A single-satellite direct positioning method based on beamforming

Abstract

The present invention relates to a single-satellite direct positioning method based on beamforming, which belongs to the field of satellite-borne positioning and solves the problem of low positioning accuracy of ground radiation sources under low signal-to-noise ratio in the prior art. The specific steps include: constructing a beamforming matrix of a satellite platform array antenna; using the satellite platform array antenna to receive ground radiation source signals, obtaining a covariance matrix of the received signals, and obtaining the amplitude of each receiving beam based on the beamforming matrix; determining an array steering vector based on the relative position between the ground radiation source and the satellite platform, and constructing a cost function for single-satellite direct positioning in combination with the covariance matrix; under spherical constraints, selecting the receiving beam with the largest amplitude and the coverage area of ​​its adjacent beams to perform grid search to optimize the cost function, obtaining a result of estimating the position of the ground radiation source, and effectively improving the positioning accuracy of the ground radiation source under low signal-to-noise ratio conditions.

Description

Technical Field

[0001] The present invention relates to the field of satellite-borne positioning, and in particular to a single-satellite direct positioning method based on beamforming. Background Art

[0002] Satellite-borne passive detection systems are a crucial means of acquiring electronic intelligence due to their global coverage and unobstructed signal propagation paths without multipath reflections. Satellite-borne passive positioning systems are categorized into multi-satellite collaborative positioning and single-satellite positioning. Multi-satellite collaborative positioning typically utilizes dual-satellite time-of-frequency difference positioning and multi-satellite time-of-difference positioning. Single-satellite positioning typically utilizes direction-finding positioning and Doppler shift positioning.

[0003] Single-satellite Doppler shift positioning requires long-term satellite motion accumulation. In actual positioning applications, the positioning result includes the true position of the radiation source and the mirror position of the radiation source relative to the projection line of the observation station's motion trajectory. This mirror position needs to be eliminated based on other information. Traditional single-satellite direction-finding positioning measures the azimuth and pitch angles of the ground radiation source. Based on the satellite's own position information and attitude angle parameters, a ray is formed to intersect with the Earth's spherical surface, and the target position is estimated at the intersection.

[0004] All of the above positioning schemes are referred to as two-step positioning methods. These methods first estimate the direction, time difference, and frequency shift parameters of the target's position signal, and then infer the target's position based on these parameters and the geometric relationship between the target and the observation station. However, the position estimation accuracy of these two-step positioning methods is severely limited by the accuracy of these parameter estimates. Especially in low signal-to-noise ratio environments, large parameter estimation errors make it difficult to achieve high-precision positioning. Summary of the Invention

[0005] In view of the above analysis, the embodiments of the present invention aim to provide a single-satellite direct positioning method based on beamforming, so as to solve the problem of large positioning error in single-satellite positioning under low signal-to-noise ratio conditions in the prior art.

[0006] The purpose of the present invention is mainly achieved through the following technical solutions:

[0007] A single-satellite direct positioning method based on beamforming comprises the following steps:

[0008] Constructing a beamforming matrix for the satellite platform array antenna so that the array antenna forms multiple observation beams at different angles within the Earth observation area;

[0009] Receive ground radiation source signals using a satellite platform array antenna to obtain a covariance matrix of the received signals, and obtain the amplitude of each receiving beam based on the beamforming matrix;

[0010] Based on the relative position between the ground radiation source and the satellite platform, an array steering vector is determined, and a cost function for single-satellite direct positioning is constructed in combination with the covariance matrix;

[0011] Under the spherical constraint, the grid area is determined based on the maximum amplitude receiving beam, and a grid search is performed to optimize the cost function to obtain the result of the ground radiation source position estimation.

