Weighted linear iteration based three-dimensional positioning method and system for spaceborne multi-base radar system

Abstract

The application provides a kind of based on weighted linear iteration's spaceborne multi-base radar system three-dimensional positioning method and system, comprising: obtaining the radar echo data of multiple receivers and effectively detecting target, search the elevation angle and spatial cone angle of target signal by two-dimensional adaptive filtering technology, obtain the two-dimensional angle estimation information of target under different base different visual angle;According to the two-dimensional angle information and slant range information of target under different visual angle, construct nonlinear equation group, and carry out first-order Taylor expansion to it, obtain corresponding linear overdetermined equation group;According to the measurement accuracy known to radar system, form accuracy matrix to the linear overdetermined equation and carry out normalization operation and iterative calculation, and calculate the three-dimensional coordinates of target in the earth-centered earth-fixed coordinate system, and then obtain the longitude and latitude and height information of target, realize the high-precision three-dimensional positioning of multi-base radar system.

Description

Technical Field

[0001] This invention relates to the field of target localization using spaceborne multi-base radar, and more specifically, to a three-dimensional localization method and system for spaceborne multi-base radar systems based on weighted linear iteration. Background Technology

[0002] Target localization technology is a crucial component of radar target detection. To achieve high-precision three-dimensional target localization using radar echo data, scholars both domestically and internationally have proposed target localization methods based on stereo SAR (Stereoscopic Resonance) technology. This method does not require prior knowledge of reference point positions and can achieve flexible three-dimensional target localization by combining multiple sets of echo data. In recent years, stereo localization technology based on SAR has been further improved, for example, through three-dimensional localization estimation techniques based on the range-Doppler equation and least-squares iteration, and by accurately modeling the multi-layer delay errors of the electromagnetic wave propagation process to improve accuracy. However, all of the above stereo localization techniques neglect the relative velocity of the scattering points of the target on the ground, and are only suitable for localizing stationary scattering points on the ground, but their effectiveness in locating moving targets in the air is not ideal. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the purpose of this invention is to provide a three-dimensional positioning method and system for spaceborne multi-base radar systems based on weighted linear iteration.

[0004] A three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration, provided by the present invention, includes:

[0005] Step S1: Acquire radar echo data from multiple receivers, and search for the elevation angle and spatial cone angle of the target signal through two-dimensional adaptive filtering to obtain two-dimensional angle estimation information of the target under different bases and different viewpoints;

[0006] Step S2: Construct a nonlinear equation system based on the two-dimensional angle information and slant range information of the target from different perspectives, and perform a first-order Taylor expansion on the nonlinear equation system to obtain the corresponding linear overdetermined equation system.

[0007] Step S3: Normalize and iteratively solve the linear overdetermined equations based on the accuracy matrix of the radar system to obtain the three-dimensional coordinates of the target in the geocentric coordinate system;

[0008] Step S4: Convert the target's three-dimensional coordinates in the geocentric coordinate system into the target's latitude, longitude, and altitude information to obtain the target's three-dimensional positioning.

[0009] Preferably, the two-dimensional adaptive filtering search in step S1 includes:

[0010]

[0011] in, The spatial cone angle of the target relative to the receiver. s is the downward view of the target relative to the receiver. tar,3D The Doppler-pitch-azimuth three-dimensional spacetime guidance vector for the target. Let X0 be the estimated clutter covariance matrix, X0 be the radar echo data vector, and |·| be the modulus operation for complex numbers. The parameter value is the value at which the function reaches its minimum; the superscript H indicates the conjugate transpose of the matrix.

[0012] Preferably, the linear overdetermined system of equations includes:

[0013]

[0014] Wherein, [Δx Δy Δz] T Update the vector for coordinates. Let be the extended gradient matrix obtained in the iteration, and its expression is:

[0015]

[0016] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0017]

[0018] In the formula, These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f2 (n) (x,y,x)f3 (n) The expressions for (x, y, x) are as follows:

[0019]

[0020] Where v0 is the receiver speed, v x v y v z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver; 31 T 32 T 33 The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system.

[0021]

[0022] in, Let be the slant range measurement from the target to the (n)th receiver. Let the spatial cone angle of the target be measured relative to the (n)th receiver. Let be the downward view of the target relative to the (n)th receiver.

