A high-precision positioning and multi-domain feature matching tracking method for space-based air defense radars

Abstract

This invention discloses a high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar. Addressing the limitations of 3D positioning accuracy and the susceptibility of false points to interference with track tracking in space-based air-to-air radar, this method first constructs geometric constraints using satellite altitude, target slant range, and estimated altitude. It then constructs a solution equation by combining the rotational transformation from the orbital frame to the antenna conical frame. After side-looking constraints and residual filtering to select a unique solution, it outputs high-precision 3D target coordinates in the WGS-84 system. Based on this, Kalman filtering is used to perform track extrapolation, candidate points are filtered using correlated gates, and the track is updated after multi-domain feature matching verification of position, velocity, acceleration, and signal-to-noise ratio, suppressing the output of non-true tracks. This invention can effectively improve the target positioning accuracy and track tracking stability of space-based air-to-air radar.

Description

Technical Field

[0001] This invention belongs to the field of space-based microwave radar technology, and particularly relates to a high-precision positioning and multi-domain feature matching tracking method for space-based air-to-ground radar. Background Technology

[0002] Space-based air surveillance radar technology deploys detection platforms in space orbit, offering advantages such as wide coverage and independence from geographical limitations, making it crucial for global air surveillance. Its core mission is to generate stable and accurate target tracks, providing continuous and reliable intelligence support for upper-level applications. To achieve this ultimate goal, two tightly coupled technical challenges across the entire chain, from initial measurements to final track generation, must be addressed. Both are indispensable and jointly determine the final accuracy of the track.

[0003] First, the cornerstone of achieving high-precision tracking is the accuracy of single-point positioning. A tracking track consists of a series of continuous positioning points; if there is a deviation in single-point positioning, any subsequent sophisticated tracking algorithm will be built on an incorrect foundation. Currently common space-based target positioning methods, such as projection positioning based on altitude assumptions, suffer from the following drawbacks: inaccurate coordinate transformations due to the complex relative motion between the satellite and the Earth, leading to accumulated errors during coordinate system transformations in traditional methods; and multi-valued ambiguity, as geometric constraint equations often generate multiple solutions, lacking effective physical constraints and residual filtering mechanisms. These shortcomings collectively constitute the primary bottleneck restricting the accuracy of the tracking source.

[0004] Secondly, ensuring high-precision tracks requires accurate track association. After obtaining high-precision measurement points, they must be correctly associated with existing tracks to form continuous and smooth tracks. The essence of track association is matching the new points in the current scanning cycle with the predicted state of existing tracks at the next moment. Kalman filtering is a mature technology for track state prediction, but existing technologies (such as global nearest neighbor) often separate extrapolation prediction from association rules. Even if a relatively accurate predicted state is obtained, it fails to fully utilize its multi-dimensional information (such as position, velocity, acceleration, etc.) for systematic discrimination and matching. Therefore, the lack of an effective track quality assessment and screening mechanism based on multi-domain features, and the inability to systematically solve the problems of "true and false track discrimination" and "accurate association," is a key reason for track interruptions, confusion, or the generation of false tracks.

[0005] In conclusion, the field of space-based air defense radar urgently needs a systematic solution that not only achieves high-precision single-point positioning from the source, but also establishes an intelligent track management strategy based on this. The key to improving the overall performance of space-based radar and achieving high-precision tracks lies in how to organically combine the output of high-precision positioning with a track matching and filtering mechanism based on multi-domain target features to form a closed-loop system of "precise point tracking - accurate correlation." Summary of the Invention

[0006] Given that existing space-based radar positioning methods suffer from problems such as the complex relative motion between satellites and the Earth affecting positioning accuracy, the multi-value problem in positioning solutions when facing target maneuvers or altitude estimation errors, and the fact that traditional global nearest neighbor data association algorithms rely on linearized predictions and suffer from decreased association accuracy, false associations, and missed associations in complex space-based radar environments, this invention aims to provide a high-precision positioning and multi-domain feature matching and tracking method for space-based air-to-ground radar, so as to achieve a full-link performance improvement from single-point accurate positioning to reliable track association.

