A tracking method for high-angle diving attack targets based on a tilt coordinate system

Abstract

The application discloses a tracking method for high-angle diving attack targets based on an inclined coordinate system, which converts the inclined flight of a target in a vehicle geographic coordinate system into the flat flight in the inclined coordinate system, avoids the enlargement of azimuth error, and reduces the filtering difficulty. After the position estimation value of the target is obtained, the inverse transformation is performed to the target in the vehicle geographic coordinate system, and the projection is performed to the XOY plane, so that the azimuth observation error variance is still enlarged. However, the result shows that the tracking method for high-angle diving attack targets based on the inclined coordinate system has higher tracking precision.

Description

Technical Field

[0001] This invention belongs to the field of anti-aircraft artillery fire control calculation technology, specifically relating to a tracking method for high-angle dive attack targets based on an inclined coordinate system. Background Technology

[0002] In modern high-tech warfare, air strikes and counter-air strikes have become the primary mode of warfare from the outset to the end, significantly influencing the outcome of battles. Air strike weapons have also undergone a qualitative change, evolving from traditional fixed-wing aircraft to missiles and precision-guided munitions. With the continuous improvement in the performance of precision-guided weapons (primarily missiles and precision-guided munitions) and other ground-attack weapons both domestically and internationally, they exhibit trends of increasing speed, maneuverability, range, and high-angle dive attacks, posing a significant threat to the defense of key military locations and important engineering projects.

[0003] High-angle dive attacks are typically categorized into large-angle dive attacks (θ≥30°) and zenith attacks (θ≥70°) based on the target's dive angle θ. When fighter jets use precision-guided munitions to attack targets, they often employ horizontal or high-angle ballistic trajectories at relatively high altitudes. This results in a higher observation angle relative to the anti-aircraft gun system when the munitions enter the system's target search and tracking range. According to domestic and international data, this observation angle can reach 40°–85°, with various bunker-buster bombs using a "high-angle dive attack" mode to strike targets at nearly 90° angles. However, most anti-aircraft gun systems use two-axis tracking sensors. This structure inherently creates a zenith blind zone, making it impossible to stably track zenith-attack targets. Furthermore, the target information measured by the tracking sensors inevitably contains noise; excessively high pointing angles of the tracker can amplify the tracker's azimuth aiming error, causing the system to fail to track. Therefore, high-angle dive attacks pose a more severe challenge to anti-aircraft gun systems. Faced with the enormous threat posed by guided munitions that dive at high angles, anti-aircraft artillery systems need to improve their combat effectiveness in several key aspects of the system.

[0004] The purpose of fire control filtering is to estimate the target's motion state based on limited observation information. In engineering applications, Kalman filtering is one of the effective methods for target tracking. In target tracking systems, the target dynamic model is usually modeled in a Cartesian coordinate system, while the sensor measurements are obtained in a spherical coordinate system. Thus, target tracking becomes a nonlinear estimation problem. One approach to solving this type of problem is tracking in a mixed coordinate system, such as EKF, UKF, PF, and CK. Another commonly used method is transformed measurement Kalman filtering, such as CMKF, DCMKF, and UCMKF, and this type of method is widely used in engineering. Summary of the Invention

[0005] In view of this, this invention addresses the problem in fire control calculations for anti-aircraft artillery weapon systems where the increased elevation angle of high-angle diving targets leads to a sharp amplification of target azimuth tracking errors, resulting in significant tracking errors. It provides a tracking method for high-angle diving targets based on an inclined coordinate system. This method utilizes the inclined coordinate system to perform Kalman filtering on the observed data, obtaining a more accurate target motion state and improving the tracking and filtering accuracy of the anti-aircraft artillery weapon system.

[0006] A method for tracking high-angle dive attack targets based on an inclined coordinate system includes:

[0007] Step 1: Transform the sensor's measurements from the spherical coordinate system to the Cartesian coordinate system, specifically as follows:

[0008] The observed signal is transformed to obtain the vehicle-mounted geographic coordinate system, specifically as follows:

[0009]

[0010] In the formula: x d y d and z d These represent the values ​​of the observed signal along the three coordinate axes in the vehicle's geographic coordinate system; D n q n and ε n These represent the distance, azimuth, and elevation angles of the observed signal in the spherical coordinate system, respectively.

[0011] Step 2: Establish a fire control tilted coordinate system based on the direction of the incoming target, and convert the observation signal to the fire control tilted coordinate system. Specifically:

[0012] Assume that the angles between the direction of attack of the observed target in the vehicle-mounted geographic coordinate system and the Y-axis and the XOY plane are α and α, respectively. dv and q dv Rotate the vehicle's geographic coordinate system by α around the Z-axis and X-axis respectively. dv and q dv The rotation matrix C is obtained respectively. dvz and C dvx This forms a fire control tilted coordinate system; the observed signal Y is transformed from the vehicle geographic coordinate system to obtain the fire control tilted coordinate system, specifically:

[0013]

[0014] In the formula: x v y v and z v These represent the values ​​of the observed signal in the three coordinate axes of the inclined fire control coordinate system.

