Target stereoscopic positioning method and system based on multi-node joint processing of spaceborne radar

Abstract

The application provides a target stereoscopic positioning method and system based on multi-node joint processing of a spaceborne radar, wherein the method comprises the following steps: deploying multiple satellites, obtaining a downward angle and a space cone angle of a target relative to the satellites; calculating three-dimensional coordinates of the target in a satellite antenna panel coordinate system; constructing a hierarchical conversion model from a geodetic coordinate system to a coordinate system of each satellite antenna panel; constructing an over-determined equation group with the target coordinates in the geodetic coordinate system as unknown quantities; solving the equation group by using a least square algorithm to obtain the three-dimensional coordinates of the target in the geodetic coordinate system; and finally converting the three-dimensional coordinates into longitude, latitude and height. The application utilizes the joint observation of multiple satellites to form redundant information, and introduces a rigorous hierarchical coordinate conversion model considering the orbit, the earth rotation and the installation attitude, so that the multi-satellite heterogeneous observation is unified to the same reference, and the over-determined equation group is solved, thereby significantly improving the accuracy and robustness of the target stereoscopic positioning.

Description

Technical Field

[0001] This invention relates to the field of spaceborne radar target positioning, specifically to a target three-dimensional positioning method and system based on multi-node joint processing of spaceborne radar. Background Technology

[0002] In spaceborne radar systems, high-precision target positioning is required for effective target tracking. Traditional spaceborne radar target positioning relies on the slant range and two-dimensional angle information of a single satellite, transforming the satellite coordinate system to achieve target positioning. However, due to issues such as angular measurement accuracy, processing errors, and the non-negligible flight altitude of the target, the accuracy of traditional single-satellite stereo positioning methods is significantly reduced.

[0003] In spaceborne radar systems, high-precision three-dimensional positioning of detected targets is fundamental for applications such as continuous tracking and situational awareness. Traditional single-satellite stereo positioning methods for spaceborne radar typically rely on target slant range, azimuth, and elevation angle information acquired from a single satellite, calculating the target's position in the Earth coordinate system through coordinate transformation. However, traditional methods have the following inherent limitations: First, the angular resolution and measurement accuracy of single-satellite angle measurement systems are limited, especially at long distances, where even small angular errors can be amplified by coordinate transformation, leading to significant positioning deviations. Second, the positioning geometry of traditional methods depends on angle-slant range intersection. When the target's flight altitude is comparable to the satellite's orbital altitude, the positioning solution model approaches singularity, becoming extremely sensitive to measurement errors, resulting in a sharp drop in positioning accuracy or even failure. Furthermore, a single satellite can only provide a single observation perspective, making it impossible to suppress random errors and systematic biases through redundant observations. More importantly, traditional coordinate transformation models are often oversimplified, failing to fully consider the Earth's rotation, complex satellite orbital parameters (such as the six-element system), and the antenna panel's installation attitude, introducing model errors during multi-satellite data fusion and limiting further improvements in positioning accuracy.

[0004] A patent search revealed an invention patent with publication number CN113721276A, which discloses a target positioning method, device, electronic device, and computer-readable medium based on multiple satellites. The method includes: acquiring multiple direction-finding positioning datasets and multiple time-frequency difference data of multiple satellites for the target object based on the target object's positioning request; wherein the direction-finding positioning datasets include direction-finding positioning data from multiple periods; training a machine learning model based on the multiple direction-finding positioning datasets and multiple time-frequency difference data to generate a multi-satellite positioning model; and inputting the multiple direction-finding positioning datasets into the multi-satellite positioning model to obtain the target object's position. This patent relies excessively on a large amount of training data, resulting in a sharp drop in positioning accuracy when data is missing or there is noise interference; the model training process is complex and lacks real-time performance, making it difficult to adapt to dynamic target positioning requirements; the adaptation boundary between data and model is not clearly defined, and key influencing factors such as satellite orbital parameters are not considered, leading to insufficient stability and reliability.

[0005] Patent CN121276492A, which uses a nonlinear equation system to achieve target positioning through iterative solution, simplifies the coordinate transformation process and fails to adequately consider the influence of the six elements of satellite orbit and Earth's rotation on the observation geometry. Patent CN115980740B uses the least squares method to solve for the target's position in the satellite orbit coordinate system, but its transformation model is based solely on satellite attitude angle rotation, making it difficult to describe the complex transformation relationship from the Earth-fixed coordinate system to the antenna panel coordinate system. These methods still suffer from limited positioning accuracy when dealing with long-distance, highly dynamic targets due to the accumulation of model errors. Therefore, there is an urgent need for a multi-satellite joint positioning method that integrates satellite orbit dynamics, Earth's rotation effect, and antenna installation attitude into the coordinate transformation model to fundamentally improve the accuracy and robustness of target positioning.

