Satellite navigation polarization anti-interference method and device

Abstract

The invention provides a satellite navigation polarization anti-interference method and device, and the method comprises the steps: obtaining a vertical polarization response vector and a horizontal polarization response vector of a first orthogonal feed point and a second orthogonal feed point, calculating an antenna array gain norm and an antenna array polarization balance difference norm, and calculating a polarization balance difference norm of the antenna array; and a multi-polarization interference suppression performance optimization function is constructed, solving is carried out based on the unitary-like Stetill manifold constraint, a simulation domain polarization weight vector is obtained, the simulation domain polarization weight vector is input into a corresponding numerical control amplitude modulator and a numerical control phase modulator for adjustment, and positioning information after interference suppression is obtained. The method has the beneficial effects that the multi-polarization interference rejection is remarkably improved, and a theoretical foundation is laid for quantitative analysis and performance improvement of multi-polarization interference rejection of the satellite navigation antenna array. A new view angle is provided for the field of satellite navigation polarization confrontation, and an effective solution is provided for improving the polarization anti-interference capability of a GNSS system.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation, and in particular to a satellite navigation polarization anti-interference method and device. Background Art

[0002] With the development of unmanned driving and low-altitude economic industries, there have been frequent reports of incidents of satellite navigation being affected by interference signals, resulting in flight delays, drone crashes, abnormal vehicle and ship trajectories, etc. The impact is becoming more and more serious and has attracted widespread attention.

[0003] Multi-polarization interference will sharply deteriorate the anti-interference performance of antenna arrays, significantly improve interference efficiency and save interference costs. At present, it is only qualitatively pointed out that the non-ideal characteristics of antenna polarization response will lead to a decrease in interference suppression performance and additional consumption of array degrees of freedom, and that simple amplitude and phase weighting cannot eliminate this effect. There is a lack of quantitative analysis of the multi-polarization interference suppression effect, and its influencing factors and evaluation system are not clear, and an effective multi-polarization interference suppression method has not been proposed. Summary of the invention

[0004] The main purpose of the present invention is to provide a satellite navigation polarization anti-interference method and device, aiming to solve the problem that multi-polarization interference will sharply deteriorate the anti-interference performance of the antenna array.

[0005] The present invention provides a satellite navigation polarization anti-interference method, which is implemented by a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner, wherein a first orthogonal feeding point and a second orthogonal feeding point of an antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator, the digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to a combiner, the combiner is connected to a radio frequency front end of the ground navigation receiver, the radio frequency front end is connected to a baseband processing unit of the ground navigation receiver, and the method is applied to the baseband processing unit, comprising: Acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; Calculating an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector; Constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; Solving the multi-polarization interference suppression performance optimization function based on a unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; The first analog domain polarization weight vector is input into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a first orthogonal feeding point, and the second analog domain polarization weight vector is input into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a second orthogonal feeding point for adjustment to obtain positioning information after anti-interference.

[0006] Further, the step of calculating the antenna array gain norm and the antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector and the second horizontal polarization response vector includes: set up in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; According to the formula and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, , represents the vertically polarized signal of the nth antenna, represents the horizontal polarization signal of the nth antenna, represents the horizontal polarization signal of the ith antenna, represents the horizontal polarization signal of the jth antenna, represents the vertical polarization signal of the jth antenna, represents the vertically polarized signal of the ith antenna.

[0007] Furthermore, the step of constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm includes: Constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

[0008] Further, the step of solving the multi-polarization interference suppression performance optimization function based on the unitary-like Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point includes: Calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it to the Riemann gradient on the Stiefel manifold ;in Representation Matrix exist The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; set up ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential, represents the upper triangular matrix in QR decomposition, Represents the transpose of the upper triangular matrix in the QR decomposition; Determine the initial value , and calculate on ; Combined step size parameter , calculate along Geodesic equation of direction, update iterative value ; judge Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; The preset convergence condition will be reached It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

[0009] Furthermore, the antenna array of the ground navigation receiver is a seven-element satellite navigation antenna array.