[0015] Step 3, calculation of observation variance, specifically:

[0016] Assume the target's position in the spherical coordinate system (D) v q v ε v The deviation near ) is ΔD v , Δq v and Δε v When we take the differential on both sides, x becomes... v y v , z v The corresponding error Δx v Δy v and Δz v They are respectively:

[0017]

[0018] The variance of the observation error of the measured noise in the three coordinate axes under the fire control tilted coordinate system. and for:

[0019]

[0020] In the formula: and These represent the error variances of the azimuth, elevation, and distance in the fire control tilted coordinate system, respectively.

[0021] Because in the fire control tilted coordinate system, q v =q d -q dv ≈0, ε v =ε d -α dv ≈0, further simplifying the above formula to:

[0022]

[0023] The observation variance R for the corresponding state is:

[0024]

[0025] In the formula: This represents the covariance of observation errors in the X and Y directions of the measurement noise in the fire control tilted coordinate system. This represents the covariance of observation errors in the X and Z directions of the measurement noise in the fire control tilted coordinate system. This represents the observation error covariance in the Y and Z directions of the measurement noise in the fire control tilted coordinate system;

[0026] Step 4: Kalman filter solution.

[0027] Based on the measurement transformation in step 1, using the observation error variance R in the inclined coordinate system described in step 3, the target position information (x, y, y) in the inclined coordinate system obtained after the coordinate transformation in step 2 is used. v ,y v ,z v Substitute the observed signal Y(k) as the state and perform linear Kalman filtering to obtain the target position estimate;

[0028] Step 5, using the inverse rotation matrix C dvz -1 and C dvx -1 The target position estimate after filtering in step 4 is inversely transformed to obtain the target tracking position in the vehicle geographic coordinate system.

[0029] Preferably, in step 2, the rotation matrix C dvz and C dvx as follows:

[0030]

[0031]

[0032] The present invention has the following beneficial effects:

[0033] In traditional tracking methods, projecting a high-angle diving target onto the XOY plane amplifies the variance of the azimuth observation error, thus increasing filtering difficulty and reducing tracking accuracy. This invention provides a tracking method for high-angle diving targets based on an inclined coordinate system. This method transforms the target's oblique flight in the vehicle's geographic coordinate system to horizontal flight in the inclined coordinate system, avoiding the amplification of azimuth error and reducing filtering difficulty. Even after obtaining the target position estimate and inversely transforming it to the target's geographic coordinate system, projecting it onto the XOY plane still amplifies the variance of the azimuth observation error. However, results show that this tracking method for high-angle diving targets based on an inclined coordinate system achieves higher tracking accuracy. Attached Figure Description

[0034] Figure 1 This is a flowchart of the tracking method for high-angle dive attack targets based on an inclined coordinate system according to the present invention.

[0035] Figure 2 This is a comparison of RMSE values ​​in the X direction in an embodiment of the present invention.

[0036] Figure 3 This is a comparison of RMSE values ​​in the Y direction in an embodiment of the present invention.

[0037] Figure 4 This is a comparison of RMSE values ​​in the Z direction in an embodiment of the present invention. Detailed Implementation

[0038] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0039] This invention addresses the problem that increasing the elevation angle of high-angle diving targets leads to a sharp amplification of target azimuth tracking errors. It optimizes the traditional Kalman filter algorithm for conversion measurements by defining a fire control tilted coordinate system (v-frame). This fire control tilted coordinate system is a rectangular coordinate system, with its Y-axis pointing towards the target's incoming direction at the initial filtering moment, its X-axis located in the horizontal plane and perpendicular to the OY axis, and its Z-axis perpendicular to the plane containing the X and Y axes and pointing upwards. Since the anti-aircraft gun system is usually relatively close to the protected key location relative to the incoming target's position, the shortcut path of the incoming target relative to the anti-aircraft gun system is approximately considered to be 0. Therefore, the direction of the target's incoming direction at the initial filtering moment is approximately used instead of the direction of the target's incoming direction at the initial filtering moment. Compared to the traditional transform measurement Kalman filter algorithm, the core difference of the improved transform measurement Kalman filter algorithm lies in that, for high-angle dive attack targets, the target tracking algorithm does not process the target in the horizontal vehicle coordinate system or vehicle geographic coordinate system, but instead performs filtering in the fire control tilt coordinate system to obtain the target state estimate in the fire control tilt coordinate system, and then performs subsequent prediction and hit detection processing, thus obtaining a more accurate target motion state and effectively improving the tracking accuracy of high-angle dive attack targets.

