Multi-site multi-parameter space target fusion measurement method

Abstract

A multi-station multi-parameter space target fusion measurement method adopts multiple radars to collect multi-dimensional observation information of a target, converts a slant distance, a pitch angle and an azimuth angle of the target relative to the radars into rectangular coordinates of an east-north-sky coordinate system, and converts measurement results of multiple stations in a local coordinate system into a unified coordinate system. Constructing a distance observation equation set, a pitch angle observation equation set, an azimuth angle observation equation set and a distance angle fusion observation equation set, obtaining the measurement precision of each observation equation set, solving the minimum positioning error value of each observation equation set, and determining the observation equation set with the highest target measurement precision and the corresponding measurement precision.

Description

Technical Field

[0001] This invention belongs to the field of radar measurement technology, specifically relating to a multi-radar multi-dimensional measurement and calculation technology. Background Technology

[0002] Long-range space target detection places higher demands on radar detection capabilities, as the measurement accuracy of single-station radar is insufficient to meet the orbit determination and spatial positioning requirements of long-range space targets. Distributed radar systems provide an effective technical approach for high-precision measurement of long-range space targets, and can be divided into distributed interferometry and distributed fusion measurement according to their different operating methods.

[0003] Distributed interferometry utilizes the observation baselines formed between radar stations, effectively increasing the system's antenna aperture to achieve high-precision measurement of distant space targets. The accuracy of distributed interferometry is affected by the spatial-temporal-frequency synchronization accuracy between stations; therefore, high spatial-temporal-frequency accuracy is required between radar stations, necessitating the addition of extra spatial-temporal-frequency synchronization equipment.

[0004] Distributed fusion measurement fuses observation information from each station, utilizing the difference in viewing angles between different radar stations to achieve high-precision measurement of long-range targets. Distributed fusion measurement has low requirements for the spatial-temporal-frequency synchronization accuracy between radar stations, effectively enabling high-precision measurement of long-range space targets. Summary of the Invention

[0005] To address the issue that the accuracy of distributed fusion measurements is affected by the observation area and observation equation, this invention employs multiple radar stations to acquire multiple observation information of the target, constructs different target observation equations, analyzes the measurement accuracy of different observation areas and different observation equations, determines the optimal observation area and observation equation, and achieves high-precision fusion measurement of long-distance space targets using multiple stations and multiple parameters.

[0006] Step 1: Measure the spatial coordinates of the target and multiple radars, calculate the target's slant range, elevation angle, and azimuth angle relative to the radars, and use multiple radars to collect multi-dimensional observation information of the target; let the spatial coordinates of N radars be respectively... Let the spatial coordinates of the target be... The target's slant range, elevation angle, and azimuth angle relative to the radar are calculated as follows: .

[0007] Step two: Calculate the coordinate components based on the target's coordinates in the northeast-sky coordinate system of multiple radars, and convert the target's slant range, elevation angle, and azimuth angle relative to the radars into rectangular coordinates in the northeast-sky coordinate system; use... The coordinates of the target in the northeast-sky coordinate system of the i-th radar are represented by... This represents the coordinate components of the target's northeast-sky coordinates relative to the i-th radar, converting the target's slant range, elevation angle, and azimuth angle relative to the radar into rectangular coordinates in the northeast-sky coordinate system. .

[0008] Step 3: Based on the latitude and longitude of multiple radars and their coordinates in the geocentric coordinate system, and the measured coordinates of the target in the geocentric coordinate system, use a coordinate transformation matrix to convert the target's rectangular coordinates in the northeast-southeast coordinate system to coordinates in the geocentric coordinate system, and convert the measurement results from multiple stations in the local coordinate system into a unified coordinate system; use... Representing the latitude and longitude of the i-th radar, using Let the coordinates of the i-th radar in the geocentric coordinate system be represented by... , , Let each represent a coordinate transformation matrix, using... This represents the target's coordinates in the geocentric coordinate system as measured by the i-th radar, converting the target's Cartesian coordinates in the northeast-northeast coordinate system to geocentric coordinates. .

[0009] Step four: Based on the coordinates of multiple radars and the measured target coordinates, construct a set of target observation equations, including range observation equations, elevation angle observation equations, azimuth angle observation equations, and range-angle fusion observation equations; use... Representing the range observation equations, using To represent the equations for pitch angle observation, use To represent the azimuth observation equations, use The multi-station fusion measurement coordinates of the target are represented by... This represents the set of distance and angle fusion observation equations.

