An adaptive radar target tracking method based on a "current" statistical model

Abstract

The application belongs to the technical field of radar target tracking and discloses an adaptive radar target tracking method based on a "current" statistical model, which comprises the following steps: step 1, filter initialization; step 2, one-step filter prediction based on a CS model; step 3, target maneuvering determination; step 4, adaptive adjustment of model parameters and filter parameters; and step 5, filter state updating. The application guarantees the filter precision for non-maneuvering target states, realizes greater utilization of current innovations, and accelerates the adjustment speed of the filter for maneuvering states.

Description

Technical Field

[0001] This invention belongs to the field of radar target tracking technology and relates to an adaptive radar target tracking method based on a "current" statistical model. It uses a "current" statistical (CS) model to track targets and perform tracking filtering. When a target maneuver is detected, the CS model parameters and filter parameters are adaptively adjusted. This solves the problems of tracking loss and filtering divergence caused by radar tracking model mismatch when the target performs large maneuvers, and improves the radar tracking system's ability to track maneuvering targets. Background Technology

[0002] Radar target tracking is a process of filtering and estimating the target state based on current radar measurement data and past filtering results. The Kalman filter, an optimal linear mean square filter, is widely used in radar tracking systems. It combines past filtering results with the target motion model to obtain a preliminary prediction of the target state at the next moment. Based on current measurements, it obtains the error of the preliminary prediction and corrects and updates it to obtain the final filtering result. A target motion model is a crucial prerequisite for Kalman filtering, but an accurate motion model is difficult to obtain. Therefore, approximate models are usually established to approximate the target motion process. The constant velocity (CV) model and the constant acceleration (CA) model are commonly used classic models. The CV model assumes the target moves at a constant velocity in a straight line, treating small changes in velocity as white noise in the process. The CA model assumes the target moves with uniform acceleration, treating small changes in acceleration as white noise in the process. The CV and CA models are relatively accurate in describing the motion of targets with no or weak maneuvering. Kalman filters based on these two models can achieve good filtering results. However, when the target performs large maneuvers, model mismatch will occur, resulting in large model errors, which will reduce the filtering accuracy or even cause the filtering to diverge, causing the radar tracking system to lose the target.

[0003] To address the model mismatch issue during target maneuvers, a series of maneuver target models with higher maneuverability have emerged, such as the Singer model and the "Current" Statistical (CS) model. Unlike the CV and CA models, which use Gaussian white noise to simulate target maneuvers, the Singer model assumes that the target acceleration is an approximately uniformly distributed, zero-mean random process within a certain range. The CS model improves upon the Singer model by assuming that the acceleration at the next time step will only take values ​​within a certain neighborhood of the current acceleration, and uses a modified Rayleigh distribution to describe the target maneuver acceleration. The CS model assumes non-zero mean acceleration and can adjust the mean and distribution of acceleration in real time based on measurements, thus more realistically describing the target maneuver state.

[0004] Although the CS model provides a relatively realistic portrayal of the maneuvering process, the Kalman filter based on the CS model still has the following shortcomings:

[0005] 1. The CS model requires prior information, namely, the extreme values ​​of the target's acceleration and the parameters of its maneuvering frequency. These prior parameters are usually empirically determined and fixed. If the values ​​are too small, model mismatch will occur when the target performs large maneuvers, leading to problems such as filter divergence. If the values ​​are too large, the tracking accuracy will be low and the performance will degrade when the target has no or weak maneuvers.

[0006] 2. The Kalman filter takes a long time to adjust to sudden maneuvers and has poor tracking performance. Summary of the Invention

[0007] (I) Purpose of the Invention

[0008] The purpose of this invention is to address the aforementioned problems and shortcomings, and to solve the issue of low tracking accuracy or target loss in complex maneuvering situations using traditional CS model Kalman filters. This invention provides an adaptive radar target tracking method based on a "current" statistical model. When the target has no or weak maneuvering, the initial parameters are maintained for high-precision filtering and tracking. When the target performs significant maneuvering, the CS model parameters and filter gain are adaptively adjusted according to the degree of maneuvering. This avoids model mismatch caused by poor prior parameter values ​​and enhances the real-time response capability of the Kalman filter to adapt to the current target's maneuvering state, thereby improving tracking performance.

[0009] (II) Technical Solution

[0010] To address the aforementioned technical problems, this invention provides an adaptive radar target tracking method based on a "current" statistical model, comprising the following steps:

[0011] Step 1: Filter Initialization

[0012] Before starting filtering, i.e. at k=1, initialize the following parameters:

[0013] (1) Initial maneuver frequency:

[0014] α(1)=α0 (28)

[0015] Where α0 is the initial maneuver frequency, an empirically chosen value, when the target maneuver is a slow turn of the aircraft. When escaping maneuver Atmospheric disturbance α = 1.