[0012] Furthermore, the beamforming matrix is ​​constructed based on the relative positions between the satellite platform array antenna units and the angle of the observation beam, and is expressed as: M = [m1, m2, ..., m L ],

[0013] Where,

[0014] Among them, m i is the i-th element of the beamforming matrix, α i is the azimuth of the i-th observation beam in the stellar coordinate system, β i is the pitch angle of the i-th observation beam in the stellar coordinate system, L is the total number of observation beams, i=1,2,...,L, λ is the wavelength of the ground radiation source, [x bn ,y bn ,z bn ] is the relative position coordinate of the nth antenna unit in the array antenna in the celestial coordinate system, N is the total number of units in the array antenna, n=1,2...,N.

[0015] Furthermore, when there is a strong interference signal area, the method further includes performing null-steering optimization on the beamforming matrix to obtain an optimized beamforming matrix, and using the optimized beamforming matrix to obtain the amplitude of each receiving beam;

[0016] The optimized beamforming matrix is ​​expressed as: P = [p1, p2, ..., p L ], where U=[u1,u2,…,u K ],

[0017]

[0018] Wherein, P is the optimized beamforming matrix, (α k ,β k ) represents the azimuth and elevation angles of the kth observation beam that needs to be nulled in the stellar coordinate system, k = 1, 2, ..., K, where K is the total number of observation beams that need to be nulled.

[0019] Furthermore, the specific steps of the position estimation include: determining the receiving beam with the largest amplitude; determining the grid area based on the receiving beam with the largest amplitude; determining the grid division step according to the positioning accuracy index, and dividing the grid points within the grid area; calculating the array steering vector for each grid point in turn in combination with the spherical constraint condition to obtain the corresponding cost function; based on the optimal parameter solution corresponding to the maximum cost function within the grid area, obtaining the estimation result of the ground radiation source in the ground-fixed coordinate system.

[0020] Furthermore, the grid area includes: when the receiving beam with the maximum amplitude is in the middle of the observation area, the receiving beam with the maximum amplitude and the receiving beam coverage area in the four directions around it are used as the grid area range; when the receiving beam with the maximum amplitude is at the edge of the observation area, the receiving beam with the maximum amplitude and the receiving beam coverage area in the three directions around it are used as the grid area range.

[0021] Furthermore, the receiving beam is expressed as: y(t) = M·z(t), and the amplitude of the receiving beam is: A i =max{20log 10 [fft(y i (t))]}, where z(t) represents the ground radiation source signal received by the satellite array antenna, A i is the amplitude of the i-th receiving beam, y i (t) is the i-th row element of y(t), and fft(·) represents the fast Fourier transform.

[0022] Furthermore, the expression of the array steering vector is:

[0023]

[0024] Among them, (α, β) represents the azimuth and elevation angles of the radiation source in the stellar coordinate system; and the azimuth and elevation angles can be expressed as:

[0025] Among them, x bT =[x bT ,y bT ,z bT ] T represents the position of the radiation source in the stellar coordinate system; and x bT Available x T with x S Expressed as: x bT =L z (ψ)L x (φ)L y (θ)V -1 (x T -x S ),

[0026] Where, Among them, φ is the roll angle of the satellite platform, θ is the pitch angle of the satellite platform, ψ is the yaw angle of the satellite platform, and v S Represents the velocity vector of the satellite platform in the earth-fixed coordinate system.

[0027] Furthermore, the spherical constraint is:

[0028]

[0029] The ground radiation source position estimation result is expressed as:

[0030]

[0031] Among them, J represents the cost function, N r is the radius of curvature of the local Maoyou circle, H is the geodetic height, e 2 is the square of the first eccentricity.

[0032] Furthermore, the cost function is expressed as Among them, R z =E[z(t)z H (t)],R z is the covariance matrix of the received signal, E[·] represents the expectation, [·] H represents the conjugate transpose.

[0033] Furthermore, the received signal is expressed as: z(t)=a(x T ,x S )s(t)+ω(t), where z(t) represents the ground radiation source signal received by the satellite array antenna, a(x T ,x S ) is the array steering vector of the ground radiation source signal, x T =[x T ,y T ,z T ] T represents the position of the ground radiation source in the ground-fixed coordinate system, x S =[x S ,y S ,z S ] T represents the position of the satellite platform in the ground-fixed coordinate system, s(t) is the complex envelope of the received signal, and ω(t) is the array complex white Gaussian noise vector.