[0007] The objective of this invention is achieved through the following technical solution. The method first constructs geometric constraints using azimuth, slant range, and estimated altitude, and then combines coordinate system rotation transformation to achieve high-precision calculation of the target's three-dimensional coordinates. Based on this, it further organically combines high-precision track extrapolation with a multi-domain feature matching mechanism to suppress the output of non-realistic tracks. The specific steps are as follows:

[0008] 10) Calculate the pitch angle of the orbital system. and orbital coordinates Define the orbital coordinate system, such as Figure 2 As shown, the X-axis is along the direction of satellite motion, the Z-axis points towards the Earth's center, and the Y-axis is determined according to the right-hand rule. Based on the law of cosines and spatial geometry, the satellite's altitude... Target slant range Earth's radius and estimated target height Solve the pitch angle and Z-axis coordinates of the orbital system. .

[0009] 20) Establish the rotation transformation matrix from the orbital system to the antenna conical system. : Obtain satellite three-axis attitude angles: X-axis attitude angle Y-axis attitude angle Z-axis attitude angle Construct rotation matrices around the Z, Y, and X axes. , , and transformation matrix :

[0010]

[0011] 30) Construct and solve for the x-coordinate of the orbital system. A quadratic equation in one variable: azimuth angle obtained by measurement Obtain the x-coordinate of the conical system:

[0012] Solving the simultaneous linear projection equations and the unit spherical constraint:

[0013]

[0014] eliminate The standard quadratic equation is obtained. The coefficient is:

[0015]

[0016] Two sets of candidate solutions were obtained:

[0017]

[0018] 40) Determine based on radar side-looking direction Positive and negative signs are considered, and a unique solution is selected through residual comparison: Physical side-view constraint: the radar right-side view is taken, and the left-side view is taken with negative signs. The abscissa estimates of the two solutions are then calculated by back-projecting them onto the conical system.

[0019] Compare residuals: If Then lock solution 1 ( Otherwise, lock solution 2 () ).

[0020] 50) Calculate the elevation angle of the antenna conical system: using the selected unique solution ( Calculate the ordinate of the conical system:

[0021]

[0022] This leads to the pitch angle of the conical system:

[0023] 60) Solve for the target's three-dimensional coordinates and complete the coordinate system transformation: Combine this with the target's measured slope distance. azimuth of conical system With pitch angle The target vector in the conical coordinate system is calculated and transformed to the WGS-84 geodetic coordinate system; finally, the three-dimensional positioning coordinates of the target in the WGS-84 system are output. .

[0024] 70) Track extrapolation prediction: For each established stable track in the system The Kalman filter algorithm is used to extrapolate and predict the predicted state of the track at the current measurement time based on the filtered state of the track at the previous moment (including information such as position, velocity, and acceleration). This includes the predicted position, predicted velocity, predicted acceleration, and the corresponding state covariance.

[0025] 80) Filtering of traces within the associated gate: For each new trace obtained in the current measurement cycle With each flight path Using the predicted location as the center, an elliptical correlation gate is constructed using its predicted covariance. If the new trace... Falling into a certain flight path Within the associated gate, the point trace is... Considered a flight path A candidate associated point is stored in a candidate list.

[0026] 90) Multi-domain feature matching verification: Traverse each track For each candidate point in its candidate list, the following multi-domain feature matching judgment is performed sequentially to determine whether the candidate point is a valid continuation point of the track:

[0027] a) Location dimension verification: Verify the candidate points... Measurement location and track The predicted positions obtained in step 80 are compared. If the conditions are met... If the position dimension satisfies the association condition, then the position dimension is considered to satisfy the association condition. This is a preset position threshold.

[0028] b) Velocity dimension verification: If the candidate point trace It has a measured velocity (or is calculated from a series of points), which is then compared with the track. The predicted velocity obtained in step 80) is compared. If it satisfies... |, then the velocity dimension is considered to satisfy the correlation condition, where This is a preset speed threshold.

[0029] c) Acceleration dimension verification: If the candidate point trace It has an estimable acceleration, which is compared with the trajectory. The predicted acceleration obtained in step 80) is compared. If the conditions are met... Then the acceleration dimension is considered to satisfy the correlation condition, where This is a preset acceleration threshold.