[0016] (2) Initial maximum and minimum acceleration a Min0 ,a Max0 The empirical value should not be too large.

[0017] (3) Initial state transition matrix F:

[0018]

[0019] Where T is the sampling interval.

[0020] (4) Initial input control matrix G:

[0021]

[0022] (5) Initial filter weighting factor u(1):

[0023] u(1)=u0=1 (31)

[0024] (6) Initial maneuver detection threshold D: determined by querying χ 2 The distribution table was obtained.

[0025] Other parameters, such as the initial target state and the measurement noise covariance matrix R, are initialized in the same way as those in the classic Kalman filter, and will not be elaborated here.

[0026] Step 2: One-step filtering prediction based on the CS model

[0027] Let the tracking filter state estimate at time k-1 be... The covariance matrix is ​​P(k-1|k-1), and the measurement at time k is Z(k). The filtering process at time k is as follows:

[0028] (1) Predict the target state at time k in one step according to equation (5):

[0029]

[0030] in, The mean of the maneuvering acceleration is equal to the acceleration filter value at time k-1;

[0031] (2) Calculate the variance of the current acceleration at time k:

[0032]

[0033] (3) Calculate the process noise covariance:

[0034]

[0035] Where a(k) is the maneuver frequency at time k, and the elements of the matrix on the right side of the equation are shown below:

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042] (4) Perform one-step prediction of the noise covariance matrix according to equation (9):

[0043] P(k|k-1)=u(k-1)F(k)P(k-1|k-1)+Q(k) (36)

[0044] Where u(k-1) is the filter weighting induction at time k-1.

[0045] (5) Calculate the new information covariance:

[0046] S(k)=H(k)P(k|k-1)H T (k)+R(k) (37)

[0047] Where R(k) is the measurement noise covariance matrix.

[0048] Step 3: Target Maneuver Determination

[0049] Calculate the target's maneuverability d(k) and determine the maneuverability:

[0050] d(k)=v T (k)S -1 (k)v(k) (38)

[0051] Where v(k) is the news at time k:

[0052]

[0053] d(k) follows an n-dimensional (measurement dimension) degree of freedom χ 2 Distribution. The value of d(k) increases as the target maneuvers, so it can be used for maneuver determination. If D is set as the maneuver determination threshold, then:

[0054] Pr{d(k)≥D}=P false (40)

[0055] Where P false To determine the false alarm rate for mobile systems. This is done by querying χ². 2 The distribution table can be used to obtain the threshold D value that meets the system performance requirements. If d(k) < D, the target is determined to have no maneuverability or weak maneuverability; if d(k) ≥ D, the target is determined to maneuver.

[0056] Step 4: Adaptive adjustment of model and filter parameters

[0057] 4-1: The adaptive adjustment process of model parameters and filter parameters under target maneuvering conditions is as follows:

[0058] (1) Adjust the maneuver frequency and acceleration extreme values ​​of the CS model according to the degree of maneuver:

[0059] α maneu (k)=d(k)α0 (41)

[0060]

[0061] (2) Based on the principle of orthogonality, adjust the filter weighting factor u(k) according to the degree of maneuverability:

[0062]

[0063]

[0064] N(k)=V(k)-H(k)Q(k)H T (k)+R(k) (45)

[0065] M(k)=H(k)F(k)P(k|k-1)F T (k)H'(k) (46)

[0066] in, ρ is the forgetting factor, which takes a value between 0 and 1.

[0067] (3) Update the noise covariance using the adaptively adjusted maneuver frequency:

[0068]

[0069] Each element in the matrix is ​​updated accordingly according to Equation (35).

[0070] (4) Update the variance of maneuver acceleration using the adaptively adjusted acceleration extrema:

[0071]

[0072] (5) Update the state prediction covariance P(k|k-1)

[0073] P(k|k-1)=u(k)F(k)P(k-1|k-1)+Q(k) (49)

[0074] 4-2: The adaptive adjustment process of model parameters and filter parameters under the condition of no or weak target maneuvering is as follows:

[0075] If no maneuver is determined at time k-1, proceed directly to step 5;

[0076] If a maneuver is determined at time k-1, then the prediction covariance matrix P(k|k-1) applicable to the no-maneuver state is calculated using the initial parameters:

[0077] P(k|k-1)=u0F(k)P(k-1|k-1)+Q(k) (50)

[0078] Step 5: Filter state update

[0079] Calculate the new information covariance matrix S(k):

[0080] S(k)=H(k)P(k|k-1)H T (k)+R(k) (51)

[0081] Calculate the filter gain K(k):

[0082] K(k)=P(k|k-1)H T (k)S -1 (k) (52)

[0083] Target filter state update:

[0084] X(k|k)=X(k-1|k)+K(k)v(k) (53)

[0085] Covariance matrix update:

[0086] P(k|k)=P(k-1|k)+K(k)S -1 (k)K T (k) (54)

[0087] At this point, the filtering step is complete, and the target tracking filtering state X(k|k) and related filtering parameters at time k are obtained. Target tracking filtering at time k+1 can then proceed. The overall filtering and tracking implementation process at time k is as follows: Figure 1 As shown.