[0006] In summary, given the problems of the existing technologies, researching a target stereo positioning method and system based on multi-node joint processing of spaceborne radar has become a critical task that urgently needs to be addressed. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a target stereo positioning method and system based on multi-node joint processing of spaceborne radar.

[0008] A target stereo localization method based on multi-node joint processing of spaceborne radar, provided by the present invention, includes the following steps:

[0009] Step S1: Deploy multiple satellites, and each satellite obtains the target's downward viewing angle and spatial cone angle relative to each satellite through a sum-difference beam angle measurement algorithm;

[0010] Step S2: Based on the target's downward viewing angle and spatial cone angle relative to each satellite, calculate the target's three-dimensional coordinates in the antenna panel coordinate system of each satellite.

[0011] Step S3: Based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel installation tilt angle, a hierarchical transformation model is constructed from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite. The hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system, and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system.

[0012] Step S4: Based on the hierarchical transformation model constructed in step S3, which includes analytical expressions for the six orbital roots and the Earth's rotation angular frequency, and combined with the three-dimensional coordinates of the target in the coordinate system of each satellite antenna panel, an overdetermined set of equations is constructed with the target coordinates in the Earth-fixed coordinate system as unknowns.

[0013] Step S5: Solve the overdetermined set of equations based on the analytical expression of orbital dynamics constructed in step S4 using the least squares algorithm to obtain the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system.

[0014] Step S6: Convert the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system into longitude, latitude, and altitude to achieve three-dimensional positioning of the target.

[0015] Preferably, the calculation process of the sum-difference beam angle measurement algorithm in step S1 is as follows:

[0016] Based on the acquired radar echo data, the target's range cell was detected as [missing information]. The Doppler cell where the target is located is The clutter suppression result of the first azimuth channel, which includes elevation channel data, is selected as... The clutter suppression result of the second azimuth channel, which includes pitch channel data, is as follows: The azimuth dimension signal is obtained through a sum-difference beamforming network. and azimuth dimension difference signal ,

[0017] , Select the clutter suppression results of the first elevation channel containing azimuth channel data. The clutter suppression result of the second elevation channel, which includes azimuth channel data, is as follows: The elevation and sum signals are obtained through a sum-difference beamforming network. Pitch dimension difference signal ; , ;

[0018] The azimuth dimension single pulse ratio is

[0019]

[0020] Pitch-dimensional single-pulse ratio is

[0021]

[0022] In the formula, j is the imaginary unit. The spatial cone angle of the target relative to the satellite's antenna panel. The downward view of the target relative to the satellite's antenna panel. The physical spacing between azimuth antenna array elements. The physical spacing between the elevation antenna elements. Indicates the signal wavelength;

[0023] Therefore, the estimated spatial cone angle and downward angle are:

[0024]

[0025] .

[0026] Preferably, in step S2, the expression for calculating the three-dimensional coordinates of the target in the satellite's antenna panel coordinate system is as follows:

[0027]

[0028] In the formula, The target's three-dimensional coordinates are given in the satellite's antenna panel coordinate system. The slant distance from the satellite to the target. , , These are the azimuth angle, downward viewing angle, and spatial cone angle of the target relative to the satellite's antenna panel, respectively, and the azimuth angle... According to the relation Sure.

[0029] Preferably, step S3 includes the following sub-steps:

[0030] Step S3.1, Define Let the coordinates of the target be in the Earth-fixed coordinate system. The coordinates of the target in the satellite velocity coordinate system;

[0031] Step S3.2, the first transformation relationship of the target from the Earth-fixed coordinate system to the satellite velocity coordinate system is as follows:

[0032]

[0033] In the formula, For the Earth's radius, For satellite orbital altitude, matrix This is the matrix for the first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system;

[0034] Step S3.3, the second transformation relationship from the satellite velocity coordinate system to the antenna panel coordinate system is as follows:

[0035]

[0036] matrix This is the matrix for the second transformation from the satellite velocity coordinate system to the antenna panel coordinate system;

[0037] Step S3.4 yields the following transformation relationship for the target from the Earth-fixed coordinate system to the antenna panel coordinate system:

[0038] .