[0023] Preferably, step S3 involves updating the three-dimensional coordinates of the target in the geocentric-geofixed coordinate system during each iteration.

[0024] The coordinate update expression is:

[0025]

[0026] Where, x k x k+1 Let be the target 3D coordinate vector obtained in the k+1th iteration. W1 is the normalized iterative gradient matrix, and W2 is the corresponding weight matrix.

[0027] The normalized iterative gradient matrix The calculation expression is:

[0028]

[0029]

[0030] Where ||·||2 is the formula for calculating the l1 norm of a vector, and diag(·) is the formula for converting a vector into a diagonal matrix. Let be the gradient matrix of the extension;

[0031]

[0032] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0033]

[0034] in, These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f2 (n) (x,y,x)f3 (n) The expressions for (x, y, x) are as follows:

[0035]

[0036] Where v0 is the receiver speed, v x v yv z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver; 31 T 32 T 33 The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system.

[0037] W2 is the normalized measurement accuracy matrix, calculated as follows:

[0038] W2 = W1VW1

[0039] Where V is the precision matrix of the extension, and its expression is:

[0040]

[0041] Among them, V (n) Let n be the measurement accuracy matrix corresponding to the nth receiver, and its expression is:

[0042]

[0043] in, The accuracy of the two-way slant range measurement, the accuracy of the space cone angle measurement, and the accuracy of the elevation angle measurement for the transmitter-target-receiver (n) system are known parameters.

[0044] Preferably, step S4 employs the following methods:

[0045] The formulas for calculating latitude, longitude, and altitude are as follows:

[0046]

[0047] in, The estimated three-dimensional coordinates of the target obtained by the iterative method are represented by Angle(·), which is the argument operation of a complex number. e The radius is the Earth's radius.

[0048] A three-dimensional positioning system for a spaceborne multi-base radar system based on weighted linear iteration, according to the present invention, includes:

[0049] Module M1: Acquires radar echo data from multiple receivers, searches for the elevation angle and spatial cone angle of the target signal through two-dimensional adaptive filtering, and obtains two-dimensional angle estimation information of the target from different bases and different viewpoints;

[0050] Module M2: Constructs a set of nonlinear equations based on the two-dimensional angle information and slant range information of the target from different perspectives, and performs a first-order Taylor expansion on the set of nonlinear equations to obtain the corresponding linear overdetermined equations.

[0051] Module M3: Based on the accuracy matrix of the radar system, the linear overdetermined equations are normalized and iteratively solved to obtain the three-dimensional coordinates of the target in the geocentric coordinate system;

[0052] Module M4: Converts the target's three-dimensional coordinates in the geocentric coordinate system into the target's latitude, longitude, and altitude information to obtain the target's three-dimensional positioning.

[0053] Preferably, the two-dimensional adaptive filtering search in module M1 includes:

[0054]

[0055] in, The spatial cone angle of the target relative to the receiver. s is the downward view of the target relative to the receiver. tar,3D The Doppler-pitch-azimuth three-dimensional spacetime guidance vector for the target. Let X0 be the estimated clutter covariance matrix, X0 be the radar echo data vector, and |·| be the modulus operation for complex numbers. The parameter value is the value at which the function reaches its minimum; the superscript H indicates the conjugate transpose of the matrix.

[0056] Preferably, the linear overdetermined system of equations includes:

[0057]

[0058] Wherein, [Δx Δy Δz] T Update the vector for coordinates. Let be the extended gradient matrix obtained in the iteration, and its expression is:

[0059]

[0060] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0061]

[0062] In the formula, These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f2 (n) (x,y,x)f3 (n) The expressions for (x, y, x) are as follows:

[0063]

[0064] Where v0 is the receiver speed, v x v y v z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver; 31 T 32 T 33 The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system.

[0065]

[0066] in, Let be the slant range measurement from the target to the (n)th receiver. Let the spatial cone angle of the target be measured relative to the (n)th receiver. Let be the downward view of the target relative to the (n)th receiver.

[0067] Preferably, module M3 updates the three-dimensional coordinates of the target in the geocentric-geostatic coordinate system during each iteration;

[0068] The coordinate update expression is:

[0069]

[0070] Where, x k x k+1 Let be the target 3D coordinate vector obtained in the k+1th iteration. W1 is the normalized iterative gradient matrix, and W2 is the corresponding weight matrix.