[0030] d) Signal-to-noise ratio (SNR) dimension verification: Candidate point traces signal-to-noise ratio With track Average signal-to-noise ratio of historical traces Compare them. If satisfied... If the signal-to-noise ratio dimension satisfies the correlation condition, then... This is the preset signal-to-noise ratio threshold.

[0031] 100) Track update and output:

[0032] If a candidate point trace With a certain flight path If the correlation conditions are met in multiple preset dimensions, then the point is determined to be a valid point. For the track The valid continuation point of the trace. The measured values ​​are input to the Kalman filter to analyze the flight path. The status is updated, and the updated track information is output.

[0033] If a candidate point trace If a point does not fall into any associated gate of any track, or if it fails to match the multi-domain features of all candidate tracks, then the output of that point is blocked.

[0034] If an established flight path If no valid points are associated within several consecutive cycles, the track is considered terminated and is marked or deleted.

[0035] Compared with existing technologies, the advantages of this invention are as follows: The high-precision positioning and multi-domain feature matching tracking method proposed in this invention for space-based air-to-ground radar effectively overcomes the dual shortcomings of existing technologies in terms of positioning accuracy and track reliability by organically combining high-precision positioning with intelligent track management, and achieves full-link performance improvement from single-point positioning to track tracking.

[0036] In terms of positioning accuracy, this invention effectively improves the accuracy and reliability of track data. By constructing a precise coordinate transformation matrix and constraint equations, this invention simplifies the nonlinear positioning problem into a low-complexity solution; by combining radar physical characteristics and residual criteria, it eliminates the ambiguity of multi-valued coordinate calculations, ensuring that the final output WGS-84 coordinates have high accuracy and high reliability.

[0037] In terms of track management, this invention innovatively introduces a multi-domain feature matching mechanism based on track extrapolation, building upon high-precision positioning. First, mature filtering algorithms such as Kalman filtering are used to accurately extrapolate and predict existing tracks, obtaining their high-precision position and velocity at the next moment. Then, these high-quality prediction results are used as a benchmark, and rigorous feature matching verification is performed with the track to be confirmed across multiple dimensions, including distance, velocity, and azimuth. This dual verification mechanism of "accurate prediction - multi-dimensional matching" effectively identifies and suppresses false tracks generated by interference such as multipath effects, which have specific correlations with real tracks in multiple physical dimensions. This improves the accuracy and purity of track output, avoids the contamination of air situation by false tracks, provides highly reliable target intelligence for upper-level applications, and enhances the robustness and application value of space-based radar in complex environments.

[0038] In summary, this invention forms a closed-loop technology of "precise positioning - intelligent screening - reliable output." It requires no additional hardware upgrades; system performance can be improved solely through software algorithm upgrades. This method is applicable to multi-orbit, multi-band space-based radar systems and has strong operability and broad application prospects in engineering scenarios such as space surveillance. Attached Figure Description

[0039] Figure 1 This is a flowchart of a high-precision positioning method based on space-based air-to-air radar.

[0040] Figure 2 This is a schematic diagram of the satellite orbital coordinate system.

[0041] Figure 3 This is the trajectory association result of an embodiment of the present invention. Detailed Implementation

[0042] The present invention will now be described in further detail with reference to the accompanying drawings. The embodiments provided will enable those skilled in the art to more fully understand the present invention, but will not limit the present invention in any way.

[0043] This invention provides a high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar. The method first constructs geometric constraints by using azimuth, slant range and estimated altitude, and then combines yaw compensation and coordinate system rotation transformation to achieve high-precision calculation of the target's three-dimensional coordinates. On this basis, it further organically combines high-precision track extrapolation with a multi-domain feature matching mechanism to suppress the output of non-real tracks.

