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A coordinate system transformation fusion filtering tracking method for dual base station radars, characterized in that, Comprise: Based on the kinematic characteristics of the target, the state equation and the observation equation of the dual-base station radar tracking system for the moving target are established, and the initial motion state and the initial covariance of the target are determined based on the prior information of the target in the Cartesian coordinate system; According to the motion state and covariance of the target at the time instant under the Cartesian state space are step by step predicted to obtain the motion state of the target at the time instant; the motion state of the target at the time instant comprises a target predicted state and a predicted covariance matrix; Based on the U-transformation, a set of sigma points is generated for the target predicted state and predicted covariance matrix, and a set of sigma points is generated for the target motion state in the Cartesian coordinate system predicted state and predicted covariance matrix, and a set of sigma points is generated for the target motion state in the Cartesian coordinate system predicted state and predicted covariance matrix, and a set of sigma points is generated for the target motion state in the Cartesian coordinate system The measurement data and the prediction data are fused by using a Kalman filter to obtain optimal state estimation and a covariance matrix after fusion at a first time The measurement data is obtained by radar measurement, and the prediction data is a mean value and a covariance constructed for state space prediction. Based on the U transformation, according to The optimal state estimation and the updated covariance matrix are updated at the moment The sigma points are converted into the Cartesian coordinate system by using the conversion formula, and the optimal state estimation mean and the covariance matrix in the Cartesian coordinate system are calculated by weighting. The step is cycled until the tracking is completed; The state equation and the observation equation of the dual-base station radar tracking system for the moving target are established based on the kinematic characteristics of the target, and the initial motion state and the initial covariance of the target are determined based on the prior information of the target in the Cartesian coordinate system, specifically comprising: Based on the kinematic characteristics of the target, the state equation and the observation equation of the dual-base station radar tracking system for the moving target are established, and the initial motion state and the initial covariance of the target are determined based on the prior information of the target in the Cartesian coordinate system, specifically comprising: wherein, is a state vector directly constructed from the received radar observation, which is used to represent the motion state of the target at the time, i.e., the vector is used to substitute the state at the time in the state equation of the target, are the state transition matrix, the noise coefficient matrix, the process noise and the observation function, respectively, are not correlated, and the noise covariance matrix is; the observation functionis specifically as follows:​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ wherein, is the first unnoisy true observation state at time is the distance between the receiving radar and the transmitting radar; For moving targets, the initial motion state of the target is derived based on prior information of the target in Cartesian coordinates and initial covariance .

2. The coordinate frame transformation fusion filter tracking method for dual base station radars of claim 1, wherein, The The motion state of the time target is specifically represented as: wherein , are the predicted state and predicted covariance matrix at time denotes the covariance matrix of the process noise.​ 3. The coordinate frame transformation fusion filter tracking method for dual base station radars of claim 1, wherein, The U-based transformation generates a set of sigma points for the target predicted state and predicted covariance matrix, and generates a set of sigma points for the target motion state in the Cartesian coordinate system The U-based transformation generates a set of sigma points for the target predicted state and predicted covariance matrix, and generates a set of sigma points for the target motion state in the Cartesian coordinate system The U-based transformation generates a set of sigma points for the target predicted state and predicted covariance matrix, and generates a set of sigma points for the target motion state in the Cartesian coordinate system based on the u- transformation of the target state at the current time instant and the predicted covariance matrix a set of sigma points is generated for which dimensional motion states in the cartesian coordinate system sigma points are generated, in particular as follows: wherein , , and are scaling parameters for adjusting the distribution of the sigma points; represents the sigma points generated in a Cartesian coordinate system, while represents the th sigma point, and the formula of the weight of each sigma point is embodied by the following formula: wherein is a parameter for fusing observation noise, and are weights of the mean and covariance, respectively, both being vectors; Each sigma point in the Cartesian coordinate system is converted to the constructed state space by using the conversion formula, and the constructed state space is constructed based on the position state expression and the velocity state expression of the target in the two-dimensional polar coordinate system. The distance between the target and the receiving radar , the tangential velocity of the target , the distance between the target and the transmitting radar , the normal velocity of the target , and the included angle between the target and the receiving radar are constructed as vectors for describing the state of the target, and are expressed as ; The state equation and the observation equation of the dual-base station radar tracking system for the moving target are established based on the kinematic characteristics of the target, and the initial motion state and the initial covariance of the target are determined based on the prior information of the target in the Cartesian coordinate system, specifically comprising: wherein, represents the mean weight of the th sigma point, represents the covariance weight of the th sigma point, is a nonlinear transformation function from Cartesian coordinate system to configuration space, and the specific transformation method is shown in the following formula: wherein is the distance between the receiving radar and the transmitting radar, is the target's relative direction distance to the receiving radar, direction distance, is the target's relative direction velocity to the receiving radar, direction velocity, is the target's relative direction distance to the receiving radar, direction distance, is the target's relative direction velocity to the receiving radar, direction velocity.