[0039] Preferably, in step S3.2, the matrix A of the first transformation is composed of the six orbital elements of the satellite and the analytical expression of the Earth's rotation angular frequency:

[0040]

[0041] In the formula,

[0042]

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] In the formula, This is the frequency of Earth's rotation angle. For exercise time, , , These are the right ascension of the ascending node, the orbital inclination, and the angle of depression at the point of periapsis. This is the true near point angle;

[0052] Preferably, in step S3.3, the matrix B of the second transformation is analytically expressed by the antenna panel mounting tilt angle:

[0053]

[0054] In the formula, Install the tilt angle for the antenna panel.

[0055] Preferably, the overdetermined system of equations constructed in step S4 is as follows:

[0056] ,

[0057] In the formula, Total number of satellites;

[0058] , and The targets are respectively for the first and the second. n The grain and the first The coordinates of the antenna panel of each satellite in the coordinate system. ;

[0059] , and These are respectively from the Earth-fixed coordinate system to the first and second satellites. n The grain and the first The transformation matrix of the satellite velocity coordinate system of the satellite. ;

[0060] , and They are respectively from the 1st and the 2nd. n The grain and the first The velocity coordinate system of the satellite is connected to the corresponding first and second satellites. n The grain and the first The transformation matrix of the antenna panel coordinate system of each satellite. ;

[0061] , and The first and the second are respectively the first and the second. n The grain and the first The orbital altitude of the satellite, .

[0062] Preferably, the expression for solving the three-dimensional coordinates of the target in the Earth-fixed coordinate system using the least squares algorithm in step S5 is as follows:

[0063]

[0064] In the formula, This indicates the transpose operation. This is the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system obtained through the solution process.

[0065] Preferably, in step S6, the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system is converted into a calculation expression for longitude, latitude, and altitude as follows:

[0066]

[0067]

[0068]

[0069] This invention also provides a target stereo positioning system based on multi-node joint processing of spaceborne radar, employing the aforementioned target stereo positioning method based on multi-node joint processing of spaceborne radar, including:

[0070] Module M1 deploys multiple satellites, each of which uses a sum-difference beam angle measurement algorithm to obtain the target's downward angle and spatial cone angle relative to each satellite.

[0071] Module M2 calculates the three-dimensional coordinates of the target in the antenna panel coordinate system of each satellite based on the target's downward viewing angle and spatial cone angle relative to each satellite.

[0072] Module M3, based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel mounting tilt angle, constructs a hierarchical transformation model from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite. The hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system, and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system. The matrix of the first transformation is analytically expressed by the number of orbital elements and the Earth's rotation angular frequency, and the matrix of the second transformation is analytically expressed by the antenna panel mounting tilt angle.

[0073] Module M4, based on the hierarchical transformation model constructed from Module M3, contains analytical expressions for the six orbital roots and the Earth's rotation angular frequency. Combined with the three-dimensional coordinates of the target in the coordinate system of each satellite antenna panel, it constructs an overdetermined set of equations with the target coordinates in the Earth-fixed coordinate system as unknowns.

[0074] Module M5 uses the least squares algorithm to solve the overdetermined equations based on the analytical expression of orbital dynamics constructed in Module M4, and obtains the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system.

[0075] Module M6 converts the target's three-dimensional coordinates in the Earth-fixed coordinate system into longitude, latitude, and altitude, enabling the target's three-dimensional positioning.

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] 1. This invention deploys multiple satellites to form a joint detection network, acquiring observation data of the same target under multiple different spatial geometries. By establishing an overdetermined set of equations and solving them using the least squares algorithm, the observation redundancy is utilized, which can effectively suppress the influence of random errors in single-satellite measurements and significantly improve the accuracy and stability of positioning solutions.

[0078] 2. This invention constructs a rigorous, layered, and reversible transformation model from the Earth-fixed coordinate system to the coordinate system of each satellite antenna panel. This model is not a simple coordinate rotation, but rather rigorously incorporates key physical parameters such as the six orbital elements (right ascension of the ascending node, orbital inclination, argument of perigee, and true anomaly), Earth's rotational angular frequency, and the antenna panel mounting tilt angle through analytical expressions. This mathematical model is the core of unifying observational data from multiple satellites under different physical references into the same Earth coordinate system, fundamentally overcoming systematic errors caused by model simplification and laying a solid foundation for high-precision positioning.