[0010] Furthermore, the antenna is a microstrip antenna.

[0011] The present invention also provides a satellite navigation polarization anti-interference device, comprising a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner, wherein the first orthogonal feeding point and the second orthogonal feeding point of the antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator, the digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to the combiner, the combiner is connected to the radio frequency front end of the ground navigation receiver, the radio frequency front end is connected to the baseband processing unit of the ground navigation receiver, and the baseband processing unit comprises: An acquisition module, configured to acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; A calculation module, configured to calculate an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector; A construction module, used to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; A solving module, used for solving the multi-polarization interference suppression performance optimization function based on a unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; An input module is used to input the first analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a first orthogonal feeding point, and to input the second analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a second orthogonal feeding point for adjustment to obtain positioning information after anti-interference.

[0012] Furthermore, the calculation module includes: Set up submodules for setting in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; The norm calculation submodule is used to calculate the and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, , represents the vertically polarized signal of the nth antenna, represents the horizontal polarization signal of the nth antenna, represents the horizontal polarization signal of the ith antenna, represents the horizontal polarization signal of the jth antenna, represents the vertical polarization signal of the jth antenna, represents the vertically polarized signal of the ith antenna.

[0013] Furthermore, the building block includes: A construction submodule is used to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm. ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

[0014] Furthermore, the solution module includes: A gradient calculation submodule is used to calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it onto the Riemann gradient on the Stiefel manifold. ;in Representation Matrix exist The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; Setting submodule, used to set ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential, represents the upper triangular matrix in QR decomposition, represents the transpose of the upper triangular matrix in the QR decomposition; Determine the submodule, used to determine the initial value , and calculate on ; Geodesic equation calculation submodule, used to combine step size parameters , calculate along Geodesic equation of direction, update iterative value ; Inventory submodule, used to judge Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; The vector calculation submodule is used to achieve the preset convergence conditions It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

[0015] The present invention also provides a computer device, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of any one of the above methods when executing the computer program.

[0016] The present invention also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of any of the above-mentioned methods are implemented.

[0017] The beneficial effects of the invention are: the multi-polarization interference suppression is significantly improved, which lays a theoretical foundation for the quantitative analysis and performance improvement of the multi-polarization interference suppression of satellite navigation antenna arrays. It not only provides a new perspective in the field of satellite navigation polarization countermeasures, but also provides an effective solution for improving the polarization anti-interference capability of GNSS systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 It is a schematic flow chart of a satellite navigation polarization anti-interference method according to an embodiment of the present invention; Figure 2 It is a schematic block diagram of the structure of a satellite navigation polarization anti-interference device according to an embodiment of the present invention; Figure 3 A schematic block diagram of the structure of a computer device according to an embodiment of the present application.

[0019] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0020] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, front, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly. The connection can be a direct connection or an indirect connection.

[0022] The term "and / or" in this article is only a description of the association relationship of associated objects, indicating that there may be three relationships. For example, A and B can represent three situations: A exists alone, A and B exist at the same time, and B exists alone.

[0023] In addition, in the present invention, descriptions such as "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, the technical solutions between the various embodiments can be combined with each other, but they must be based on the ability of ordinary technicians in the field to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0024] Reference Figure 1 The present invention proposes a satellite navigation polarization anti-interference method, which is implemented by a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner. The first orthogonal feeding point and the second orthogonal feeding point of the antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator. The digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to the combiner. The combiner is connected to the radio frequency front end of the ground navigation receiver. The radio frequency front end is connected to the baseband processing unit of the ground navigation receiver. The method is applied to the baseband processing unit, including: S1: Acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; S2: calculating an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector and the second horizontal polarization response vector; S3: constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; S4: Solving the multi-polarization interference suppression performance optimization function based on a unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; S5: Input the first analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a first orthogonal feeding point, and input the second analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a second orthogonal feeding point for adjustment to obtain positioning information after anti-interference.

