Large-scale MIMO multi-satellite positioning and direction estimation method and system based on angle information

Abstract

The invention discloses a large-scale MIMO multi-satellite positioning and direction estimation method and system based on angle information. The method comprises the following steps: firstly, obtaining channel matrix estimation between each satellite and a user by sending a pilot signal; then, obtaining estimated values of channel parameters by using a tensor-ESPRIT algorithm, wherein the estimated values comprise an angle of departure and an angle of arrival; according to the estimated departure angles, direction vectors between the user and all satellites are obtained, an optimization problem on spherical manifold is established, altitude constraints are considered, and a Riemann conjugate gradient method is used for solving and obtaining a user position estimation value; and finally, according to the estimated user position and arrival angle, establishing an optimization problem on the SO (3) manifold, and solving by using a Riemannian gradient descent method to obtain an estimated value of a user array rotation matrix. According to the method, positioning and direction estimation are performed by combining channel information between a plurality of satellites and users, and altitude constraints are considered during positioning, so that compared with single-satellite and non-constraint conditions, the positioning performance can be remarkably improved, and meanwhile, the method has good direction estimation performance.

Description

Technical Field

[0001] This invention relates to the field of satellite communication and positioning, and in particular to a method and system for large-scale MIMO multi-satellite positioning and orientation estimation considering altitude constraints. Background Technology

[0002] Low Earth Orbit (LEO) satellite constellations have attracted significant attention due to their low transmission latency and minimal path loss. Furthermore, the expanding constellations allow a single user to be served by multiple satellites simultaneously, enabling multi-satellite joint positioning and orientation estimation. Massive MIMO systems can significantly increase the degrees of freedom in the spatial domain, and applying MIMO technology to LEO satellite systems can improve positioning accuracy. Positioning capabilities support many location-dependent services and are crucial for 6G systems. Terrestrial networks are widely used for 2D location estimation; however, due to the short distance between users and base stations, these studies typically assume that users and base stations lie in the same plane. But because of the wide coverage of LEO, locating terrestrial users using satellite networks constitutes a problem on a non-Euclidean manifold, as terrestrial users satisfy altitude constraints, which can be considered prior information to further improve positioning accuracy. Current research on LEO satellite positioning largely focuses on precoding design to reduce the Cramer-Rao lower bound of positioning errors; therefore, further research on specific positioning algorithms is needed. Summary of the Invention

[0003] Purpose of the invention: To address the shortcomings of existing technologies, the purpose of this invention is to provide a large-scale MIMO multi-satellite positioning and orientation estimation method and system that considers multi-satellite joint positioning and the prior information of altitude constraints, thereby significantly improving positioning and orientation estimation performance.

[0004] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0005] A large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information, wherein multiple low-Earth orbit satellites provide services to multiple antenna users, and simultaneously estimates the user's position and array orientation; the method includes the following steps:

[0006] Channel matrix estimation between each satellite and the user is obtained by transmitting pilot signals;

[0007] The channel parameters, including the departure angle and the angle of arrival, are estimated using the tensor-ESPRIT algorithm.

[0008] Based on the estimated departure angle, the direction vectors between the user and each satellite are obtained. An optimization problem is established on the spherical manifold. Considering the altitude constraint, the Riemann conjugate gradient method is used to solve the estimated user position.

[0009] Based on the estimated user location and angle of arrival, an optimization problem is established on the SO(3) manifold, and the estimated value of the user array rotation matrix is ​​obtained by using the Riemann gradient descent method.

[0010] Furthermore, in the method, a rotational position vector between satellite m and the user is defined:

[0011]

[0012]

[0013] in, and Let p represent the position and orientation of satellite m, respectively, and p = [p x ,p y ,p z ] T and o ut These represent the user's position and orientation, respectively. and Let the satellite array rotation matrix and user array rotation matrix be represented respectively, and let the departure angle and arrival angle be represented as... and The relationship between the departure angle, arrival angle, and position parameters is expressed as follows:

[0014]

[0015] Where ||·||2 represents the L2 norm.