[0034] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0035] 1. The present invention proposes a cost function for direct positioning of a single satellite based on the covariance moment of the received signal and in combination with the array steering vector. A weighting matrix is ​​obtained through the beamforming matrix, and a grid search is performed on the coverage area of ​​the maximum amplitude receiving beam and its adjacent beams in combination with spherical constraints to optimize the cost function to achieve ground radiation source positioning. On the one hand, the beamforming matrix is ​​constructed to superimpose the signals, and the beamforming amplitude corresponding to the corresponding ground radiation source position is the largest. Compared with a grid search of the entire observation area, only the grid search is performed on the coverage area of ​​the maximum amplitude receiving beam and its adjacent beams, which can narrow the search range of the observation area. On the other hand, the ground radiation source position is located through a grid search based on the original data to optimize the cost function, eliminating the need to estimate related parameters, thereby improving the accuracy of the positioning results under low signal-to-noise ratios and achieving lower positioning errors.

[0036] 2. By performing null-stuck optimization through the beamforming matrix, the corresponding receive beam amplitude is obtained based on the optimized beamforming matrix, thereby completing the beamforming of the single-satellite direct positioning of the ground radiation source. This can suppress the influence of strong interference signals in the observation area and realize the positioning of the ground radiation source.

[0037] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The accompanying drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like parts throughout the drawings.

[0039] Figure 1 This is a flow chart of the single-satellite direct positioning method according to Example 1 of the present invention;

[0040] Figure 2 This is a single satellite platform positioning scene diagram of Example 1 of the present invention;

[0041] Figure 3 Schematic diagram of the relative positions of the array antennas according to embodiment 1 of the present invention;

[0042] Figure 4 The three-dimensional diagram of the observation beam of Example 1 of the present invention;

[0043] Figure 5 is an amplitude diagram of each receiving beam in embodiment 1 of the present invention;

[0044] Figure 6This is a cost function simulation diagram of Example 1 of the present invention;

[0045] Figure 7 This is a three-dimensional diagram of the observation beam with nulling according to embodiment 2 of the present invention;

[0046] Figure 8 A two-dimensional top view of an observation beam with a null according to embodiment 2 of the present invention;

[0047] Figure 9 This is a graph showing how the root mean square error of positioning changes with the signal-to-noise ratio for the method described in Example 1 of the present invention and the traditional two-step single-satellite direction-finding positioning method;

[0048] Figure 10 This is a graph showing how the root mean square error of positioning between the method described in Example 1 of the present invention and the traditional two-step single-satellite direction-finding positioning method changes with the number of sampling points. DETAILED DESCRIPTION

[0049] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, and are not used to limit the scope of the present invention.

[0050] Example 1

[0051] A specific embodiment of the present invention discloses a single-satellite direct positioning method based on beamforming, such as Figure 1 As shown, the following steps are included:

[0052] Step S1: Constructing a beamforming matrix for the satellite platform array antenna so that the array antenna forms multiple observation beams at different angles within the Earth observation area. The beamforming matrix is ​​constructed based on the relative positions between the satellite platform array antenna units and the angles of the observation beams.

[0053] Step S2: using a satellite platform array antenna to receive a ground radiation source signal, obtaining a covariance matrix of the received signal, obtaining multiple receiving beams based on the beamforming matrix, and calculating the amplitude of each receiving beam;

[0054] Step S3: determining an array steering vector based on the relative position between the ground radiation source and the satellite platform, and constructing a cost function for single-satellite direct positioning in combination with the covariance matrix;

[0055] Step S4: Under the spherical constraint condition, determine the grid area based on the maximum amplitude receiving beam, and perform grid search to optimize the cost function to obtain the result of the ground radiation source position estimation.