4. The coordinate frame transformation fusion filter tracking method for dual base station radars of claim 1, wherein, The first The optimal state estimate and covariance matrix at time k are denoted as: wherein is the Kalman gain at time is the updated optimal state estimate at time is the updated covariance matrix, is the identity matrix, is the observation matrix of receiving radar observation targets, is the observation vector of receiving radar observation targets at time is the observation vector of receiving radar observation targets at time​​ 5. The coordinate frame transformation fusion filter tracking method for dual base station radars of claim 1, wherein, The U-based transformation is based on The optimal state estimation and the updated covariance matrix are updated at the moment The sigma points are converted into the Cartesian coordinate system by using the conversion formula, and the optimal state estimation mean and the covariance matrix in the Cartesian coordinate system are calculated by weighting, specifically including: Based on U transformation, by The optimal state estimation updated at the moment The updated covariance matrix Generate Sigma points, the specific formula is: wherein, is the sigma point generated within the constructed space, is the first sigma point; The state equation and the observation equation of the dual-base station radar tracking system for the moving target are established based on the kinematic characteristics of the target, and the initial motion state and the initial covariance of the target are determined based on the prior information of the target in the Cartesian coordinate system, specifically comprising: wherein is a nonlinear conversion function from the state space to the Cartesian coordinate system, the specific conversion method is shown in the following formula: wherein, is the distance between the receiving radar and the transmitting radar, is the sum of the distance of the moving target from the transmitting radar and the receiving radar.

6. The coordinate frame transformation fusion filter tracking method for dual base station radars of claim 1, wherein, The target motion state in the state space is represented as: wherein, denotes the distance of the moving target from the receiving radar at the time instant, denotes the radial velocity of the moving target relative to the receiving radar at the time instant, denotes the distance of the moving target from the transmitting radar at the time instant, denotes the tangential velocity of the moving target relative to the receiving radar at the time instant, denotes the angle of the moving target relative to the receiving radar at the time instant.

7. A coordinate frame transformation fused filter tracking system for dual base station radars based on the method of any of claims 1-6, characterized in that, Comprise: The initial state construction module is used for establishing the state equation and the observation equation of the dual-base station radar tracking system for the moving target based on the kinematic characteristics of the target, and determining the initial motion state and the initial covariance of the target based on the prior information of the target in the Cartesian coordinate system; a one-step prediction module, configured to perform one-step prediction on the motion state and covariance of the target at the time instant in the Cartesian state space to obtain a predicted motion state of the target at the time instant ; the predicted motion state of the target at the time instant comprises a target predicted state and a predicted covariance matrix ; and the one-step prediction module comprises a first prediction module, a second prediction module and a third prediction module. ​ a first U transform module configured to generate a set of sigma points for the target prediction state and the prediction covariance matrix based on a U transform, and generate a set of sigma points for the target position and velocity state in a Cartesian coordinate system based on a U transform state generation sigma points, and weightedly compute a mean and a covariance for constructing a state space prediction; The fusion module is used to fuse measurement data and prediction data using a Kalman filter to obtain the fused result. The optimal state estimate and covariance matrix at time t; the measurement data are obtained from radar measurements; the prediction data are the mean and covariance of the state-space prediction. The second U transform module is configured to generate, based on a U transform, the optimal state estimation mean value and the covariance matrix in the Cartesian coordinate system according to The optimal state estimation mean value and the covariance matrix in the Cartesian coordinate system are generated based on the optimal state estimation mean value and the covariance matrix in the sigma coordinate system. The optimal state estimation mean value and the covariance matrix in the Cartesian coordinate system are generated based on the optimal state estimation mean value and the covariance matrix in the sigma coordinate system. The optimal state estimation mean value and the covariance matrix in the Cartesian coordinate system are generated based on the optimal state estimation mean value and the covariance matrix in the sigma coordinate system. The cycle module is used for cycling the step until the tracking is completed.

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