[0016] Furthermore, in the method, based on the beam domain channel model, the least squares estimate of the channel matrix between each satellite and the user is obtained, and the received signal is represented as... ;in, Let the pilot matrix on the nth subcarrier transmitted by satellite m satisfy the following condition: This represents the beam-domain channel matrix after Doppler frequency shift compensation. Represents the beam domain noise components; the least squares estimate of the beam domain channel matrix can be obtained from the received signal. in, This indicates the estimation error caused by noise.

[0017] Furthermore, in obtaining the estimated channel parameters using the tensor-ESPRIT algorithm, the beam domain channel matrix is ​​represented in tensor form:

[0018]

[0019] in, and N represents the number of radio frequency chains on the satellite side and the user side, respectively.sc f represents the number of subcarriers. s α represents the subcarrier spacing. m τ represents the channel gain. m Indicates the propagation delay; Represents the beam domain array manifold. Let a represent the transformation matrix. r (·) denotes an array manifold. It represents the outer product.

[0020] Furthermore, in the method, the estimated value of the departure angle is used. Obtain the direction vectors between the user and each satellite:

[0021]

[0022] Define a series of half-lines based on the direction vector. Due to channel estimation errors, these lines are non-planar. Considering altitude constraints, estimating user locations is transformed into the following problem:

[0023]

[0024] Where M represents the number of satellites, R e R represents the Earth's radius. h Indicates the user's altitude. This represents the sphere where the user is located.

[0025] Furthermore, the Riemann conjugate gradient method is used to solve the optimization problem, specifically including:

[0026] Simplify the problem to:

[0027] min p f(p)

[0028]

[0029] in, I represents the identity matrix; position p is iterated according to the following formula:

[0030]

[0031] Where, p (k) and p (k+1) This represents the position obtained in rounds k and k+1, β (k) and D (k) Indicates the step size and iteration direction; The projection operator is represented as:

[0032]

[0033] The Euclidean gradient of the objective function at point p is:

[0034]

[0035] Projecting the Euclidean gradient onto the tangent space, it is represented as: The Riemann gradient is obtained and expressed as:

[0036]

[0037] The step size selection satisfies:

[0038]

[0039] Where 0 < c1 < c2 < 1, and <·,·> denote the inner product;

[0040] D (k) Represented as:

[0041]

[0042] Where, γ (k) The conjugate coefficient is defined as:

[0043]

[0044] in, This represents vector transport, moving a vector from the tangent space. Projected to

[0045] Furthermore, in the method, an estimate of the user's location is obtained. and the estimation of the angle of arrival Then, the representation of the position vector in the local coordinate system. Recorded as:

[0046]

[0047] Here, the matrix is ​​defined. The optimization problem concerning the user array rotation matrix R is as follows:

[0048]

[0049] stR∈SO(3)

[0050] in, Q = [q1, ..., q M ], Let M be a row vector of all 1s with M elements. It represents the Kronecker product.

[0051] Furthermore, the rotation matrix R is estimated using the Riemann gradient algorithm, and the Euclidean gradient of the objective function is expressed as:

[0052]

[0053] Projecting the Euclidean gradient onto the tangent space yields the Riemann gradient, denoted as:

[0054]

[0055] Where Skew(X) = (XX T The rotation matrix R is iterated as follows: (2 / 2)

[0056] R (k+1) =Ret R(k) (-α k grad SO(3) f(R (k) ))

[0057] Where, α k Ret represents the step size, determined by the backtracking search; R (X) represents the contraction operation on the SO(3) manifold, denoted as:

[0058] Ret R (X)=(R+X)(I3+X T X) -1 / 2

[0059] Based on the same inventive concept, this invention provides a large-scale MIMO multi-satellite positioning and orientation estimation system based on angle information, in which multiple low-Earth orbit satellites provide positioning and orientation estimation services to multi-antenna users, including:

[0060] The single-satellite channel estimation module is used to obtain channel matrix estimates between each satellite and the user by transmitting pilot signals; and to obtain estimated channel parameters, including departure angle and arrival angle, using the tensor-ESPRIT algorithm.

[0061] The user position estimation module is used to obtain the direction vector between the user and each satellite based on the estimated departure angle, establish an optimization problem on a spherical manifold, consider the altitude constraint, and use the Riemann conjugate gradient method to obtain the estimated user position value.