[0056] The above method uses a satellite platform, i.e., a single satellite, to locate the ground target radiation source without estimating relevant parameters. The beamforming matrix is ​​used to narrow the grid search range, and the cost function is optimized through grid search to directly estimate the position, thereby improving the positioning accuracy of the ground target radiation source in a low signal-to-noise ratio environment. This makes up for the shortcoming of the existing single-satellite positioning technology that has large positioning errors under low signal-to-noise ratio.

[0057] Specifically, the beamforming matrix in step S1 is expressed as:

[0058] M=[m1,m2,…,m L ]

[0059] Where,

[0060] Among them, m i is the i-th element of the beamforming matrix, α i is the azimuth of the i-th observation beam in the stellar coordinate system, β i is the pitch angle of the i-th observation beam in the stellar coordinate system, L is the total number of observation beams, i=1,2,...,L, λ is the wavelength of the ground radiation source, [x bn ,y bn ,z bn ] is the relative position coordinate of the nth antenna unit in the array antenna in the celestial coordinate system, N is the total number of array antenna units, n=1,2…,N, usually assume [x b1 ,y b1 ,z b1 ]=[0,0,0].

[0061] Furthermore, the received signal in step S2 is represented as:

[0062] z(t)=a(x T ,x S )s(t)+ω(t)

[0063] Among them, z(t) represents the ground radiation source signal received by the satellite array antenna, a(x T ,x S ) is the array steering vector of the ground radiation source signal, x T =[x T ,y T ,z T ] T represents the position of the ground radiation source in the ground-fixed coordinate system, x S =[x S ,y S ,z S ] Trepresents the position of the satellite platform in the earth-fixed coordinate system, s(t) is the complex envelope of the received signal, and ω(t) is the array complex white Gaussian noise vector;

[0064] The covariance matrix of the received signal is calculated as:

[0065] R z =E[z(t)z H (t)]

[0066] Among them, R z is the covariance matrix of the received signal, E[·] represents the expectation, [·] H represents the conjugate transpose.

[0067] In step S2, the received signal is passed through the beamforming matrix to obtain multiple receiving beams, which are expressed as:

[0068] y(t)=M·z(t)

[0069] Calculate the amplitude corresponding to the received beam as:

[0070] A i =max{20log 10 [fft(y i (t))]}

[0071] Among them, A i is the amplitude of the i-th receiving beam, y i (t) is the i-th row element of y(t), and fft(·) represents the fast Fourier transform.

[0072] Furthermore, in step S3, based on the relative position between the ground radiation source and the satellite platform, the expression of the array steering vector is determined as follows:

[0073]

[0074] Among them, (α, β) represents the azimuth and elevation angles of the ground radiation source in the stellar coordinate system; and the azimuth and elevation angles can be expressed as:

[0075]

[0076] Among them, x bT =[x bT ,y bT ,z bT ] T represents the position of the ground radiation source in the stellar coordinate system; and x bT Available x T with x S Expressed as:

[0077] x bT =Lz (ψ)L x (φ)L y (θ)V -1 (x T -x S )

[0078] Where,

[0079]

[0080] Among them, φ is the roll angle of the satellite platform, θ is the pitch angle of the satellite platform, ψ is the yaw angle of the satellite platform, and v S Represents the motion velocity vector of the satellite platform in the earth-fixed coordinate system;

[0081] Furthermore, the cost function in step S3 is:

[0082]

[0083] For a ground radiation source, the spherical constraint condition is satisfied, and the spherical constraint is:

[0084]

[0085] By solving the cost function in combination with the spherical constraint condition, the result of the ground radiation source position estimation can be obtained. The ground radiation source position estimation can be expressed as:

[0086]

[0087] Among them, N r is the radius of curvature of the local Maoyou circle, H is the geodetic height, e 2 is the square of the first eccentricity.