[0088] As can be seen from the above steps, this invention adaptively improves the Kalman filter based on the CS model from two directions: the model and the filter. It adds real-time maneuver determination of the target motion, introducing a target maneuvering degree parameter. The maneuvering degree is used to determine whether the target is maneuvering and serves as a reference value for subsequent adaptive parameter adjustment. If the target is determined not to be maneuvering, a preset model and filtering parameters are used to ensure filtering accuracy for non-maneuvering processes; if the target is maneuvering, an adaptive parameter adjustment step is initiated to enhance the tracking performance during maneuvering processes.

[0089] (III) Beneficial Effects

[0090] The adaptive radar target tracking method based on the "current" statistical model provided by the above technical solution has the following advantages:

[0091] (1) It reduces the dependence on prior information about the target's motion state, ensuring high tracking accuracy for targets in non-maneuvering states. Fixed-parameter filtering methods typically select large prior parameter values ​​to adapt to strong maneuvers, resulting in low tracking accuracy for non-maneuvering targets. The method of this invention can adaptively increase the parameter value during maneuvers, thus selecting parameters more suitable for non-maneuvering states as preset parameter values ​​for filtering estimation in the non-maneuvering phase, ensuring filtering accuracy for non-maneuvering target states;

[0092] (2) It avoids the model mismatch problem when the target is maneuvering. When the target is maneuvering, the prior parameters of the CS model are increased according to the degree of maneuvering, including the acceleration extremum and the maneuvering frequency, so that it is more consistent with the current dynamic state of the target and avoids filter divergence caused by model mismatch;

[0093] (3) Improved robustness and tracking performance of the Kalman filter for target maneuvers. Based on the degree of maneuver, the filtered data from past moments are weighted, and the weights affecting the current filtering process are adjusted in real time, thereby maximizing the utilization of current information and accelerating the filter's adjustment speed to maneuver states. Attached Figure Description

[0094] Figure 1 This is a flowchart of the adaptive radar target tracking method of the present invention.

[0095] Figure 2 This is a diagram illustrating the simulated target acceleration in an embodiment of the present invention.

[0096] Figure 3 This is a diagram illustrating the x-direction tracking filtering results in an embodiment of the present invention.

[0097] Figure 4 This is a diagram illustrating the y-direction tracking filtering results in an embodiment of the present invention.

[0098] Figure 5 This is a diagram illustrating the z-direction tracking filtering results in an embodiment of the present invention. Detailed Implementation

[0099] To make the objectives, contents, and advantages of the present invention clearer, the specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples.

[0100] The following simulation example illustrates the specific implementation effect of the adaptive radar target tracking method based on the CS model in this embodiment.

[0101] Consider filtering and tracking the target in three-dimensional space (x, y, z). The radar data sampling period is 40 ms. Assume the measurement noise is zero-mean white noise with a standard deviation of 10 m. The target's initial position is (x = -1.4 m, y = 0 m, z = 0 m), and its initial velocity is (v...). x =0.1m / s,v x =0m / s,v x =0m / s), acceleration change as Figure 2 As shown. The initial acceleration extrema of the CS model are:

[0102] (a xmax =100m / s 2 ,a ymax =100m / s 2 ,a zmax =100m / s 2 )

[0103] (a xmin =100m / s 2 ,a ymin =100m / s 2 ,a zmin =100m / s 2 )

[0104] Initial maneuver frequency The maneuver detection threshold D = 6.251 (false alarm rate 10%). 500 Monte Carlo simulations were performed using the method of this invention, and the tracking performance was described using the root mean square error (RMSE).

[0105] Figures 3-5 The filtering performance of this invention on maneuvering targets in the x, y, and z dimensions is demonstrated. It can be seen that from 0 to 100 points, the target's maneuvering changes significantly in space. Traditional fixed-parameter filters exhibit high tracking errors and long adjustment times, while the adaptive-parameter filter of this invention offers higher filtering accuracy and better robustness. From 100 to 430 points, the target performs weaker maneuvers. Due to the smaller selected parameters, the fixed-parameter filter in this stage exhibits good tracking performance. The adaptive-parameter filter of this invention also switches to a weak-maneuvering mode, using the initial parameters to ensure filtering accuracy comparable to the fixed-parameter filter.