[0079] 3. This invention proceeds from the sum and difference beam angle measurement of the original radar echo signal, to the preliminary coordinate calculation in the panel coordinate system, and then to the construction of an overdetermined set of equations based on a rigorous transformation model and the solution of the Earth coordinates, finally outputting the latitude, longitude and altitude of the target. It is highly systematic, can be automated, and is suitable for on-board or ground processing systems, thus improving the overall positioning efficiency of the spaceborne radar system. Attached Figure Description

[0080] 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:

[0081] Figure 1 This is a flowchart of a target stereo localization method based on multi-node joint processing of spaceborne radar in an embodiment of the present invention;

[0082] Figure 2 This is a flowchart of the angle measurement process using the sum and difference beam method in this embodiment of the invention;

[0083] Figure 3 This is a comparison chart of the target positioning error curves of the present invention and traditional single-base positioning. Detailed Implementation

[0084] 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.

[0085] This invention discloses a target stereo positioning method and system based on multi-node joint processing of spaceborne radar, aiming to solve the problems of low accuracy and poor stability of traditional single-satellite positioning methods under complex geometries. The method includes deploying multiple satellites, each using a sum-difference beam angle measurement algorithm to obtain the target's downward viewing angle and spatial cone angle relative to each satellite; calculating the target's three-dimensional coordinates in the satellite's antenna panel coordinate system based on the downward viewing angle, spatial cone angle, and slant range; constructing a hierarchical transformation model from the Earth-fixed coordinate system to each satellite's antenna panel coordinate system based on the satellite's orbital elements, Earth's rotation parameters, and antenna panel installation tilt angle; implementing this model sequentially through transformations from the Earth-fixed coordinate system to the satellite velocity coordinate system and then to the antenna panel coordinate system; constructing an overdetermined system of equations with the target's coordinates in the Earth-fixed coordinate system as unknowns based on this transformation model and the target's coordinates in the antenna panel coordinate system; solving this system of equations using a least squares algorithm to obtain the target's three-dimensional coordinates in the Earth-fixed coordinate system; and finally converting these coordinates into longitude, latitude, and altitude. This invention utilizes joint observations from multiple satellites to generate redundant information, and by introducing a rigorous hierarchical coordinate transformation model that considers orbit, Earth's rotation, and installation attitude, it unifies multi-satellite observations to the same reference. Combined with the solution of overdetermined equations, it significantly improves the accuracy and robustness of target stereo positioning.

[0086] Example 1:

[0087] Figure 1 This is a flowchart of a target stereo localization method based on multi-node joint processing of spaceborne radar in an embodiment of the present invention.

[0088] like Figure 1 As shown, this embodiment provides a target stereo localization method based on multi-node joint processing of spaceborne radar, including the following steps:

[0089] Step S1: Deploy multiple satellites. Each satellite uses a sum-difference beam angle measurement algorithm to obtain the target's downward viewing angle and spatial cone angle relative to each satellite.

[0090] like Figure 2 As shown, in step S1, the calculation process of the sum-difference beam angle measurement algorithm is as follows:

[0091] Based on the acquired radar echo data, the target's range cell was detected as [missing information]. The Doppler cell where the target is located is The clutter suppression result of the first azimuth channel, which includes elevation channel data, is selected as... The clutter suppression result of the second azimuth channel, which includes pitch channel data, is as follows: The azimuth dimension signal is obtained through a sum-difference beamforming network. and azimuth dimension difference signal ,

[0092] , Select the clutter suppression results of the first elevation channel containing azimuth channel data. The clutter suppression result of the second elevation channel, which includes azimuth channel data, is as follows: The elevation and sum signals are obtained through a sum-difference beamforming network. Pitch dimension difference signal ; , ;

[0093] The azimuth dimension single pulse ratio is:

[0094]

[0095] The pitch-dimensional single-pulse ratio is:

[0096]

[0097] In the formula, j is the imaginary unit. The spatial cone angle of the target relative to the satellite's antenna panel. The downward view of the target relative to the satellite's antenna panel. The physical spacing between azimuth antenna array elements. The physical spacing between the elevation antenna elements. Indicates the signal wavelength;

[0098] Therefore, the estimated spatial cone angle and downward angle are:

[0099]

[0100] .

[0101] Step S2: Based on the target's downward viewing angle and spatial cone angle relative to each satellite, calculate the target's three-dimensional coordinates in the antenna panel coordinate system of each satellite.