[0025] As described in step S1 above, for any far-field fully polarized electromagnetic wave, its electric field direction is perpendicular to the propagation direction of the electromagnetic wave, so the electric field can be decomposed into two orthogonal polarization components: vertical polarization and horizontal polarization. Then the Jones electric field vector of the far-field electromagnetic wave is expressed as: in, The polarization vector of electromagnetic waves, and are the vertical polarization component and the horizontal polarization component respectively, is the envelope signal, is the vector angle between the electric field and the vertical polarization component, is the leading phase of the vertical polarization component relative to the horizontal polarization component. It should be noted that the s in the previous s(t) is bold and is different from the subsequent s(t). The former is a vector and the latter is an envelope signal.

[0026] The polarization pattern of the satellite navigation antenna can be expressed as: in, is the antenna polarization pattern, are the azimuth and elevation angles, Indicates the antenna, and They are the directional diagrams of the antenna for vertically polarized signals and horizontally polarized signals respectively.

[0027] Then the polarization response of the satellite navigation antenna receiving signal can be expressed as: Represents the polarization response of the satellite navigation antenna receiving signal.

[0028] Under strong interference conditions, considering that the satellite navigation signal power is much weaker than the interference signal and noise power, in order to simplify the analysis, the satellite navigation signal is usually not considered. Then the satellite navigation antenna array receives multiple incoherent polarization interference signals from the same direction, which can be expressed as: in, in, Indicates time, represents the number of multi-polarization interferences, Indicates the number of satellite navigation antennas, The satellite navigation antenna array receives the data vector, is the multi-polarization interference signal steering vector, express dimensional Gaussian white noise data vector, Indicates that the satellite navigation array antenna receives The polarization response of a polarization interference, Indicates The receiving data of the satellite navigation antenna, Indicates The antenna receives The polarization response of a polarization interference, is the incident signal wavelength, For the The three-dimensional coordinates of the array elements, is the plane wave unit propagation vector, in, ; ; is the transpose of the three-dimensional coordinates of the Nth array element.

[0029] definition but: Since the polarization characteristics of each element of the satellite navigation antenna array are not ideal, the ratio of the horizontal polarization response to the vertical polarization response of each satellite navigation antenna is not equal. and Nonlinear correlation. When , the multi-polarization interference will correspond to two steering vectors, and therefore will be equivalent to interference from two directions.

[0030] As described in step S2 above, the antenna array gain norm and the antenna array polarization equalization difference norm are calculated according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector and the second horizontal polarization response vector.

[0031] In one embodiment, step S2 of calculating the antenna array gain norm and the antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector includes: S201: in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; S202: According to the formula and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, , represents the vertically polarized signal of the nth antenna, represents the horizontal polarization signal of the nth antenna, represents the horizontal polarization signal of the ith antenna, represents the horizontal polarization signal of the jth antenna, represents the vertical polarization signal of the jth antenna, represents the vertically polarized signal of the ith antenna.

[0032] Specifically, in order to obtain a general law conclusion, it is assumed that the same direction transmits countless interferences with different polarizations, that is, , and set its total power fixed. Then the signal covariance matrix received by the antenna array is: The covariance matrix is ​​simplified to: In the satellite navigation anti-interference performance analysis based on the signal orthogonal subspace theory, the interference signal covariance matrix can be decomposed into interference subspace and noise subspace. And multi-polarization interference corresponds to two steering vectors, which will form two interference subspaces. Then the covariance matrix of the antenna array receiving multi-polarization interference is The eigenvalue decomposition of can be expressed as: in , , , and are the eigenvectors that constitute the interference subspace and the noise subspace respectively, and are the eigenvalues ​​corresponding to the polarization interference subspace and the noise subspace, respectively, and . Then the interference signal power can be fooled and The impact of but: Define the Antenna Array Gain Norm (AGN) as , define the Antenna Array Polarization Equilibrium Difference Norm (APEDN) as According to the signal orthogonal subspace theory, the second eigenvalue value is It determines the multi-polarization interference suppression effect. The smaller the value, the better the inhibition effect. When it tends to 0, it means that MPI degenerates into a common interference type, consuming only one array degree of freedom.