[0088] Specifically, the position estimation step in step S4 includes: i}(i=1,2,…,L) determine the receiving beam with the largest amplitude; determine the grid search range according to the receiving beam with the largest amplitude, including when the receiving beam with the largest amplitude is in the middle of the observation area, taking the receiving beam with the largest amplitude and the adjacent receiving beam coverage areas in four directions around it as the grid area; when the receiving beam with the largest amplitude is at the edge of the observation area, there are only three adjacent beams in three directions around the receiving beam with the largest amplitude, taking the receiving beam with the largest amplitude and the adjacent receiving beam coverage areas in the three directions as the grid area; determine the grid division step size according to the positioning accuracy index, and divide the grid points within the grid search range; calculate the array steering vector for each grid point in turn in combination with the spherical constraint condition to obtain the corresponding cost function; based on the optimal parameter solution corresponding to the maximum cost function in the grid area, obtain the estimation result of the ground radiation source in the ground-fixed coordinate system.

[0089] The estimated results are transformed into the WGS84 geodetic coordinate system to obtain the latitude and longitude estimation results of the ground radiation source position:

[0090]

[0091] Where R represents the radius of the Earth.

[0092] For example, the single satellite platform positioning scenario of the embodiment of the present invention is shown as follows: Figure 2 The latitude and longitude of the satellite platform in the geodetic coordinate system are [L, B, h] = [120°, 10°, 500km], and the satellite motion speed v S =[-4.78,-3.49,4.01] T km / s, the satellite platform's roll angle φ = 0°, pitch angle θ = 0°, and yaw angle ψ = 0°. The relative positions of the array antennas on the satellite in the embodiment of the present invention are as follows: Figure 3 As shown in Figure 1, the satellite array antenna is a uniform planar array with 10 rows and 8 columns. Assuming the array antenna on the satellite observes the Earth vertically, the azimuth angle range of the observation area is α∈[0,360°), and the elevation angle range is β∈[0°,70°], where the elevation angle β=0° represents the sub-satellite point. An observation beam is formed for every 10° of azimuth and elevation angle within the observation area, corresponding to the beamforming of the sub-satellite horizontal and vertical angles, as shown in Figure 1. Figure 4 As shown, it is a three-dimensional diagram of the observation beam formed by an embodiment of the present invention, and the ground observation angle range in the horizontal direction and the vertical direction under the satellite is [-70°, 70°].

[0093] For example, assume that the wavelength of the signal from the ground target radiation source is 1.33m, the latitude and longitude of the target radiation source are (120.16°, 5.22°), the signal receiving signal-to-noise ratio (SNR) is 5dB, and the number of signal sampling points is set to 1024 points. Figure 5 The figure shows the amplitude diagram of each receiving beam in the embodiment of the present invention. Based on the spherical constraint, the grid points are divided in the coverage area of ​​the receiving beam with the largest amplitude and its adjacent beams and the array steering vector is calculated to obtain the optimization cost function, as shown in the figure below. Figure 6 As shown, it can be seen that the cost function forms a sharper spectrum peak at the target radiation source position, while other areas are relatively flat.

[0094] The positioning root mean square error of the method described in this embodiment and the traditional two-step single-satellite direction finding positioning method is compared as the signal-to-noise ratio changes. Figure 9 As shown in the figure, it can be seen that compared with the traditional two-step single-satellite direction finding positioning, the positioning method described in this embodiment has a lower positioning error under low signal-to-noise ratio. Figure 10The figure shows a curve of the root mean square error of the positioning method described in an embodiment of the present invention and the traditional two-step single-star direction finding positioning method as the number of sampling points changes. It can be seen from the figure that compared with the traditional two-step single-star direction finding positioning method, the positioning method has a lower positioning error when the same number of points are used.

[0095] Compared to existing technologies, this embodiment provides a single-satellite direct positioning method based on beamforming. This method calculates the covariance matrix of ground-radiating source signals received by a satellite platform's array antenna and constructs a cost function for single-satellite direct positioning based on array steering vectors. A weighting matrix is ​​then generated using the beamforming matrix. In combination with spherical constraints, a grid search is performed within the coverage area of ​​the maximum-amplitude receiving beam and its adjacent beams to optimize the cost function and locate the ground-radiating source. This method uses the constructed beamforming matrix to superimpose signals, resulting in the ground-radiating source location corresponding to the location with the largest beamforming amplitude. Compared to a full-observation-area grid search, this method narrows the search range by only performing a grid search within the coverage area of ​​the maximum-amplitude receiving beam and its adjacent beams. Furthermore, the cost function is optimized based on the raw data to locate the ground-radiating source, eliminating the need to estimate relevant parameters. This improves the accuracy of positioning results under low signal-to-noise ratio conditions and reduces positioning error.