[0040] This invention provides a method for tracking high-angle dive attack targets based on an inclined coordinate system, such as... Figure 1 As shown, using observation data collected by the tracking system, measurements are converted in real time. Based on the initial target position, a fire control system tilted coordinate system is established. Kalman filtering is performed in the fire control system tilted coordinate system to obtain the target state estimate in the fire control tilted coordinate system. Finally, the calculated target state information is restored to the vehicle-mounted geographic coordinate system. The method of this invention specifically includes the following steps:

[0041] Step 1: Convert the sensor's measurements from the spherical coordinate system to the Cartesian coordinate system.

[0042] In target tracking systems, the target dynamic model is typically modeled in a geographic coordinate system, while sensor measurements are obtained in a spherical coordinate system. Therefore, in filtering algorithms, the observed signal is usually obtained from the target measurement through coordinate transformation to the vehicle's geographic coordinate system, specifically:

[0043]

[0044] In the formula: x d y d and z d These represent the values ​​of the observed signal in the X, Y, and Z directions of the vehicle-mounted geographic coordinate system O-XYZ, respectively; D n q n and εn These represent the distance, azimuth, and elevation angle of the observed signal in the spherical coordinate system, respectively.

[0045] Step 2: Establish a fire control tilted coordinate system based on the direction of the incoming target, and convert the observation signal into the fire control tilted coordinate system.

[0046] For targets attacking at high angles, the target tracking algorithm does not process the data in the horizontal vehicle-mounted geographic coordinate system, but instead performs filtering in the fire control tilted coordinate system to obtain the target state estimate in the fire control tilted coordinate system. It is assumed that the angles between the incoming direction of the observed target in the vehicle-mounted geographic coordinate system and the Y-axis and XOY plane are α and α, respectively. dv and q dv Rotate the vehicle's geographic coordinate system by α around the Z-axis and X-axis respectively. dv and q dv The rotation matrix C is obtained respectively. dvz and C dvx This forms a fire control tilted coordinate system. The observed signal Y is transformed from the vehicle's geographic coordinate system to the fire control tilted coordinate system, specifically:

[0047]

[0048] Where the rotation matrix C dvz and C dvx as follows:

[0049]

[0050]

[0051] In the formula: x v y v and z v These represent the values ​​of the observed signal in the X, Y, and Z directions in the inclined fire control coordinate system, respectively.

[0052] Step 3, calculate the observation variance.

[0053] Assume the target's position in the spherical coordinate system (D) v q v ε v There is a very small deviation ΔD near ) v , Δq v and Δε v When we take the differential on both sides, x becomes... v y v , z v The corresponding error Δx v Δy v and Δz v It can be represented as:

[0054]

[0055] The variance of the observation error in the X, Y, and Z directions of the noise measurement in the fire control tilted coordinate system. and for:

[0056]

[0057] In the formula: and These represent the error variances of the azimuth, elevation, and distance in the fire control tilted coordinate system, respectively.

[0058] Because in the fire control tilted coordinate system, q v =q d -q dv ≈0, ε v =ε d -α dv ≈0, the above formula can be further simplified to:

[0059]

[0060] The observation variance R for the corresponding state is:

[0061]

[0062] In the formula: This represents the covariance of observation errors in the X and Y directions of the measurement noise in the fire control tilted coordinate system. This represents the covariance of observation errors in the X and Z directions of the measurement noise in the fire control tilted coordinate system. This represents the covariance of the observation error in the Y and Z directions of the measured noise in the fire control tilted coordinate system.

[0063] Step 4: Kalman filter solution.

[0064] Based on the measurement transformation in step 1, using the observation error variance R in the inclined coordinate system described in step 3, the target position information (x, y, y) in the inclined coordinate system obtained after the coordinate transformation in step 2 is used. v ,y v ,z v Substitute the observed signal Y(k) as the state and perform linear Kalman filtering to obtain the target position estimate.

[0065] The Kalman filtering process is as follows:

[0066] In a Cartesian coordinate system, the state equation and measurement equation of the discrete linear system are as follows:

[0067] S(k+1)=Φ(k+1,k)S(k)+w(k) (9)

[0068] Y(k)=Θ(k)S(k)+V(k) (10)

[0069] In the formula: k is the discrete time, the target state of the system at time k is S(k); Y(k) is the observed signal of the corresponding state; w(k) is the input white noise; V(k) is the observed noise; Φ(k+1,k) is the state transition matrix.

[0070] The basic process of the Kalman filter algorithm is as follows:

[0071] State prediction in one step:

[0072]

[0073] Status Update:

[0074]

[0075] Filter gain matrix:

[0076] K(k+1)=P(k+1|k)Θ T (k+1)[Θ(k+1)P(k+1|k)Θ T (k+1)+R(k+1)] -1 (13)

[0077] In the formula: Θ is the observation matrix.