[0071] The normalized iterative gradient matrix The calculation expression is:

[0072]

[0073]

[0074] Where, ||·||2 is the vector Norm calculation formula, diag(·) is the calculation formula for converting a vector to a diagonal matrix. Let be the gradient matrix of the extension;

[0075]

[0076] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0077]

[0078] in, These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f3 (n) The expressions for (x, y, x) are as follows:

[0079]

[0080] Where v0 is the receiver speed, v x v y v z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver; 31 T 32 T 33 The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system.

[0081] W2 is the normalized measurement accuracy matrix, calculated as follows:

[0082] W2 = W1VW1

[0083] Where V is the precision matrix of the extension, and its expression is:

[0084]

[0085] Among them, V (n) Let n be the measurement accuracy matrix corresponding to the nth receiver, and its expression is:

[0086]

[0087] in, The accuracy of the two-way slant range measurement, the accuracy of the space cone angle measurement, and the accuracy of the elevation angle measurement for the transmitter-target-receiver (n) system are known parameters.

[0088] Preferably, the module M4 adopts:

[0089] The formulas for calculating latitude, longitude, and altitude are as follows:

[0090]

[0091] in, The estimated three-dimensional coordinates of the target obtained by the iterative method are represented by Angle(·), which is the argument operation of a complex number. e The radius is the Earth's radius.

[0092] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a stereo positioning method based on a spaceborne multi-base radar system. This method can achieve high-precision three-dimensional stereo positioning of target signals in a multi-base radar system, overcoming the shortcomings of existing mono-base radars that cannot accurately estimate the height information of targets and multi-base radars that can only locate stationary targets on the ground. Furthermore, by estimating the accuracy of distance and angle measurements and weighting the iterative process, high-precision three-dimensional stereo positioning of moving targets in a multi-base radar system can be achieved. Attached Figure Description

[0093] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0094] Figure 1 This is a flowchart of a stereo positioning method based on a spaceborne multi-base radar system provided in an embodiment of the present invention;

[0095] Figure 2 This is a comparison chart of the target positioning and range-Doppler equation multi-base target positioning error curves of the present invention and traditional single-base positioning. Detailed Implementation

[0096] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0097] Example 1

[0098] The purpose of this invention is to provide a three-dimensional positioning method and apparatus for a spaceborne multi-static radar system based on weighted linear iteration, which addresses the shortcomings of monostatic radar systems in being unable to perform three-dimensional positioning of moving targets due to insufficient target information, and multistatic radar systems in being unable to perform high-precision three-dimensional positioning of aerial targets due to the additional radial velocity of moving targets.

[0099] According to the present invention, a three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration is provided, such as... Figure 1 As shown, it includes the following steps:

[0100] The echo sample data from the receiver is acquired and converted into a Doppler-azimuth-elevation column vector after moving target detection.

[0101] Based on the echo data column vector, estimate the covariance matrix of the target, clutter, and noise, and perform a two-dimensional adaptive search for the target's pitch angle and spatial cone angle;

[0102] Based on the measured values ​​of the target pitch angle and spatial cone angle, as well as the target's two-way slant range, a nonlinear equation system is established. The number of equations in the equation system is 3N, where N is the number of receivers.

[0103] The nonlinear equations are linearized into an overdetermined system of equations through Taylor first-order expansion. An accuracy matrix is ​​formed based on radar system parameter estimates. The three-dimensional coordinates of the target are then solved through weighted linearization iteration.

[0104] The latitude, longitude, and altitude of the target are calculated based on the calculated three-dimensional coordinates of the target, thus achieving high-precision three-dimensional positioning of the target.

[0105] Furthermore, the two-dimensional angle adaptive search expression is:

[0106]

[0107] In the formula, The spatial cone angle of the target relative to the receiver. s is the downward view of the target relative to the receiver. tar,3D The Doppler-pitch-azimuth three-dimensional spacetime guidance vector for the target. Let X0 be the estimated clutter covariance matrix, X0 be the radar echo data vector, and |·| be the modulus operation for complex numbers. This refers to the operation of finding the parameter value when the function reaches its minimum value.