[0096] Example 2

[0097] A single-satellite direct positioning method based on beamforming in areas with strong interference signals is provided. This method is a further optimization of Example 1 and includes the following steps:

[0098] Nulling is performed on the area with strong interference signals, and the beamforming matrix M constructed in step S1 of embodiment 1 is further optimized. The optimized beamforming matrix is ​​expressed as:

[0099] P=[p1,p2,…,p L ]

[0100] Where, U=[u1,u2,…,u K ],

[0101]

[0102] Where P is the optimized beamforming matrix, (α k ,β k ) represents the azimuth and elevation angles of the kth observation beam that needs to be nulled in the stellar coordinate system, k = 1, 2, ..., K, where K is the total number of observation beams that need to be nulled.

[0103] By performing nulling in areas with strong interfering signals, a beamforming matrix is ​​obtained after suppressing the strong interfering signals. The amplitudes of each receive beam are obtained using the optimized beamforming matrix. Combined with the methods of steps S2 through S4 in Example 1, a single-satellite direct positioning result is obtained after suppressing the strong interfering signals.

[0104] For example, assume that there is a strong interference signal at an azimuth angle α = 265° and an elevation angle β = 65° in the satellite observation area, and the beam in this direction needs to be nulled. The corresponding horizontal angle is -2.58° and the vertical angle is -29.47°. Figure 7 As shown in FIG, this is a three-dimensional diagram of the observation beam with null sinking in this embodiment, as shown in FIG. Figure 8 As shown in FIG, it is a top view of the observation beam after the null sink in this embodiment. Figure 7 and Figure 8 It can be seen that a deeper null beam is formed at the corresponding horizontal and vertical angles.

[0105] Compared with the prior art, the beamforming-based single-satellite direct positioning method provided in this embodiment in areas with strong interference signals performs nulling processing on the beamforming matrix to perform single-satellite direct positioning, which can suppress the influence of strong interference signals in the observation area and achieve position estimation of ground target radiation sources.

[0106] Those skilled in the art will appreciate that all or part of the process steps of the above-described embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, such as a magnetic disk, an optical disk, a read-only memory, or a random access memory.

[0107] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection of the present invention.

Claims

1. A single-satellite direct positioning method based on beamforming, characterized in that: The steps include: Constructing a beamforming matrix for the satellite platform array antenna so that the array antenna forms multiple observation beams at different angles within the Earth observation area; Receive ground radiation source signals using a satellite platform array antenna to obtain a covariance matrix of the received signals, and obtain the amplitude of each receiving beam based on the beamforming matrix; Based on the relative position between the ground radiation source and the satellite platform, an array steering vector is determined, and a cost function for single-satellite direct positioning is constructed in combination with the covariance matrix; Under the spherical constraint, the grid area is determined based on the maximum amplitude receiving beam, and a grid search is performed to optimize the cost function to obtain the result of the ground radiation source position estimation.

2. The single-satellite direct positioning method based on beamforming according to claim 1, characterized in that: The beamforming matrix is ​​constructed based on the relative positions between the satellite platform array antenna units and the angle of the observation beam, and is expressed as: M = [m1, m2, ..., m L ], where Among them, m i is the i-th element of the beamforming matrix, α i is the azimuth of the i-th observation beam in the stellar coordinate system, β i is the pitch angle of the i-th observation beam in the stellar coordinate system, L is the total number of observation beams, i=1,2,...,L, λ is the wavelength of the ground radiation source, [x bn ,y bn ,z bn ] is the relative position coordinate of the nth antenna unit in the array antenna in the celestial coordinate system, N is the total number of units in the array antenna, n=1,2...,N.