[0062] And an orientation estimation module, which is used to establish an optimization problem on the SO(3) manifold based on the estimated user position and angle of arrival, and use the Riemann gradient descent method to obtain the estimated value of the user array rotation matrix.

[0063] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information.

[0064] Beneficial effects: This invention utilizes joint positioning based on channel information from multiple satellites and the user, reducing the accumulation of position estimation errors caused by channel parameter estimation errors and improving the accuracy of positioning and orientation estimation. Simultaneously, by using altitude constraints as prior information, it further enhances positioning accuracy. This invention solves the originally non-convex optimization problem within a manifold optimization framework, reducing the complexity of problem solving and physical layer implementation, and accelerating computation. Attached Figure Description

[0065] Figure 1 This is a schematic diagram of the overall method flow of an embodiment of the present invention.

[0066] Figure 2 The figure shows the simulation results of the position estimation error as a function of the signal-to-noise ratio.

[0067] Figure 3 The figure shows the simulation results of the direction estimation error as a function of the signal-to-noise ratio. Detailed Implementation

[0068] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0069] like Figure 1 As shown in the embodiment of the present invention, a large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information is disclosed. Multiple low-orbit satellites provide services to multiple antenna users, and the position and array orientation of the users are estimated at the same time. The method includes: obtaining the channel matrix estimation between each satellite and the user by sending pilot signals; obtaining the estimated values ​​of channel parameters, including departure angle and arrival angle, using the tensor-ESPRIT algorithm; obtaining the orientation vector between the user and each satellite based on the estimated departure angle, establishing an optimization problem on a spherical manifold, considering altitude constraints, and solving the estimated value of the user position using the Riemann conjugate gradient method; establishing an optimization problem on an SO(3) manifold based on the estimated user position and arrival angle, and solving the estimated value of the user array rotation matrix using the Riemann gradient descent method.

[0070] The method of this embodiment will be explained in more detail below with a specific scenario.

[0071] Part 1: Constructing a Large-Scale MIMO Multi-Satellite Positioning and Orientation Estimation System Model

[0072] Specifically, a spatial rectangular coordinate system is established with the Earth's center as the center and the Earth's radius is denoted as R. e The positioning system has M satellites, each equipped with a uniform planar array, with the number of antennas in the x and y directions being respectively... and The satellite collection is denoted as The position and orientation of each satellite m are known, denoted as ... and

[0073] , ψ m and ζ m Let x and y represent the rotation angles around the positive y-axis and negative x'-axis, respectively, where x'-axis is the rotated x-axis. The satellite serves some users equipped with uniform planar arrays, and the number of antennas in the x and y directions are respectively... and Taking one user as an example, the user's position and direction are unknown, represented as p = [p x ,p y ,p z ] T and o ut =[φ1,φ2] T Where φ1 and φ2 represent the rotation angles around the positive y-axis and negative x'-axis, respectively. Orthogonal frequency division multiplexing is used for downlink transmission in the system, with a bandwidth of B. w N sc and f c These represent the number of subcarriers and the carrier frequency, respectively. Positioning depends on N. p Information on each pilot symbol.

[0074] Define the rotational position vector between the user and satellite m:

[0075]

[0076] in, and R(o) ut Let represent the satellite array rotation matrix and the user array rotation matrix, respectively. The departure angle and arrival angle between the user and satellite m are expressed as... The relationship between position parameters and angle parameters is expressed as follows:

[0077]

[0078]

[0079] The satellite-side and user-side array response vectors are represented as follows:

[0080]

[0081] in:

[0082]

[0083] To reduce the number of radio frequency chains in massive MIMO systems, hybrid precoding is employed on both the satellite and user sides, resulting in a combined total number of radio frequency chains on both sides. and The m-th subcarrier between the user and satellite m p The beam domain channel matrix of OFDM symbols is represented as:

[0084]

[0085] in, This represents the satellite-side precoding and user-side combination matrix. and Represents the transformation matrix. Definition Where ν m α represents the Doppler frequency shift caused by satellite motion. m τ represents the channel gain. m Indicates the propagation delay.