[0033] It can be seen that the multi-polarization interference suppression effect of the satellite navigation antenna array is completely determined by AGN and APEND. Taking partial derivatives of AGN and APEND respectively, we can get: Since the second eigenvalue of the multi-polarization interference covariance matrix is ​​opposite to the multi-polarization interference suppression performance, it can be seen that when AGN is constant, the satellite navigation polarization interference suppression performance decreases with the increase of APEDN, and when APEDN is constant, the satellite navigation polarization interference suppression performance improves with the increase of AGN.

[0034] As described in the above step S3, a multi-polarization interference suppression performance optimization function is constructed based on the antenna array gain norm and the antenna array polarization equalization difference norm.

[0035] In one embodiment, the step S3 of constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm includes: S301: Constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

[0036] Since GNSS signals are right-hand circularly polarized signals, GNSS antennas are also circularly polarized antennas. The most common circular polarization method for patch antennas is the orthogonal feeding method, that is, the feeding point positions are orthogonal in space, and the vertical and horizontal linear polarization waves with equal amplitudes and 90-degree phase difference are combined through phase shifting and power division networks.

[0037] However, the amplitude and phase weighting of the traditional satellite navigation anti-interference algorithm will produce the same amplitude and phase weighting for the vertical polarization response and the horizontal polarization response. The proportional change of the vertical polarization response and the horizontal polarization response cannot improve the multi-polarization interference suppression performance. Therefore, in order to avoid the problem that the polarization characteristics of the satellite navigation antenna cannot be changed after the design is completed, the digital control amplitude modulator and the digital control phase modulator are connected after the orthogonal feeding points (feeding point x and feeding point y) of the traditional satellite navigation circular polarization patch antenna, and then the combiner is combined. After the combined analog signal is sampled by the RF front end and ADC, it is weighted in the digital domain and spatial domain, thereby realizing two-level analog-to-digital adaptive anti-interference. This method can be equivalent to introducing a polarization equalization factor in the analog domain. By adjusting the polarization equalization factor, the AGN can be improved or the APEDN can be reduced, thereby improving the satellite navigation multi-polarization interference suppression performance.

[0038] but: in, , , and are the vertical polarization response and horizontal polarization response vector of the patch antenna feed x and feed y respectively. Then the multi-polarization interference suppression performance optimization function expression after amplitude and phase weighting of the analog domain polarization equalization factor is: in, In order to avoid the polarization equalization factor optimization trending to 0 and ensure the normal reception of satellite navigation signals, a constant energy constraint is constructed. Then, the optimization target of the multi-polarization interference suppression performance from a certain part of space is: As described in step S4 above, the multi-polarization interference suppression performance optimization function is solved based on the unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

[0039] In one embodiment, the step S4 of solving the multi-polarization interference suppression performance optimization function based on the unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point includes: S401: Calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it to the Riemann gradient on the Stiefel manifold ;in Represents the matrix in The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; S402: Settings ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential, represents the upper triangular matrix in QR decomposition, represents the transpose of the upper triangular matrix in the QR decomposition; S403: Determine initial value , and calculate on ; S404: Combined step size parameters , calculate along Geodesic equation of direction, update iterative value ; S405: Judgment Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; S406: The preset convergence condition will be reached It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

[0040] because Contains amplitude and phase information, both are complex vectors, then is a complex function. To optimize a complex function, it is necessary to use the Cauchy-Riemann CR condition to determine whether the function is a holomorphic function and whether the derivative is analytic.

[0041] by For example, suppose =0, , , ,but: The necessary condition for a complex function to be differentiable, namely the CR condition, is: but: Apparently If the CR condition is not met, The CR condition is also not met. is a non-holomorphic function, which essentially has no actual derivative, and its derivative values ​​approaching a certain point from all directions are not consistent. Therefore, Non-holomorphic complex variable functions. For non-holomorphic complex variable functions, formal derivatives, namely Wirtinger derivatives, are usually used to represent the function gradient, which mainly includes holomorphic derivatives and formal anti-holomorphic derivatives. For example, the holomorphic derivative and the formal anti-holomorphic derivative are: because: Then according to the chain rule: It can be seen that the Wirtinger derivative is a combination of the derivatives of the real and imaginary parts of the function, so Consider it as a derivative of a complex function form.