[0108] Furthermore, the linear overdetermined system of equations includes:

[0109]

[0110] Wherein, [Δx Δy Δz] T Update the vector for coordinates. Let be the extended gradient matrix obtained in the iteration, and its expression is:

[0111]

[0112] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0113]

[0114] In the formula, These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f2 (n) (x,y,x)f3 (n) The expressions for (x, y, x) are as follows:

[0115]

[0116] Where v0 is the receiver speed, v x v y v z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver; 31 T 32 T 33 The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system.

[0117]

[0118] in, Let be the slant range measurement from the target to the (n)th receiver. Let the spatial cone angle of the target be measured relative to the (n)th receiver. Let be the downward view of the target relative to the (n)th receiver.

[0119] Furthermore, a weighted linearized iterative method is used to calculate the target's three-dimensional coordinates. The target coordinates are updated in each iteration, and the iterative update expression for the target coordinates is as follows:

[0120]

[0121] In the formula x k x k+1 Let be the target 3D coordinate vector obtained in the k+1th iteration. W1 is the normalized iterative gradient matrix, W2 is the normalized measurement accuracy matrix, and W1 is the corresponding normalized matrix.

[0122] Furthermore, the normalized iterative matrix The calculation expression is:

[0123]

[0124]

[0125] In the formula, ||·||2 is the vector Norm calculation formula, diag(·) is the calculation formula for converting a vector to a diagonal matrix. The gradient matrix of the extension

[0126]

[0127] N is the total number of receivers, G (n) Let n = 1, ..., N be the measurement gradient matrix corresponding to the (n)th receiver, and its expression is:

[0128]

[0129] In the formula These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively, and the function f1. (n) (x,y,x), f2 (n) (x,y,x)f3 (n) The expressions for (x, y, x) are respectively

[0130]

[0131] In the formula, v0 is the speed of the receiver, v x v y v z Let x be the components of the receiver velocity on the three-dimensional coordinate axes. T ,y T ,z T ( ) represents the transmitter's position coordinates. Let T be the position coordinates of the (n)th receiver. 31 T 32 T 33 This is the transformation coefficient for converting the Earth-fixed coordinate system to the receiver antenna panel coordinate system.

[0132] W2 is the normalized measurement accuracy matrix, calculated as follows:

[0133] W2=W1VW1(14)

[0134] In the formula, V is the accuracy matrix of the extension, and its expression is:

[0135]

[0136] In the formula V (n) Let n be the measurement accuracy matrix corresponding to the nth receiver, and its expression is:

[0137]

[0138] In the formula The accuracy of the two-way slant range measurement, the accuracy of the space cone angle measurement, and the accuracy of the elevation angle measurement for the transmitter-target-receiver (n) system are known parameters.

[0139] Furthermore, the calculation expression for calculating the target's latitude, longitude, and altitude based on the target's three-dimensional coordinates is as follows:

[0140]

[0141] In the formula, The estimated three-dimensional coordinates of the target obtained by the iterative method are represented by Angle(·), which is the argument operation of a complex number. e The radius is the Earth's radius.

[0142] The present invention also provides a three-dimensional positioning system for a spaceborne multi-base radar system based on weighted linear iteration. The three-dimensional positioning system for a spaceborne multi-base radar system based on weighted linear iteration can be implemented by executing the process steps of the three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration. That is, those skilled in the art can understand the three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration as a preferred embodiment of the three-dimensional positioning system for a spaceborne multi-base radar system based on weighted linear iteration.

[0143] Example 2

[0144] Example 2 is a preferred example of Example 1.

[0145] A stereo positioning method based on a spaceborne multi-base radar system provided by the present invention includes:

[0146] All implementation steps in this embodiment are performed on the MATLAB 2018 simulation platform.

[0147] The implementation steps of this embodiment include:

[0148] Step S1: Acquire target echo data input to the receiver L and M are the number of azimuth channels and elevation channels of the receiving antenna, respectively. The elevation angle and spatial cone angle of the target relative to the receiving antenna are estimated using a two-dimensional angle adaptive search according to formula (1).

[0149] Step S2: Establish a system of nonlinear equations based on the pitch angle and space cone angle estimation information, as well as the target slant range information;

[0150] In this simulation experiment, the two-way slant range information of receiver 1 and the target corresponding to the receiver is 8372.219km and 7219.677km, respectively.