[0086] The pilot matrix on the nth subcarrier emitted by satellite m is represented as... satisfy By N p pilot vectors It is spliced ​​together, and the received m-th subcarrier from satellite m is the n-th subcarrier. p The signal on each symbol is represented as:

[0087]

[0088] in, This represents the m-th subcarrier between the user and satellite m. p Channel matrix over symbols, Each element is independent and identically distributed additive complex white Gaussian noise. Due to the deterministic movement of the satellite, the Doppler shift caused by the satellite movement can be pre-compensated, and the compensated beam-domain channel matrix is ​​expressed as:

[0089]

[0090] Position and orientation estimation depends on N p The OFDM symbols are combined and represented as follows:

[0091]

[0092] in,

[0093] Part Two: Position and Orientation Estimation

[0094] Step S1, Satellite-by-Satellite Channel Estimation: Obtain channel matrix estimates between each satellite and the user by sending pilot signals, and use the tensor-ESPRIT algorithm to obtain estimated channel parameters.

[0095] Specifically, the estimated value of the beam domain channel matrix can be obtained by the following formula:

[0096]

[0097] in, This represents the estimation error caused by noise. The high-dimensional beam-domain channel matrix can be represented in tensor form. For convenience, we indicate R5 = N sc , but:

[0098]

[0099] in,

[0100] ω m,5 =-2πf s τ m . The beam domain array manifold is represented as:

[0101]

[0102] Where a r (ω m,n () represents the array manifold. The beam-domain channel matrix observations in the noisy version are represented as:

[0103]

[0104] The tensor-ESPRIT algorithm can be used to... The values ​​of the channel parameters are estimated from this.

[0105] Step S2, Multi-satellite Joint Position Estimation: Based on the estimated departure angle, obtain the direction vectors between the user and each satellite, establish an optimization problem on the spherical manifold, consider the altitude constraint, and use the Riemann conjugate gradient method to obtain the estimated user position value.

[0106] Specifically, the direction vectors between the user and each satellite can be obtained by estimating the departure angle:

[0107]

[0108] Based on the direction vector, a series of half-lines can be defined. Due to channel estimation errors, these lines are skewed. Considering altitude constraints, estimating the user's location can be transformed into the following problem:

[0109]

[0110] Among them, R e R represents the Earth's radius. h This represents the user's altitude. To accelerate convergence, the Riemann conjugate gradient method is used for solving the problem. First, the problem is simplified to:

[0111] min p f(p)

[0112]

[0113] in, The iterative process of user location p is represented as:

[0114]

[0115] Where, p (k) and p (k+1) Let β represent the positions obtained in the k-th and k+1-th iterations, respectively. (k) and D (k) Indicates the step size and iteration direction. The projection operator is represented as:

[0116]

[0117] The Euclidean gradient of the objective function at p is:

[0118]

[0119] Projecting the Euclidean gradient onto the tangent space, denoted as . The Riemann gradient can be obtained, expressed as:

[0120]

[0121] To ensure convergence and convergence efficiency, the step size β... (k) The following conditions must be met:

[0122]

[0123] Where 0 < c1 < c2 < 1. Using the conjugate gradient method to achieve faster convergence, then D... (k) Represented as:

[0124]

[0125] Where, γ (k) The conjugate coefficient is defined by the following formula:

[0126]

[0127] in, This represents vector transport, specifically moving the vector from the tangent space in the previous steps. Projected to Represented as:

[0128]

[0129] Step S3, User Orientation Estimation: Based on the estimated user position and angle of arrival, establish an optimization problem on the SO(3) manifold, and use the Riemann gradient descent method to obtain the estimated value of the user array rotation matrix.

[0130] Specifically, after obtaining an estimate of the user's location, the representation of the location vector in the local coordinate system can be obtained, that is... Recorded as:

[0131]

[0132] Define matrix The optimization problem concerning the rotation matrix R is as follows:

[0133]

[0134] stR∈SO(3)

[0135] in, Q = [q1, ..., q M The rotation matrix R is estimated using the Riemann gradient algorithm, and the Euclidean gradient of the objective function is expressed as:

[0136]

[0137] Projecting the Euclidean gradient onto the tangent space yields the Riemann gradient, denoted as:

[0138]

[0139] Where Skew(X) = (XX T The rotation matrix R is iterated as follows: (2 / 2)

[0140]

[0141] Where, α k Ret represents the step size. R(X) represents the contraction operation on the SO(3) manifold, denoted as:

[0142] Ret R (X)=(R+X)(I3+X T X) -1 / 2

[0143] To ensure sufficient descent, the step size α k Determined by backtracking search.