[0106] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An adaptive radar target tracking method based on a "current" statistical model, characterized in that, Includes the following steps: Step 1: Filter initialization; Step 2: One-step filtering prediction based on the CS model; Step 3: Target maneuver determination; Step 4: Adaptive adjustment of model and filter parameters; Step 5: Update the filter state; In step 1, before starting filtering, i.e. at k=1, the following parameters are initialized: (1) Initial maneuver frequency: α(1)＝α0 (1) Where α0 is the initial maneuver frequency, which is taken empirically; (2) Initial maximum and minimum acceleration a Min0 ,a Max0 Empirical values; (3) Initial state transition matrix F: Where T is the sampling interval; (4) Initial input control matrix G: (5) Initial filter weighting factor u(1): u(1)=u0=1 (4) (6) Initial maneuver detection threshold D: determined by querying χ 2 The distribution table was obtained; In step 2, the one-step filtering prediction process based on the CS model is as follows: Let the tracking filter state estimate at time k-1 be... The covariance matrix is ​​P(k-1|k-1), and the measurement at time k is Z(k). The filtering process at time k is as follows: (1) Perform one-step target state prediction at time k; (2) Calculate the current acceleration variance; (3) Calculate the noise covariance during the process; (4) Perform one-step prediction of the noise covariance matrix; (5) Calculate the new information covariance; In step 2, the one-step target state prediction at time k is performed according to equation (5): in, The mean of the maneuvering acceleration is equal to the acceleration filter value at time k-1; In step 2, the formula for calculating the variance of the current acceleration at time k is: The formula for calculating the noise covariance during the process is: Where α(k) is the maneuver frequency at time k, and the elements of the matrix on the right-hand side of the equation are shown below: (4) Perform one-step prediction of the noise covariance matrix according to equation (9): P(k|k-1)=u(k-1)F(k)P(k-1|k-1)+Q(k) (9) Where u(k-1) is the filter weighting induction at time k-1; (5) Calculate the new information covariance: S(k)=H(k)P(k|k-1)H T (k)+R(k) (10) Where R(k) is the measurement noise covariance matrix; In step 3, the target maneuver determination process is as follows: Calculate the target's maneuverability d(k) and determine the maneuverability: d(k)=v T (k)S -1 (k)v(k) (11) Where v(k) is the news at time k: d(k) follows an n-dimensional χ²-degree-of-freedom system. 2 The distribution shows that the value of d(k) increases as the target maneuvers; if D is set as the maneuver decision threshold, then: Pr{d(k)≥D}=P false (13) Among them, P false To determine the false alarm rate, the χ² value is used. 2 The distribution table yields the threshold D value that meets the system performance requirements. If d(k) < D, the target is determined to have no maneuverability or weak maneuverability; if d(k) ≥ D, the target is determined to maneuver. In step 4, the adaptive adjustment process of model parameters and filter parameters under target maneuvering conditions is as follows: (1) Adjust the maneuver frequency and acceleration extreme values ​​of the CS model according to the degree of maneuver: a maneu (k)=d(k)α0 (14) (2) Based on the principle of orthogonality, adjust the filter weighting factor u(k) according to the degree of maneuverability: N(k)=V(k)-H(k)Q(k)H T (k)+R(k) (18) L(k)=H(k)F(k)P(k|k-1)F T (k)H'(k) (19) in, ρ is the forgetting factor, which takes a value between 0 and 1; (3) Update the noise covariance using the adaptively adjusted maneuver frequency: Each element in the matrix is ​​updated accordingly according to Equation (8); (4) Update the variance of maneuver acceleration using the adaptively adjusted acceleration extrema: (5) Update the state prediction covariance P(k|k-1) P(k|k-1)=u(k)F(k)P(k-1|k-1)+Q(k) (22) In step 4, the adaptive adjustment process of model parameters and filter parameters under the condition of no maneuvering or weak maneuvering of the target is as follows: If no maneuver is determined at time k-1, proceed directly to step 5; If a maneuver is determined at time k-1, then the prediction covariance matrix P(k|k-1) applicable to the no-maneuver state is calculated using the initial parameters: P(k|k-1)=u0F(k)P(k-1|k-1)+Q(k) (23) In step 5, the filter state update includes: Calculate the new information covariance matrix S(k): S(k)=H(k)P(k|k-1)H T (k)+R(k) (25) Calculate the filter gain K(k): K(k)=P(k|k-1)H T (k)S -1 (k) (27) Target filter state update: X(k|k)=X(k-1|k)+K(k)v(k) (29) Covariance matrix update: P(k|k)=P(k-1|k)+K(k)S -1 (k)K T (k) (31) At this point, the filtering step is complete, and the target tracking filtering state X(k|k) and related filtering parameters at time k are obtained. Target tracking filtering at time k+1 will then continue.

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