[0044] In this embodiment, the parameters for the space-based radar and the target scene are set as follows:

[0045] Satellite orbital altitude: approximately 400 km (≈6771km)

[0046] Earth's radius: 6371 km

[0047] Estimated altitude of the target: 10km

[0048] Radar operating wavelength λ: 0.03m (X-band)

[0049] Antenna Aperture 2.5m

[0050] Coordinate system definitions: orbital system (X-axis velocity, Z-axis geocentric, Y-axis right-hand rule); antenna conical system; J2000 inertial system; WGS-84 geodetic system.

[0051] The specific steps are as follows:

[0052] S1: High-precision three-dimensional positioning module

[0053] 10) Calculate the pitch angle of the orbital system. and orbital coordinates Define the orbital coordinate system as follows: Figure 2 As shown, the X-axis is along the direction of satellite motion, the Z-axis points towards the Earth's center, and the Y-axis is determined according to the right-hand rule. Based on the law of cosines and spatial geometry, the satellite's altitude... Target slant range Earth's radius and estimated target height Solve for the pitch angle of the orbital system:

[0054]

[0055] The Z-axis coordinate of the orbital system is:

[0056]

[0057] 11) By satellite altitude =6871km, target slant range R (assumed to be 500km), Earth radius =6371km and estimated target altitude Solve for the pitch angle of the orbital system:

[0058]

[0059] The Z-axis coordinate of the orbital system is:

[0060]

[0061] 20) Establish the rotation transformation matrix from the orbital system to the antenna conical system. : Obtain satellite three-axis attitude angles: X-axis attitude angle Y-axis attitude angle Z-axis attitude angle Construct rotation matrices around the Z, Y, and X axes:

[0062]

[0063]

[0064]

[0065] Transformation matrix It can be represented as:

[0066]

[0067] 21) Assume the satellite's three-axis attitude angles: X-axis attitude angle = 0.5° = 0.008727 rad, Y-axis attitude angle = 0.3° = −0.005236 rad, Z-axis attitude angle =0.2°=0.003491rad. The rotation matrices around the Z, Y, and X axes are calculated. , , and transformation matrix :

[0068]

[0069]

[0070] 30) Construct and solve for the x-coordinate of the orbital system. A quadratic equation in one variable: derived from the compensated azimuth angle Obtain the x-coordinate of the conical system:

[0071] Solving the simultaneous linear projection equations and the unit spherical constraint:

[0072]

[0073] eliminate The standard quadratic equation is obtained. The coefficient is:

[0074]

[0075] Two sets of candidate solutions were obtained:

[0076]

[0077] 31) Assume the measured value is... =30°, then the x-coordinate of the cone system

[0078] =sin(30°)=0.50

[0079] Solve the linear projection equations and the unit sphere constraint simultaneously to eliminate The standard quadratic equation is obtained. The coefficient is:

[0080]

[0081] Two sets of candidate solutions were obtained:

[0082]

[0083] 40) Determine based on radar side-looking direction Positive and negative values, and a unique solution is selected by comparing residuals: Physical side-look constraint: Radar right-side view. The left side is considered to have a negative sign.

[0084] Calculate the estimated abscissa values ​​of the two sets of solutions back-projected onto the conical system:

[0085]

[0086] Compare residuals: If Then lock solution 1 ( Otherwise, lock solution 2 () ).

[0087] 41) Assuming a right-side viewing pattern, then:

[0088]

[0089] Calculate the estimated abscissa values ​​of the two sets of solutions back-projected onto the conical system:

[0090]

[0091] Based on the above calculation results, a unique solution has been identified.

[0092] 50) Calculate the elevation angle of the antenna conical system: using the selected unique solution ( Calculate the ordinate of the conical system:

[0093]

[0094] This leads to the pitch angle of the conical system:

[0095] 51) Utilizing the selected unique solution ( Calculate the ordinate of the conical system:

[0096]

[0097] Obtain the pitch angle of the conical system:

[0098] 60) Solve for the target's three-dimensional coordinates and complete the coordinate system transformation: Combine this with the target's measured slope distance. azimuth of conical system With pitch angle The target vector in the conical coordinate system is calculated and transformed to the WGS-84 geodetic coordinate system. Finally, the three-dimensional positioning coordinates of the target in the WGS-84 system are output. .