[0144] The following simulation experiment demonstrates the effectiveness of the invention. The experimental settings are as follows: carrier frequency f c =2GHz, system bandwidth B w =10MHz, number of subcarriers is 512, subcarrier spacing f s =15kHz; satellite position set to q1=[0,0,6578] T km, q2 = [300, 300, 6564] T The low-Earth orbit satellites have an orbital altitude of 200 km, and the orientation of each satellite is set to [π / 6, 0]. T Each satellite is equipped with a 24×24 dimension UPA and 16×16 radio frequency links. Users are equipped with an 8×8 UPA and 4×4 radio frequency links. The user's altitude is 0.

[0145] Figure 2 This illustrates how positioning error varies with signal-to-noise ratio, such as... Figure 2 As shown, when the signal-to-noise ratio increases, the positioning error of all three schemes is significantly reduced. The comparison shows that the proposed scheme can significantly reduce the position estimation error compared with the single-satellite and unconstrained cases.

[0146] Figure 3 The diagram illustrates the variation of direction estimation error with signal-to-noise ratio. Since direction estimation requires at least two satellites, the simulation results only compare constrained and unconstrained cases. Figure 3 As shown, the direction estimation error under the constrained two-star condition is significantly lower than that under the unconstrained two-star condition.

[0147] Based on the same inventive concept, this invention discloses a large-scale MIMO multi-satellite positioning and orientation estimation system based on angle information. Multiple low-orbit satellites provide positioning and orientation estimation services to multiple antenna users. The system includes: a single-satellite channel estimation module, used to obtain channel matrix estimation between each satellite and the user by transmitting pilot signals; and to obtain estimated values ​​of channel parameters, including departure angle and arrival angle, using the tensor-ESPRIT algorithm; a user position estimation module, used to obtain the orientation vector between the user and each satellite based on the estimated departure angle, establish an optimization problem on a spherical manifold, consider altitude constraints, and solve for the user position estimate using the Riemann conjugate gradient method; and an orientation estimation module, used to establish an optimization problem on an SO(3) manifold based on the estimated user position and arrival angle, and solve for the estimated value of the user array rotation matrix using the Riemann gradient descent method.

[0148] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of the large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information.

Claims

1. A method for large-scale MIMO multi-satellite positioning and orientation estimation based on angle information, characterized in that, Multiple low-Earth orbit satellites provide services to multiple antenna users while simultaneously estimating the user's location and array orientation; the method includes the following steps: Channel matrix estimation between each satellite and the user is obtained by transmitting pilot signals; The channel parameters, including the departure angle and the angle of arrival, are estimated using the tensor-ESPRIT algorithm. Based on the estimated departure angle, the direction vectors between the user and each satellite are obtained. An optimization problem is established on the spherical manifold. Considering the altitude constraint, the Riemann conjugate gradient method is used to solve the estimated user position. Based on the estimated user location and angle of arrival, an optimization problem is established on the SO(3) manifold, and the estimated value of the user array rotation matrix is ​​obtained by using the Riemann gradient descent method.

2. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 1, characterized in that, Define the rotational position vector between satellite m and the user: in, and Let p represent the position and orientation of satellite m, respectively, and p = [p x ,p y ,p z ] T and o ut These represent the user's location and orientation, respectively. and R(o) ut Let represent the satellite array rotation matrix and the user array rotation matrix, respectively, and let the departure angle and arrival angle be expressed as . and The relationship between the departure angle, arrival angle, and position parameters is expressed as follows: Where ||·||2 represents the L2 norm.

3. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 1, characterized in that, Based on the beam domain channel model, the least squares estimate of the channel matrix between each satellite and the user is obtained, and the received signal is represented as follows: in, Let the pilot matrix on the nth subcarrier transmitted by satellite m satisfy the following condition: This represents the beam-domain channel matrix after Doppler frequency shift compensation. Represents the beam domain noise components; the least squares estimate of the beam domain channel matrix can be obtained from the received signal. in, This indicates the estimation error caused by noise.

4. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 1, characterized in that, In the estimation of channel parameters obtained using the tensor-ESPRIT algorithm, the beam domain channel matrix is ​​represented in tensor form: in, R5 = N sc , ω m,5 =2πf s τ m , and N represents the number of radio frequency chains on the satellite side and the user side, respectively. sc Indicates the number of subcarriers. and f represents the departure angle and the arrival angle, respectively. s α represents the subcarrier spacing. m τ represents the channel gain. m Indicates the propagation delay; Represents the beam domain array manifold. Let a represent the transformation matrix. r (·) denotes an array manifold. It represents the outer product.

5. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 1, characterized in that, Through the estimated value of the departure angle Obtain the direction vectors between the user and each satellite: Based on the direction vector, define a series of half-lines l T,m ={q m +ξ m f T,m |ξ m >0}, where q m and These represent the position and orientation of satellite m, respectively. Let represent the satellite array rotation matrix; due to channel estimation errors, these lines are skewed. Considering altitude constraints, estimating user locations is transformed into the following problem: Where M represents the number of satellites, p represents the user's location, and R e R represents the Earth's radius. h Indicates the user's altitude. This represents the sphere where the user is located.

6. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 5, characterized in that, The Riemann conjugate gradient method is used to solve the optimization problem, specifically including: Simplify the problem to: min p f(p) in, I represents the identity matrix; position p is iterated according to the following formula: Where, p (k) and p (k+1) Let β represent the positions obtained in the k-th and k+1-th iterations, respectively. (k) and D (k) Indicates the step size and iteration direction. The projection operator is represented as: The Euclidean gradient of the objective function at point p is: Projecting the Euclidean gradient onto the tangent space, it is represented as: The Riemann gradient is obtained and expressed as: The step size selection satisfies: Where 0 < c1 < c2 < 1, and <·,·> denote the inner product; D (k) Represented as: Where, γ (k) The conjugate coefficient is defined as: in, This represents vector transport, moving a vector from the tangent space. Projected to 7. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 1, characterized in that, Obtain an estimate of the user's location. and the estimation of the angle of arrival Then, the representation of the position vector in the local coordinate system. Recorded as: Where, q m Represent the position of satellite m; define the matrix. for M represents the number of satellites; the optimization problem regarding the user array rotation matrix R is: stR∈SO(3) in, Q = [q1, ..., q M ], Let M be a row vector of all 1s with M elements. It represents the Kronecker product.

8. The large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to claim 7, characterized in that, The rotation matrix R is estimated using the Riemann gradient algorithm, and the Euclidean gradient of the objective function is expressed as: Projecting the Euclidean gradient onto the tangent space yields the Riemann gradient, denoted as: Where Skew(X) = (XX T ) / 2; The rotation matrix R is iterated in the following way: Where, α k Ret represents the step size, determined by the backtracking search; R (X) represents the contraction operation on the SO(3) manifold, denoted as: Ret R (X)=(R+X)(I3+X T X) -1 / 2 Where I3 is the identity matrix.

9. A large-scale MIMO multi-satellite positioning and orientation estimation system based on angle information, characterized in that, Multiple low-Earth orbit satellites provide positioning and orientation estimation services to multi-antenna users, including: The single-satellite channel estimation module is used to obtain channel matrix estimates between each satellite and the user by transmitting pilot signals; and to obtain estimated channel parameters, including departure angle and arrival angle, using the tensor-ESPRIT algorithm. The user position estimation module is used to obtain the direction vector between the user and each satellite based on the estimated departure angle, establish an optimization problem on a spherical manifold, consider the altitude constraint, and use the Riemann conjugate gradient method to obtain the estimated user position value. And an orientation estimation module, which is used to establish an optimization problem on the SO(3) manifold based on the estimated user position and angle of arrival, and use the Riemann gradient descent method to obtain the estimated value of the user array rotation matrix.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the large-scale MIMO multi-satellite positioning and orientation estimation method based on angle information according to any one of claims 1-8.

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