[0102] Specifically, in step S2, the expression for calculating the three-dimensional coordinates of the target in the satellite's antenna panel coordinate system is as follows:

[0103]

[0104] In the formula, The target's three-dimensional coordinates are given in the satellite's antenna panel coordinate system. The slant distance from the satellite to the target. , , These are the azimuth angle, downward viewing angle, and spatial cone angle of the target relative to the satellite's antenna panel, respectively, and the azimuth angle... According to the relation Sure.

[0105] Step S3: Based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel installation tilt angle, a hierarchical transformation model is constructed from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite. The hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system. The matrix of the first transformation is analytically expressed by the number of orbital elements and the Earth's rotation angular frequency, and the matrix of the second transformation is analytically expressed by the antenna panel installation tilt angle.

[0106] Specifically, step S3 includes the following sub-steps:

[0107] Step S3.1, Define Let the coordinates of the target be in the Earth-fixed coordinate system. The coordinates of the target in the satellite velocity coordinate system;

[0108] Step S3.2, the first transformation relationship of the target from the Earth-fixed coordinate system to the satellite velocity coordinate system is as follows:

[0109]

[0110] In the formula, For the Earth's radius, For satellite orbital altitude, matrix This is the matrix for the first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system;

[0111] Furthermore, the matrix A of the first transformation is composed of the six orbital elements of the satellite and the analytical expression of the Earth's rotation angular frequency:

[0112]

[0113] In the formula,

[0114]

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123] In the formula, This is the frequency of Earth's rotation angle. For exercise time, , , These are the right ascension of the ascending node, the orbital inclination, and the angle of depression at the point of periapsis. This is the true near point angle;

[0124] Step S3.3, the second transformation relationship from the satellite velocity coordinate system to the antenna panel coordinate system is as follows:

[0125]

[0126] matrix The matrix representing the second transformation from the satellite velocity coordinate system to the antenna panel coordinate system is composed of the analytical expression for the antenna panel mounting tilt angle.

[0127] Furthermore, the matrix B of the second transformation is analytically expressed by the antenna panel mounting tilt angle:

[0128]

[0129] In the formula, Install the tilt angle for the antenna panel.

[0130] Step S3.4 yields the following transformation relationship for the target from the Earth-fixed coordinate system to the antenna panel coordinate system:

[0131] .

[0132] Step S4: Based on the transformation relationship from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite, and combined with the three-dimensional coordinates of the target in the corresponding satellite's antenna panel coordinate system, construct an overdetermined set of equations.

[0133] Specifically, the overdetermined system of equations constructed in step S4 is as follows:

[0134] ,

[0135] In the formula, Total number of satellites;

[0136] , , The targets are respectively for the first and the second. n grain, number The coordinates of the antenna panel of each satellite in the coordinate system. ;

[0137] , , These are respectively from the Earth-fixed coordinate system to the first and second satellites. n grain, number The transformation matrix of the satellite velocity coordinate system of the satellite. ;

[0138] , , They are respectively from the 1st and the 2nd. n grain, number The velocity coordinate system of the first satellite to the second satellite. n grain, number The transformation matrix of the antenna panel coordinate system of each satellite. ;

[0139] , , The first and the second are respectively the first and the second. n grain, number The orbital altitude of the satellite, .

[0140] Step S5: Based on the overdetermined equations, the least squares algorithm is used to calculate the three-dimensional coordinates of the target in the Earth-fixed coordinate system.

[0141] Specifically, in step S5, the expression for solving the three-dimensional coordinates of the target in the Earth-fixed coordinate system using the least squares algorithm is as follows:

[0142]

[0143] In the formula, This indicates the transpose operation. This is the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system obtained through the solution process.

[0144] Step S6: Convert the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system into longitude, latitude, and altitude to achieve three-dimensional positioning of the target.

[0145] Specifically, in step S6, the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system is converted into calculation expressions for longitude, latitude, and altitude as follows:

[0146]

[0147]

[0148]

[0149] Example 2:

[0150] In this embodiment, the slant distances of satellite 1 and satellite 2 to the target are set to 1200km and 2195km, respectively.

[0151] Through simulation experiments, the absolute distance error obtained from 1000 Monte Carlo repeated trials of the target 3D positioning achieved according to the present invention is compared with the target positioning error curve of traditional single-base positioning. Figure 3 As shown, compared with traditional methods, the method provided by this invention can achieve higher precision three-dimensional positioning of aerial targets, with a positioning accuracy improvement of more than 10%.