[0099] 61) Solve for the target's three-dimensional coordinates and complete the coordinate system transformation: Combine this with the target's measured slope distance. azimuth of conical system With pitch angle The target vector in the conical coordinate system is calculated and transformed to the WGS-84 geodetic coordinate system; the final output of the target's three-dimensional positioning coordinates (latitude, longitude, and altitude coordinates, with altitude in km) in the WGS-84 system is as follows:

[0100] .

[0101] S1: Track Association Module

[0102] 70) Track extrapolation prediction: For each established stable track in the system The Kalman filter algorithm is used to extrapolate and predict the current state of the track at time k based on the filtered state at the previous time k-1. Assume that for the track... After extrapolation, its predicted state at time k is obtained as follows:

[0103] Predicted location : (116.410°E, 39.901°N, 10.0)

[0104] Predicting speed 250 m / s

[0105] Predicted acceleration 2 m / s²

[0106] State covariance A 3x3 matrix used for subsequent gate and threshold calculations.

[0107] 80) Filtering points within the associated gate: based on the track Predicted location Centered on this, we utilize its predictive covariance. Establish an elliptical correlation gate. The new dot pattern is determined... It fell into the associated gate, therefore, regarded as a track A candidate associated point trace.

[0108] 90) Multi-domain feature matching verification: The system verifies candidate point traces. With track The predicted state is subjected to multi-domain feature matching verification to determine Is it a valid continuation point of the flight path?

[0109] a) Location dimension verification: Verify the candidate points... Measurement location and track Predicted location A comparison was made. The distance difference between the two is approximately 500m, which is less than the preset position threshold. If the value is 600m, then the position dimension is considered to satisfy the association condition.

[0110] b) Velocity dimension verification: Pass The measured velocity was calculated from the previous associated point. (Assuming a speed of 255 m / s), compare it with the flight path. Prediction speed A comparison was made. The speed difference was |255-250|=5m / s, which is less than the preset speed threshold. If (e.g., 14 m / s), then the velocity dimension is considered to satisfy the correlation condition.

[0111] c) Acceleration dimension verification: via The measured acceleration was obtained by calculating the previous point traces. (Assuming a speed of 2.5 m / s²), compare it with the flight path. Predicted acceleration A comparison was made. The acceleration difference was |2.5-2|=0.5m / s², which is less than the preset acceleration threshold. (For example, 3 m / s²), then the acceleration dimension is considered to satisfy the correlation condition.

[0112] d) Signal-to-noise ratio (SNR) dimension verification: acquiring the trace signal-to-noise ratio (Assuming a value of 25dB), and the track Average signal-to-noise ratio of historical traces (Assuming a signal-to-noise ratio of 23dB) a comparison is made. The signal-to-noise ratio difference is |25 - 23| = 2dB, which is less than the preset signal-to-noise ratio threshold. If the signal-to-noise ratio is 10dB (e.g., 10dB), then the signal-to-noise ratio dimension is considered to meet the correlation condition.

[0113] 100) Track update and output:

[0114] Due to candidate traces With track If the correlation conditions are met in all four preset dimensions—position, velocity, acceleration, and signal-to-noise ratio—the system determines that the point is a valid track. For the track The valid continuation point of the trace. The measured values ​​are input to the Kalman filter to analyze the flight path. The status is updated, and the updated track information is output. If If no match is found with any track, the output is prevented from becoming a new track point. Following the steps described above, the track association result in this embodiment is as follows: Figure 3 As shown, some of the points (blue) that meet the matching rules are output as tracks, while the other part of the points (orange) are considered false tracks because they do not meet all the matching rules, and the track output process is suppressed.

Claims

1. A high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar, characterized in that, Includes the following steps: 10) Calculate the pitch angle of the orbital system. and orbital coordinates ; 20) Establish the rotation transformation matrix from the orbital system to the antenna conical system. ; 30) Construct and solve for the x-coordinate of the orbital system. The quadratic equation of 40) Determine based on radar side-looking direction The positive and negative signs are determined, and a unique solution is selected by comparing the residuals. 50) Calculate the elevation angle of the antenna conical system; 60) Solve for the target's three-dimensional coordinates and complete the coordinate system transformation; 70) Track extrapolation prediction; 80) Filtering of dots within the associated gate; 90) Multi-domain feature matching verification; 100) Track update and output.

2. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 1, characterized in that, Step 10) specifically includes: defining an orbital coordinate system, with the X-axis along the satellite's motion direction, the Z-axis pointing towards the Earth's center, and the Y-axis determined according to the right-hand rule. Based on the law of cosines and spatial geometric relationships, the Y-axis is determined from the satellite's altitude... Target slant range Earth's radius and estimated target height Solve the pitch angle and Z-axis coordinates of the orbital system. ; Step 20) specifically includes: obtaining the satellite's three-axis attitude angles: X-axis attitude angle Y-axis attitude angle Z-axis attitude angle Construct rotation matrices around the Z, Y, and X axes. , , and transformation matrix ; Step 30) specifically includes: the azimuth angle obtained by measurement. By obtaining the abscissa of the conical system, and combining the linear projection equations with the unit spherical constraint, two sets of candidate solutions are obtained.

3. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 2, characterized in that, Step 40) specifically includes: Physical side-view constraints: The radar takes a view from the right side and a negative view from the left side, and calculates the estimated abscissa values ​​of the two solutions back-projected onto the conical system. ; Compare residuals: If Then lock solution 1 ( Otherwise, lock solution 2 () ).

4. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 3, characterized in that, Step 50) specifically includes: Using the selected unique solution ( Calculate the ordinate of the conical system: ； This leads to the pitch angle of the conical system: .

5. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 4, characterized in that, Step 60) specifically includes: Combined with target measurement of slope distance azimuth of conical system With pitch angle The target vector in the conical coordinate system is calculated and transformed to the WGS-84 geodetic coordinate system; finally, the three-dimensional positioning coordinates of the target in the WGS-84 system are output. .

6. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 5, characterized in that, Step 70) specifically includes: For each established stable track in the system The Kalman filter algorithm is used to extrapolate and predict the predicted state of the track at the current measurement time based on the filtering state of the track at the previous moment, including the predicted position, predicted velocity, predicted acceleration and the corresponding state covariance.

7. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 6, characterized in that, Step 80) specifically includes: For each new point obtained in the current measurement cycle With each flight path Centered on the predicted location, an elliptical correlation gate is established using its predicted covariance. If the new point trace... Falling into a certain flight path Within the associated gate, the point trace is... Considered a flight path A candidate associated point is stored in a candidate list.

8. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 7, characterized in that, Step 90) specifically includes: Traversing every flight path For each candidate point in its candidate list, the following multi-domain feature matching judgment is performed sequentially to determine whether the candidate point is a valid continuation point of the track; a) Position dimension verification: If the absolute value of the difference between the measured position of the candidate point and the predicted position of the track is less than the preset position threshold, the position dimension verification passes. b) Velocity dimension verification: If the absolute value of the difference between the measured velocity of the candidate point and the predicted velocity of the track is less than the preset velocity threshold, the velocity dimension verification passes. c) Acceleration dimension verification: If the absolute value of the difference between the measured acceleration of the candidate point and the predicted acceleration of the track is less than the preset acceleration threshold, the acceleration dimension verification passes. d) Signal-to-noise ratio (SNR) dimension verification: If the absolute value of the difference between the SNR of the candidate point and the average SNR of the historical points of the track is less than the preset SNR threshold, then the SNR dimension verification passes.

9. The high-precision positioning and multi-domain feature matching tracking method for space-based air-to-air radar according to claim 8, characterized in that, Step 100) specifically includes: If a candidate point trace With a certain flight path If the correlation conditions are met in multiple preset dimensions, then the point is determined to be a valid point. For the track The valid continuation point, the trace of this point. The measured values ​​are input to the Kalman filter to analyze the flight path. The status is updated, and the updated track information is output; If a candidate point trace If the associated gate does not fall into any track, or if the multi-domain feature matching with all candidate tracks fails, then the output of that track is blocked. If an established flight path If no valid points are associated within several consecutive cycles, the track is considered terminated and is marked or deleted.

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