3. The single-satellite direct positioning method based on beamforming according to claim 2, characterized in that: When there is a strong interference signal area, the method further includes performing null-steering optimization on the beamforming matrix to obtain an optimized beamforming matrix, and obtaining the amplitude of each receiving beam using the optimized beamforming matrix; The optimized beamforming matrix is ​​expressed as: P = [p1, p2, ..., p L ], where Wherein, P is the optimized beamforming matrix, (α k ,β k ) represents the azimuth and elevation angles of the kth observation beam that needs to be nulled in the stellar coordinate system, k = 1, 2, ..., K, where K is the total number of observation beams that need to be nulled.

4. A single-satellite direct positioning method based on beamforming according to any one of claims 1 to 3, characterized in that: The specific steps of the position estimation include: determining the receiving beam with the largest amplitude; determining the grid area based on the receiving beam with the largest amplitude; determining the grid division step size based on the positioning accuracy index, and dividing the grid points within the grid area; calculating the array steering vector for each grid point in turn in combination with the spherical constraint condition to obtain the corresponding cost function; and obtaining the estimation result of the ground radiation source in the ground-fixed coordinate system based on the optimal parameter solution corresponding to the maximum cost function in the grid area.

5. The single-satellite direct positioning method based on beamforming according to claim 4, characterized in that: The grid area includes: when the receiving beam with the maximum amplitude is in the middle of the observation area, the receiving beam with the maximum amplitude and the receiving beam coverage areas in the four directions around it are used as the grid area range; when the receiving beam with the maximum amplitude is at the edge of the observation area, the receiving beam with the maximum amplitude and the receiving beam coverage areas in the three directions around it are used as the grid area range.

6. The single-satellite direct positioning method based on beamforming according to claim 4, characterized in that: The receiving beam is expressed as: y(t) = M·z(t), and the amplitude of the receiving beam is: A i =max{20log 10 [fft(y i (t))]}, where z(t) represents the ground radiation source signal received by the satellite array antenna, A i is the amplitude of the i-th receiving beam, y i (t) is the i-th row element of y(t), and fft(·) represents the fast Fourier transform.

7. The single-satellite direct positioning method based on beamforming according to claim 1, characterized in that: The expression of the array steering vector is: Among them, (a, β) represents the azimuth and elevation angles of the radiation source in the stellar coordinate system; and the azimuth and elevation angles can be expressed as: Among them, x bT =[x bT ,y bT ,z bT ] T represents the position of the radiation source in the stellar coordinate system; and x bT Available x T with x S Expressed as: x bT =L z (ψ)L x (φ)L y (θ)V -1 (x T -x S ), Where, Among them, φ is the roll angle of the satellite platform, θ is the pitch angle of the satellite platform, ψ is the yaw angle of the satellite platform, and v S Represents the velocity vector of the satellite platform in the earth-fixed coordinate system.

8. The single-satellite direct positioning method based on beamforming according to claim 7, characterized in that: The spherical constraint is: The ground radiation source position estimation result is expressed as: Among them, J represents the cost function, N r is the radius of curvature of the local Maoyou circle, H is the geodetic height, e 2 is the square of the first eccentricity.

9. The single-satellite direct positioning method based on beamforming according to claim 8, characterized in that: The cost function is expressed as: Among them, R z =E[z(t)z H (t)],R z is the covariance matrix of the received signal, E[·] represents the expectation, [·] H represents the conjugate transpose.

10. The single-satellite direct positioning method based on beamforming according to claim 1, characterized in that: The received signal is expressed as: z(t)=a(x T ,x S )s(t)+ω(t), where z(t) represents the ground radiation source signal received by the satellite array antenna, a(x T ,x S ) is the array steering vector of the ground radiation source signal, x T =[x T ,y T ,z T ] T represents the position of the ground radiation source in the ground-fixed coordinate system, x S =[x S ,y S ,z S ] T represents the position of the satellite platform in the ground-fixed coordinate system, s(t) is the complex envelope of the received signal, and ω(t) is the array complex white Gaussian noise vector.

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