[0152] Example 3:

[0153] The present invention also provides a target stereo positioning system based on multi-node joint processing of spaceborne radar. The target stereo positioning system based on multi-node joint processing of spaceborne radar can be implemented by executing the process steps of the target stereo positioning method based on multi-node joint processing of spaceborne radar. That is, those skilled in the art can understand the target stereo positioning method based on multi-node joint processing of spaceborne radar as a preferred embodiment of the target stereo positioning system based on multi-node joint processing of spaceborne radar.

[0154] Specifically, the target stereo positioning system based on multi-node joint processing of spaceborne radar includes:

[0155] Module M1 deploys multiple satellites, each of which uses a sum-difference beam angle measurement algorithm to obtain the target's downward angle and spatial cone angle relative to each satellite.

[0156] Module M2 calculates the three-dimensional coordinates of the target in the antenna panel coordinate system of each satellite based on the target's downward viewing angle and spatial cone angle relative to each satellite.

[0157] Module M3, based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel mounting tilt angle, constructs a hierarchical transformation model from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite. The hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system, and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system. The matrix of the first transformation is analytically expressed by the number of orbital elements and the Earth's rotation angular frequency, and the matrix of the second transformation is analytically expressed by the antenna panel mounting tilt angle.

[0158] Module M4, based on the hierarchical transformation model constructed from Module M3, contains analytical expressions for the six orbital roots and the Earth's rotation angular frequency. Combined with the three-dimensional coordinates of the target in the coordinate system of each satellite antenna panel, it constructs an overdetermined set of equations with the target coordinates in the Earth-fixed coordinate system as unknowns.

[0159] Module M5 uses the least squares algorithm to solve the overdetermined equations based on the analytical expression of orbital dynamics constructed in Module M4, and obtains the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system.

[0160] Module M6 converts the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system into longitude, latitude, and altitude, enabling the target's three-dimensional positioning.

[0161] like Figure 2 As shown, the calculation process of the sum-difference beam angle measurement algorithm in module M1 is as follows:

[0162] Based on the acquired radar echo data, the target's range cell was detected as [missing information]. The Doppler cell where the target is located is The clutter suppression result of the first azimuth channel, which includes elevation channel data, is selected as... The clutter suppression result of the second azimuth channel, which includes pitch channel data, is as follows: The azimuth dimension signal is obtained through a sum-difference beamforming network. and azimuth dimension difference signal ,

[0163] , Select the clutter suppression results of the first elevation channel containing azimuth channel data. The clutter suppression result of the second elevation channel, which includes azimuth channel data, is as follows: The elevation and sum signals are obtained through a sum-difference beamforming network. Pitch dimension difference signal ; , ;

[0164] The azimuth dimension single pulse ratio is:

[0165]

[0166] The pitch-dimensional single-pulse ratio is:

[0167]

[0168] In the formula, j is the imaginary unit. The spatial cone angle of the target relative to the satellite's antenna panel. The downward view of the target relative to the satellite's antenna panel. The physical spacing between azimuth antenna array elements. The physical spacing between the elevation antenna elements. Indicates the signal wavelength;

[0169] Therefore, the estimated spatial cone angle and downward angle are:

[0170]

[0171] .

[0172] Specifically, in module M2, the expression for calculating the three-dimensional coordinates of the target in the satellite's antenna panel coordinate system is as follows:

[0173]

[0174] In the formula, The target's three-dimensional coordinates are given in the satellite's antenna panel coordinate system. The slant distance from the satellite to the target. , , These are the azimuth angle, downward viewing angle, and spatial cone angle of the target relative to the satellite's antenna panel, respectively, and the azimuth angle... According to the relation Sure.

[0175] Specifically, module M3 includes the following sub-modules:

[0176] Module M3.1, definition Let the coordinates of the target be in the Earth-fixed coordinate system. The coordinates of the target in the satellite velocity coordinate system;

[0177] Module M3.2, the first transformation relationship of the target from the Earth-fixed coordinate system to the satellite velocity coordinate system is as follows:

[0178]

[0179] In the formula, For the Earth's radius, For satellite orbital altitude, matrix This is the matrix for the first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system.