[0078] One-step prediction of covariance matrix:

[0079] P(k+1|k)=ΦP(k|k)Φ T +ΓQΓ T (14)

[0080] In the formula: Q is the system error covariance matrix; Γ is the noise driving matrix.

[0081] Covariance update:

[0082] P(k+1∣k+1)=[IK(k+1)Θ(k+1)]P(k+1|k) (15)

[0083] In the formula: I is the identity matrix.

[0084] Step 5, using the inverse rotation matrix C dvz -1 and C dvx -1 The target position estimate after filtering in step 4 is inversely transformed to obtain the target tracking position in the vehicle geographic coordinate system.

[0085] To verify the effectiveness of the transformation measurement Kalman filter technique based on the fire control tilted coordinate system in improving the tracking accuracy of high-angle diving targets, a noisy target path was generated through flight path simulation. The initial position coordinates of the target in the geographic coordinate system were (8000m, 8000m, 20000m), and the target dive angle was approximately 61°. The standard deviations of the noise superimposed on the target range, aiming azimuth angle, and aiming elevation angle were 10m, 3mrad, and 3mrad, respectively. The data sampling period was 0.001s, and the number of Monte Carlo simulations was 100. The root mean square error (RMSE) of the acquired position was used to evaluate the simulation performance. The RMSE is defined as follows:

[0086]

[0087] in, Let M represent the result of estimating the position of the target in a certain direction at time k in the i-th Monte Carlo trial, where M is the total number of Monte Carlo trials and L is the total number of samples in one Monte Carlo trial.

[0088] The simulation results compare the tracking methods for high-angle dive attack targets based on tilted coordinate systems and conventional methods. Figure 2 , Figure 3 and Figure 4 .

[0089] Depend on Figure 2 As shown in 3 and 4, compared with the conventional method, the tracking method for high-angle dive attack targets based on an inclined coordinate system significantly improves the tracking filtering accuracy in the X and Y axes while maintaining good tracking accuracy in the Z-axis direction, especially in the early stage of tracking filtering.

[0090] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for tracking a high-angle dive attack target based on an inclined coordinate system, characterized in that, include: Step 1: Transform the sensor's measurements from the spherical coordinate system to the Cartesian coordinate system, specifically as follows: The observed signal is transformed to obtain the vehicle-mounted geographic coordinate system, specifically as follows: ； In the formula: , and These represent the values ​​of the observed signal along the three coordinate axes in the vehicle's geographic coordinate system; , and These represent the distance, azimuth, and elevation angles of the observed signal in the spherical coordinate system, respectively. Step 2: Establish an inclined fire control coordinate system based on the direction of the incoming target, and convert the observation signal to the inclined fire control coordinate system. Specifically: Assume that the angles between the direction of attack of the observed target in the vehicle-mounted geographic coordinate system and the Y-axis and the XOY plane are respectively... and Rotate the vehicle's geographic coordinate system around the Z-axis and X-axis respectively. and The rotation matrices are obtained respectively. and This forms an inclined fire control coordinate system; observation signals The tilted fire control coordinate system is obtained from the vehicle's geographic coordinate system through coordinate transformation, specifically as follows: ； In the formula: , and These represent the values ​​of the observed signal in the three coordinate axes of the inclined fire control coordinate system; Step 3, calculation of observation error variance, specifically: Assuming the target's position in spherical coordinates The deviation in the vicinity is , and When we take the differential on both sides, then... , , Corresponding error , and They are respectively: ； The variance of the observation error of the measured noise in the three coordinate axes under the tilted fire control coordinate system. , and for: ； In the formula: , and These represent the error variances of the azimuth, elevation, and distance in the tilted fire control coordinate system, respectively. Because in the tilted fire control coordinate system , The above formula can be further simplified to: ； Variance of observation error for corresponding state for: ； In the formula: This represents the observation error covariance in the X and Y directions of the measurement noise in the tilted fire control coordinate system. This represents the covariance of observation errors in the X and Z directions for measurement noise in an inclined fire control coordinate system. Indicates the measurement noise in the tilted fire control coordinate system and Covariance of observation error in direction; Step 4, Kalman filter solution: Based on the measurement transformation in step 1, the observation error variance in the inclined fire control coordinate system described in step 3 is used. The target position information in the tilted fire control coordinate system obtained after coordinate transformation in step 2. Substitute the observed signal as the state. A linear Kalman filter is applied to obtain the target position estimate; Step 5, using the inverse rotation matrix and The target position estimate after filtering in step 4 is inversely transformed to obtain the target tracking position in the vehicle geographic coordinate system.

2. The tracking method for a high-angle dive attack target based on an inclined coordinate system as described in claim 1, characterized in that, In step 2, the rotation matrix and as follows: ； 。

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