[0010] Step 5: Calculate the partial derivatives of each variable with respect to both ends of the range observation equations, azimuth observation equations, elevation observation equations, and range-angle fusion observation equations. Then calculate the covariance and positioning error of each equation set to obtain the measurement accuracy of each observation equation set. Calculate the partial derivatives of each variable with respect to both ends of the range observation equations to obtain... ,make , , Then the covariance of the positioning error Positioning error Where E() represents the expected value, obtaining the positioning accuracy of the target by the range observation equations; and the partial derivatives of each variable on both sides of the azimuth observation equations are taken, assuming... ,have to ,make , , Then the positioning error covariance Positioning error To obtain the positioning accuracy of the target using the azimuth observation equations; to calculate the partial derivatives of each variable in the elevation observation equations, let... ,make , , ,have to Then the covariance of the positioning error Positioning error To obtain the positioning accuracy of the target using the elevation angle observation equations; to calculate the partial derivatives of each variable at both ends of the range-angle fusion observation equations, let... , , ,make ,have to ,Right now Then the covariance of the positioning error Positioning error The positioning accuracy of the target is obtained by using the distance and angle fusion observation equations.

[0011] Step 6: Measure the distance, elevation angle, and azimuth angle measurement errors of multiple radars at each station. Substitute these errors, along with the target's slant range, elevation angle, and azimuth angle relative to the radar, into the positioning error calculation formula to solve for the minimum positioning error of each set of observation equations. Determine the set of observation equations with the highest target measurement accuracy and its corresponding measurement accuracy. Attached Figure Description

[0012] Figure 1 It is the measurement process.

[0013] Figure 2 These are the relative position coordinates of the target and the radar.

[0014] Figure 3 It represents the positioning error of each set of observation equations. Detailed Implementation

[0015] The following uses three radars as an example to illustrate the technical solution of the present invention in detail with reference to the accompanying drawings.

[0016] Measurement process as follows Figure 1As shown: Step 1, measure the spatial coordinates of the target and multiple radars, calculate the slant range, elevation angle, and azimuth angle of the target relative to the radars, and use multiple radars to collect multi-dimensional observation information of the target; Step 2, calculate the coordinate components based on the target's coordinates in the northeast-sky coordinate system of multiple radars, and convert the target's slant range, elevation angle, and azimuth angle relative to the radars into rectangular coordinates in the northeast-sky coordinate system; Step 3, based on the latitude and longitude of multiple radars and their coordinates in the geocentric coordinate system, and the measured coordinates of the target in the geocentric coordinate system, use a coordinate transformation matrix to convert the target's rectangular coordinates in the northeast-sky coordinate system into coordinates in the geocentric coordinate system, and convert the measurement results of multiple stations in the local coordinate system into a unified coordinate system; Step 4, construct a system based on the coordinates of multiple radars and the measured target coordinates. The target observation equation set includes the range observation equation set, elevation angle observation equation set, azimuth angle observation equation set, and range-angle fusion observation equation set. Step five: Calculate the partial derivatives of each variable at both ends of the range observation equation set, azimuth angle observation equation set, elevation angle observation equation set, and range-angle fusion observation equation set, respectively, and calculate the covariance and positioning error of each equation set to obtain the measurement accuracy of each observation equation set. Step six: Measure the range, elevation angle, and azimuth angle measurement errors of multiple radars at each station, and substitute them, along with the target's slant range, elevation angle, and azimuth angle relative to the radar, into the positioning error calculation formula to solve for the minimum positioning error of each observation equation set, and determine the observation equation set with the highest target measurement accuracy and its corresponding measurement accuracy.

[0017] The spatial coordinates of the three radars were measured as follows: The target's slant range, elevation angle, and azimuth angle relative to the radar are converted into rectangular coordinates in the northeast-northeast coordinate system. ,have to A set of target observation equations was constructed, and the range measurement errors of the three radars at each station were measured. Pitch angle measurement error Azimuth measurement error Together with the target's slant range relative to the radar Pitch angle Azimuth Substituting into the formula for calculating the positioning error GDOP, as follows: Figure 3 As shown, the positioning error GDOP obtained by solving the four observation equations is as follows: , , , The minimum value is selected, and the observation equation set with the highest target measurement accuracy and its corresponding measurement accuracy is determined to be 449m.