[0151] Step S3: Based on the nonlinear equation system, linearize it into an overdetermined equation system through Taylor expansion, and solve the unknowns of the equation system using the weighted iteration method according to formula (8);

[0152] The accuracy matrix for this simulation experiment is set as follows:

[0153]

[0154] Step S4: Convert the calculated three-dimensional coordinates of the target into latitude, longitude and altitude information of the target according to formula (17) to achieve three-dimensional positioning of the target.

[0155] The absolute distance error obtained by the target three-dimensional stereo positioning device according to the present invention after 50 Monte Carlo repeated tests is compared with the monostatic stereo positioning method and the multistatic stereo positioning method based on the range Doppler equation, as shown in the curve. Figure 2 As shown in the figure. The results demonstrate that the method provided by this invention can achieve high-precision three-dimensional positioning of moving targets in the air.

[0156] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0157] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration, characterized in that, include: Step S1: Acquire radar echo data from multiple receivers, and search for the elevation angle and spatial cone angle of the target signal through two-dimensional adaptive filtering to obtain two-dimensional angle estimation information of the target under different bases and different viewpoints; Step S2: Construct a nonlinear equation system based on the two-dimensional angle information and slant range information of the target from different perspectives, and perform a first-order Taylor expansion on the nonlinear equation system to obtain the corresponding linear overdetermined equation system. Step S3: Normalize and iteratively solve the linear overdetermined equations based on the accuracy matrix of the radar system to obtain the three-dimensional coordinates of the target in the geocentric coordinate system; Step S4: Convert the target's three-dimensional coordinates in the geocentric coordinate system into the target's latitude, longitude, and altitude information to obtain the target's three-dimensional positioning; Step S3 involves updating the three-dimensional coordinates of the target in the geocentric coordinate system during each iteration. The coordinate update expression is: in, , For the first k , k The target 3D coordinate vector obtained after +1 iterations The normalized iterative gradient matrix, This is the corresponding weight matrix; ; Update the vector for coordinates. Let be the gradient matrix of the extension; The normalized iterative gradient matrix The calculation expression is: in, For vectors Norm calculation formula The calculation formula for converting a vector into a diagonal matrix. Let be the gradient matrix of the extension; N The total number of receivers, For the first n Each receiver corresponds to a measurement gradient matrix, the expression of which is: ； in, , , Functions with respect to coordinates x , y , z Partial derivative calculation formula, function , , The expressions are as follows: in, For the receiver speed, , , The components of the receiver velocity on the three-dimensional coordinate axes. The position coordinates of the transmitter, For the first n The position coordinates of each receiver; , , The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system. The normalized measurement accuracy matrix is ​​calculated as follows: in, Let be the precision matrix of the extension, and its expression is: in, For the first n The measurement accuracy matrix corresponding to each receiver is expressed as follows: in, , , Transmitter-Target-Receiver n The accuracy of the system's two-way slant distance measurement, spatial cone angle measurement, and pitch angle measurement are known parameters.

2. The three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration according to claim 1, characterized in that, The two-dimensional adaptive filtering search in step S1 includes: in, The spatial cone angle of the target relative to the receiver. The target's downward viewing angle relative to the receiver. The Doppler-pitch-azimuth three-dimensional spacetime guidance vector for the target. For the estimated clutter covariance matrix, For radar echo data vectors, For the modulo operation of complex numbers, The parameter value at which the function reaches its minimum; superscript This represents the conjugate transpose operation of a matrix.

3. The three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration according to claim 1, characterized in that, The linear overdetermined equation system includes: in, Update the vector for coordinates. Let be the gradient matrix of the extension, and its expression is: N is the total number of receivers. Let be the measurement gradient matrix corresponding to the nth receiver, and its expression is: In the formula, , , These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively. , , The expressions are as follows: in, For the receiver speed, , , The components of the receiver velocity on the three-dimensional coordinate axes. The position coordinates of the transmitter, These are the position coordinates of the nth receiver; , , The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system. in, Let be the slant range measurement from the target to the nth receiver. The spatial cone angle measurement of the target relative to the nth receiver. Let be the downward view of the target relative to the nth receiver.