[0042] Same reason The Wirtinger derivative of can be expressed as: Stiefel manifold: A Stiefel manifold is a The Riemann manifold is composed of a collection of semi-orthogonal matrices.

[0043] in, for dimensional identity matrix.

[0044] Stiefel manifold gradient: When the first-order continuously differentiable function on the Stiefel manifold is When , the gradient in Euclidean space Gradient of the tangent space projected onto the Stiefel manifold The relationship is: Stiefel manifold geodesic: The geodesic represents the shortest curve between two points on a Riemann manifold, so the gradient of the Riemann manifold should be iterated along the geodesic direction of the Riemann manifold. The geodesic of the direction is: in, represents the matrix exponential, Represents QR decomposition.

[0045] The constant energy constraint is very similar to that of the Stiefel manifold, except that: . Then the constant energy constraint can be approximately equivalent to a unitary Stiefel manifold constraint, which can be expressed as: It is essentially still an embedded submanifold of Euclidean space. The tangent space is is defined as: in .

[0046] because is an antisymmetric matrix, and ,but Then given the optimization function In Euclidean space The derivative of the point can be used to calculate the Riemann gradient of the unitary Stiefel manifold : in, Represents the matrix in Projection.

[0047] Unitifel-like manifolds Along The geodesic equation of direction can be generalized to: in, Indicates Iteration , Indicates Iteration .

[0048] Therefore, the gradient descent algorithm under the unitary Stiefel manifold constraint can be expressed as follows: 1. Determine the initial value , and calculate on ; 2. Combined step size parameters , calculate along Geodesic equation of direction, update iterative value ; 3. Judgment Whether the convergence condition is met, if not, then Iterate as a new starting point until convergence.

[0049] As described in step S5 above, the first analog domain polarization weight vector is input into the digital controlled amplitude modulator and the digital controlled phase modulator connected to the first orthogonal feeding point, and the second analog domain polarization weight vector is input into the digital controlled amplitude modulator and the digital controlled phase modulator connected to the second orthogonal feeding point for adjustment to obtain the positioning information after anti-interference. That is, after obtaining the corresponding first analog domain polarization weight vector and the second analog domain polarization weight vector, they are input into the corresponding digital controlled amplitude modulator and the digital controlled phase modulator, and accurate positioning information of the UAV can be achieved. Thereby, the multi-polarization interference suppression is significantly improved, and the theoretical foundation is laid for the quantitative analysis and performance improvement of the multi-polarization interference suppression of the satellite navigation antenna array. It not only provides a new perspective for the field of satellite navigation polarization countermeasures, but also provides an effective solution for improving the polarization anti-interference capability of the GNSS system.

[0050] In one embodiment, the antenna array of the ground navigation receiver is a seven-element satellite navigation antenna array. The seven-element satellite navigation antenna array is a key component used in a satellite navigation system to enhance signal reception and anti-interference capabilities. The seven-element antenna array can significantly improve positioning accuracy by optimizing signal reception and processing processes.

[0051] In one embodiment, the antenna is a microstrip antenna. Since microstrip antennas have the advantages of thin profile, small size, and easy commonality, and the satellite navigation signal is a right-hand circularly polarized signal, the satellite navigation array antennas are all designed as right-hand circularly polarized microstrip antennas. Conventional satellite navigation anti-interference research usually assumes that the satellite navigation antenna is an ideal point source, does not consider the antenna pattern characteristics, and also ignores the polarization characteristics of the antenna. However, due to the structural characteristics of the microstrip antenna, as well as the limitations of device precision and processing level, the antenna pattern is not isotropic, and the antenna polarization does not present the ideal right-hand circularly polarized characteristics, but has cross-polarization characteristics. In other words, the actual satellite navigation array antenna can not only receive right-hand circularly polarized signals, but also receive other polarization signals.