Claims

1. A multi-site multi-parameter space target fusion measurement method, characterized in that, include: Step 1: Measure the spatial coordinates of the target and multiple radars, calculate the target's slant range, elevation angle, and azimuth angle relative to the radars, and use multiple radars to collect multi-dimensional observation information of the target; Step 2: Calculate the coordinate components based on the target's coordinates in the northeast-sky coordinate system of multiple radars, and convert the target's slant range, elevation angle, and azimuth angle relative to the radars into rectangular coordinates in the northeast-sky coordinate system. Step 3: Based on the latitude and longitude of multiple radars and their coordinates in the geocentric coordinate system, and the measured coordinates of the target in the geocentric coordinate system, use a coordinate transformation matrix to convert the target's rectangular coordinates in the northeast-southeast coordinate system into coordinates in the geocentric coordinate system, and convert the measurement results of multiple stations in the local coordinate system into a unified coordinate system. Step 4: Based on the coordinates of multiple radars and the target coordinates they measured, construct a set of target observation equations, including range observation equations, elevation angle observation equations, azimuth angle observation equations, and range-angle fusion observation equations. Step 5: Calculate the partial derivatives of each variable at both ends of the range observation equation set, azimuth observation equation set, elevation observation equation set, and range-angle fusion observation equation set respectively, calculate the covariance and positioning error of each equation set, and obtain the measurement accuracy of each observation equation set. Step 6: Measure the distance, elevation angle, and azimuth angle measurement errors of multiple radars at each station. Substitute these errors, along with the target's slant range, elevation angle, and azimuth angle relative to the radar, into the positioning error calculation formula to solve for the minimum positioning error of each set of observation equations. Determine the set of observation equations with the highest target measurement accuracy and its corresponding measurement accuracy.

2. The multi-site, multi-parameter spatial target fusion measurement method according to claim 1, characterized in that, The step one comprises: setting spatial coordinates of N radars respectively are , setting spatial coordinates of the target are , calculating the slant range, the pitch angle and the azimuth angle of the target relative to the radars respectively are .

3. The multi-site, multi-parameter spatial target fusion measurement method according to claim 2, characterized in that, The step two comprises: The target coordinate in the northeast sky coordinate system of the i radar is represented by The target coordinate component in the northeast sky coordinate of the i radar is represented by The slant distance, the pitch angle and the azimuth angle of the target relative to the radar are converted into the northeast sky coordinate system rectangular coordinates.

4. The multi-site, multi-parameter spatial target fusion measurement method according to claim 3, characterized in that, Step three includes: using Representing the latitude and longitude of the i-th radar, using Let the coordinates of the i-th radar in the geocentric coordinate system be represented by... , , Let each represent a coordinate transformation matrix, using... This represents the target's coordinates in the geocentric coordinate system as measured by the i-th radar, converting the target's Cartesian coordinates in the northeast-northeast coordinate system to geocentric coordinates. 。 5. The multi-site, multi-parameter spatial target fusion measurement method according to claim 4, characterized in that, Step four includes: using Representing the range observation equations, using To represent the equations for pitch angle observation, use To represent the azimuth observation equations, use The multi-station fusion measurement coordinates of the target are represented by... This represents the set of distance and angle fusion observation equations.

6. The multi-site, multi-parameter spatial target fusion measurement method according to claim 5, characterized in that, Step five includes: taking the partial derivatives of each variable on both sides of the distance observation equation system to obtain... ,make , , Then the covariance of the positioning error Positioning error , where E() represents the mathematical expectation, which obtains the positioning accuracy of the target based on the distance observation equations.

7. The multi-site, multi-parameter spatial target fusion measurement method according to claim 5, characterized in that, Step five includes: taking the partial derivatives of each variable on both sides of the azimuth observation equation system, and setting... ,have to ,make , , Then the positioning error covariance Positioning error To obtain the positioning accuracy of the target using the azimuth observation equations.

8. The multi-site, multi-parameter spatial target fusion measurement method according to claim 5, characterized in that, Step five includes: taking partial derivatives of each variable on both sides of the pitch angle observation equation system, and assuming... ,make , , ,have to Then the covariance of the positioning error Positioning error To obtain the positioning accuracy of the target using the elevation angle observation equations.

9. The multi-site, multi-parameter spatial target fusion measurement method according to claim 5, characterized in that, Step five includes: taking the partial derivatives of each variable on both sides of the distance-angle fusion observation equation system, and setting... , , ,make ,have to ,Right now Then the covariance of the positioning error Positioning error The positioning accuracy of the target is obtained by using the distance and angle fusion observation equations.

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