4. The three-dimensional positioning method for a spaceborne multi-base radar system based on weighted linear iteration according to claim 1, characterized in that, Step S4 employs the following: The formulas for calculating latitude, longitude, and altitude are as follows: in, The estimated three-dimensional coordinates of the target obtained by the iterative method are: For the argument operation of complex numbers, The radius is the Earth's radius.

5. A three-dimensional positioning system for a spaceborne multi-base radar system based on weighted linear iteration, characterized in that, include: Module M1: Acquires radar echo data from multiple receivers, searches for the elevation angle and spatial cone angle of the target signal through two-dimensional adaptive filtering, and obtains two-dimensional angle estimation information of the target from different bases and different viewpoints; Module M2: Constructs a set of nonlinear equations based on the two-dimensional angle information and slant range information of the target from different perspectives, and performs a first-order Taylor expansion on the set of nonlinear equations to obtain the corresponding linear overdetermined equations. Module M3: Based on the accuracy matrix of the radar system, the linear overdetermined equations are normalized and iteratively solved to obtain the three-dimensional coordinates of the target in the geocentric coordinate system; Module M4: Converts the target's three-dimensional coordinates in the geocentric coordinate system into the target's latitude, longitude, and altitude information to obtain the target's three-dimensional positioning; The module M3 adopts the following approach: updating the three-dimensional coordinates of the target in the geocentric-ground-fixed coordinate system during each iteration; The coordinate update expression is: in, , For the first k , k The target 3D coordinate vector obtained after +1 iterations The normalized iterative gradient matrix, This is the corresponding weight matrix; ; Update the vector for coordinates. Let be the gradient matrix of the extension; The normalized iterative gradient matrix The calculation expression is: in, For vectors Norm calculation formula The calculation formula for converting a vector into a diagonal matrix. Let be the gradient matrix of the extension; N The total number of receivers, For the first n Each receiver corresponds to a measurement gradient matrix, the expression of which is: ； in, , , Functions with respect to coordinates x , y , z Partial derivative calculation formula, function , , The expressions are as follows: in, For the receiver speed, , , The components of the receiver velocity on the three-dimensional coordinate axes. The position coordinates of the transmitter, For the first n The position coordinates of each receiver; , , The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system. The normalized measurement accuracy matrix is ​​calculated as follows: in, Let be the precision matrix of the extension, and its expression is: in, For the first n The measurement accuracy matrix corresponding to each receiver is expressed as follows: in, , , Transmitter-Target-Receiver n The accuracy of the system's two-way slant distance measurement, spatial cone angle measurement, and pitch angle measurement are known parameters.

6. The three-dimensional positioning system of a spaceborne multi-base radar system based on weighted linear iteration according to claim 5, characterized in that, The two-dimensional adaptive filtering search in module M1 includes: in, The spatial cone angle of the target relative to the receiver. The target's downward viewing angle relative to the receiver. The Doppler-pitch-azimuth three-dimensional spacetime guidance vector for the target. For the estimated clutter covariance matrix, For radar echo data vectors, For the modulo operation of complex numbers, The parameter value at which the function reaches its minimum; superscript This represents the conjugate transpose operation of a matrix.

7. The three-dimensional positioning system of a spaceborne multi-base radar system based on weighted linear iteration according to claim 5, characterized in that, The linear overdetermined equation system includes: in, Update the vector for coordinates. Let be the gradient matrix of the extension, and its expression is: N is the total number of receivers. Let be the measurement gradient matrix corresponding to the nth receiver, and its expression is: In the formula, , , These are the formulas for calculating the partial derivatives of the function with respect to coordinates x, y, and z, respectively. , , The expressions are as follows: in, For the receiver speed, , , The components of the receiver velocity on the three-dimensional coordinate axes. The position coordinates of the transmitter, These are the position coordinates of the nth receiver; , , The transformation coefficients are used to convert the ground-fixed coordinate system to the receiver antenna panel coordinate system. in, Let be the slant range measurement from the target to the nth receiver. The spatial cone angle measurement of the target relative to the nth receiver. Let be the downward view of the target relative to the nth receiver.

8. The three-dimensional positioning system of a spaceborne multi-base radar system based on weighted linear iteration according to claim 5, characterized in that, The module M4 adopts: The formulas for calculating latitude, longitude, and altitude are as follows: in, The estimated three-dimensional coordinates of the target obtained by the iterative method are: For the argument operation of complex numbers, The radius is the Earth's radius.

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