[0180] Furthermore, the matrix A of the first transformation is composed of the six orbital elements of the satellite and the analytical expression of the Earth's rotation angular frequency:

[0181]

[0182] In the formula,

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189]

[0190]

[0191]

[0192] In the formula, This is the frequency of Earth's rotation angle. For exercise time, , , These are the right ascension of the ascending node, the orbital inclination, and the angle of depression at the point of periapsis. This is the true near point angle;

[0193] The second transformation relationship from the satellite velocity coordinate system to the antenna panel coordinate system in module M3.3 is as follows:

[0194]

[0195] matrix The matrix representing the second transformation from the satellite velocity coordinate system to the antenna panel coordinate system is composed of the analytical expression for the antenna panel mounting tilt angle.

[0196] Furthermore, the matrix B of the second transformation is analytically expressed by the antenna panel mounting tilt angle:

[0197]

[0198] In the formula, Install the tilt angle for the antenna panel.

[0199] Module M3.4 provides the following transformation relationship for the target from the Earth-fixed coordinate system to the antenna panel coordinate system:

[0200] .

[0201] Specifically, the overdetermined system of equations constructed in module M4 is as follows:

[0202] ,

[0203] In the formula, Total number of satellites;

[0204] , , The targets are respectively for the first and the second. n grain, number The coordinates of the antenna panel of each satellite in the coordinate system. ;

[0205] , , These are respectively from the Earth-fixed coordinate system to the first and second satellites. n grain, number The transformation matrix of the satellite velocity coordinate system of the satellite. ;

[0206] , , They are respectively from the 1st and the 2nd. n grain, number The velocity coordinate system of the first satellite to the second satellite. n grain, number The transformation matrix of the antenna panel coordinate system of each satellite. ;

[0207] , , The first and the second are respectively the first and the second. n grain, number The orbital altitude of the satellite, .

[0208] Specifically, the expression for calculating the target's three-dimensional coordinates in the Earth-fixed coordinate system using the least squares algorithm in module M5 is as follows:

[0209]

[0210] In the formula, This indicates the transpose operation. This is the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system obtained through the solution process.

[0211] Specifically, in module M6, the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system is converted into calculation expressions for longitude, latitude, and altitude as follows:

[0212]

[0213]

[0214]

[0215] 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.

[0216] 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 target stereo localization method based on multi-node joint processing of spaceborne radar, characterized in that, Includes the following steps: Step S1: Deploy multiple satellites, and each satellite obtains the target's downward viewing angle and spatial cone angle relative to each satellite through a sum-difference beam angle measurement algorithm; Step S2: Based on the target's downward viewing angle and spatial cone angle relative to each satellite, calculate the target's three-dimensional coordinates in the antenna panel coordinate system of each satellite; Step S3: Based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel installation tilt angle, a hierarchical transformation model is constructed from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite. The hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system, and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system. Step S4: Based on the analytical expressions of the orbital six roots and the Earth's rotation angular frequency contained in the hierarchical transformation model, and combined with the three-dimensional coordinates of the target in the coordinate system of each satellite antenna panel, an overdetermined set of equations is constructed with the target coordinates in the Earth fixed coordinate system as unknowns. Step S5: Solve the overdetermined system of equations using the least squares algorithm to obtain the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system. Step S6: Convert the optimal estimate into longitude, latitude and altitude to achieve three-dimensional positioning of the target.

2. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 1, characterized in that, In step S1, the calculation process of the sum-difference beam angle measurement algorithm is as follows: Based on the acquired radar echo data, the target's range cell was detected as [missing information]. The Doppler cell where the target is located is The clutter suppression result of the first azimuth channel, which includes elevation channel data, is selected as... The clutter suppression result of the second azimuth channel, which includes pitch channel data, is as follows: The azimuth dimension signal is obtained through a sum-difference beamforming network. and azimuth dimension difference signal , , Select the clutter suppression results of the first elevation channel, which contains azimuth channel data. The clutter suppression result of the second elevation channel, which includes azimuth channel data, is as follows: The elevation and sum signals are obtained through a sum-difference beamforming network. Pitch dimension difference signal ; , ; The azimuth dimension single pulse ratio is: The pitch-dimensional single-pulse ratio is: In the formula, j The imaginary unit, The spatial cone angle of the target relative to the satellite's antenna panel. The downward viewing angle of the target relative to the satellite's antenna panel. The physical spacing between azimuth antenna array elements. The physical spacing between the elevation antenna elements. Indicates the signal wavelength; The obtained spatial cone angle is: The downward perspective is: 。 3. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 2, characterized in that, In step S2, the expression for calculating the three-dimensional coordinates of the target in the satellite's antenna panel coordinate system is as follows: In the formula, Let be the three-dimensional coordinates of the target in the satellite's antenna panel coordinate system. The slant range from the satellite to the target is... , , These are the azimuth angle, downward viewing angle, and spatial cone angle of the target relative to the satellite's antenna panel, respectively, and the azimuth angle... According to the relation Sure.

4. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 3, characterized in that, Step S3 includes the following sub-steps: Step S3.1, Define Let these be the coordinates of the target in the Earth-fixed coordinate system. The coordinates of the target in the satellite velocity coordinate system; Step S3.2, the first transformation relationship of the target from the Earth-fixed coordinate system to the satellite velocity coordinate system is as follows: In the formula, For the Earth's radius, For satellite orbital altitude, matrix This is the matrix for the first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system; Step S3.3, the second transformation relationship from the satellite velocity coordinate system to the antenna panel coordinate system is as follows: matrix This is the matrix for the second transformation from the satellite velocity coordinate system to the antenna panel coordinate system; Step S3.4, the transformation relationship of the target from the Earth-fixed coordinate system to the antenna panel coordinate system is obtained as follows: 。 5. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 4, characterized in that, In step S3.2, the matrix A of the first transformation is composed of the six orbital elements of the satellite and the analytical expression of the Earth's rotation angular frequency: In the formula, In the formula, This is the frequency of Earth's rotation angle. For exercise time, , , These are the right ascension of the ascending node, the orbital inclination, and the angle of depression at the point of periapsis. This is the true near-point angle.

6. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 5, characterized in that, In step S3.3, the matrix B of the second transformation is analytically expressed by the antenna panel mounting tilt angle: In the formula, Install the tilt angle for the antenna panel.

7. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 6, characterized in that, The overdetermined system of equations constructed in step S4 is as follows: ， In the formula, Total number of satellites; , , The targets are respectively for the first and second. n grain, number The coordinates of the antenna panel of each satellite in the coordinate system. ; , , These are respectively from the Earth-fixed coordinate system to the first and second satellites. n grain, number The transformation matrix of the satellite velocity coordinate system of the satellite. ; , , They are respectively from the 1st and the 2nd. n grain, number The velocity coordinate system of the satellite is connected to the corresponding first and second satellites. n grain, number The transformation matrix of the antenna panel coordinate system of each satellite. ; , , The first and the second are respectively the first and the second. n grain, number The orbital altitude of the satellite, .

8. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 7, characterized in that, In step S5, the least squares algorithm is used to calculate the three-dimensional coordinates of the target in the Earth-fixed coordinate system, and the expression is as follows: In the formula, This indicates the transpose operation. This is the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system obtained by the solution.

9. The target stereo positioning method based on multi-node joint processing of spaceborne radar according to claim 8, characterized in that, In step S6, the optimal estimate of the target's three-dimensional coordinates in the Earth-fixed coordinate system is converted into a calculation expression for longitude, latitude, and altitude as follows: 。 10. A target stereo positioning system based on multi-node joint processing of spaceborne radar, employing the target stereo positioning method based on multi-node joint processing of spaceborne radar as described in any one of claims 1-9, characterized in that, include: Module M1 deploys multiple satellites, each of which uses a sum-difference beam angle measurement algorithm to obtain the target's downward angle and spatial cone angle relative to each satellite. Module M2 calculates the three-dimensional coordinates of the target in the antenna panel coordinate system of each satellite based on the target's downward viewing angle and spatial cone angle relative to each satellite. Module M3, based on the number of orbital elements of the satellite, the Earth's rotation angular frequency, and the antenna panel installation tilt angle, constructs a hierarchical transformation model from the Earth-fixed coordinate system to the antenna panel coordinate system of each satellite; the hierarchical transformation model is achieved by sequentially performing a first transformation from the Earth-fixed coordinate system to the satellite velocity coordinate system, and a second transformation from the satellite velocity coordinate system to the antenna panel coordinate system; Module M4, based on the analytical expressions of the orbital six roots and Earth's rotation angular frequency contained in the hierarchical transformation model, and combined with the three-dimensional coordinates of the target in the coordinate system of each satellite antenna panel, constructs an overdetermined set of equations with the target coordinates in the Earth-fixed coordinate system as unknowns. Module M5 uses the least squares algorithm to solve the overdetermined set of equations based on the analytical expression of orbital dynamics constructed by module M4, and obtains the optimal estimate of the three-dimensional coordinates of the target in the Earth-fixed coordinate system. Module M6 converts the optimal estimate into longitude, latitude, and altitude to achieve three-dimensional positioning of the target.

Images