[0052] Reference Figure 2 The present invention also provides a satellite navigation polarization anti-interference device, comprising a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner, wherein the first orthogonal feeding point and the second orthogonal feeding point of the antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator, the digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to the combiner, the combiner is connected to the radio frequency front end of the ground navigation receiver, the radio frequency front end is connected to the baseband processing unit of the ground navigation receiver, and the baseband processing unit comprises: An acquisition module 10 is used to acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; A calculation module 20, configured to calculate an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector; A construction module 30, configured to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; A solving module 40, configured to solve the multi-polarization interference suppression performance optimization function based on a unitary-like Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; The input module 50 is used to input the first analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to the first orthogonal feeding point, and to input the second analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to the second orthogonal feeding point for adjustment to obtain the positioning information after anti-interference.

[0053] In one embodiment, the calculation module 20 includes: Set up submodules for setting in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; The norm calculation submodule is used to calculate the and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, .

[0054] In one embodiment, the building module 30 includes: A construction submodule is used to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm. ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

[0055] In one embodiment, the solution module 40 includes: A gradient calculation submodule is used to calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it onto the Riemann gradient on the Stiefel manifold. ;in Representation Matrix exist The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; Setting submodule, used to set ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential; Determine the submodule, used to determine the initial value , and calculate on ; Geodesic equation calculation submodule, used to combine step size parameters , calculate along Geodesic equation of direction, update iterative value ; Inventory submodule, used to judge Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; The vector calculation submodule is used to achieve the preset convergence conditions It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

[0056] In one embodiment, the antenna array of the ground navigation receiver is a seven-element satellite navigation antenna array.

[0057] In one embodiment, the antenna is a microstrip antenna.

[0058] In a specific embodiment, CST Studio Suite 2023 is used to simulate the Beidou B3I frequency (1268MHz) 7-element satellite navigation antenna array. The vertical polarization response and horizontal polarization response of each satellite navigation antenna at different azimuth and elevation angles are obtained. According to the multi-polarization interference suppression analysis model based on the signal orthogonal subspace and the AGN and APEND index calculation method, the first eigenvalue and second eigenvalue of the AGN and APEND and signal covariance matrix at each elevation and azimuth angle are calculated and solved. The satellite navigation antenna array is affected by the mutual coupling of the array elements and the position of the array elements. The specific manifestations of AGN and APEND are relatively complex and difficult to express with specific expressions. However, it can still be seen that both AGN and APEND decrease with the increase of the elevation angle. When the elevation angle is constant, APEND fluctuates with the change of the azimuth angle, while the fluctuation of AGN is not obvious.

[0059] When AGN is constant, the satellite navigation polarization interference suppression performance increases with the increase of APEDN, and when APEDN is constant, the satellite navigation polarization interference suppression performance decreases with the increase of APEDN. This is because the relationship between interference suppression performance and pitch angle cannot be directly determined by AGN or APEND.

[0060] The magnitude of the first and second eigenvalues ​​of the signal covariance matrix also depends mainly on the pitch angle, and decreases with the increase of the pitch angle. Under the condition of a certain elevation angle, the magnitude of the second eigenvalue fluctuates with the change of the azimuth angle, and the fluctuation is very obvious at high elevation angles, while the first eigenvalue fluctuates less.

[0061] Since the multi-polarization interference suppression performance of the satellite navigation antenna array is completely dependent on the second eigenvalue, the multi-polarization interference suppression performance eventually improves with the increase of the pitch angle, and the maximum difference in suppression performance is greater than 15dB. The suppression performance fluctuates periodically with the change of the azimuth angle, and the fluctuation range increases with the increase of the pitch angle. In addition, APEND is basically consistent with the change of the second eigenvalue, so the satellite navigation polarization interference suppression performance depends more on APEDN.

[0062] The DOA range of multi-polarization interference is set to [x°, y°], where x is the elevation angle range and y is the azimuth angle range. The analog domain polarization equalization factor corresponding to different multi-polarization interference DOA ranges is solved using the multi-polarization interference suppression performance optimization algorithm based on QUSM-ADAM. The interference suppression effect is compared with that of traditional satellite navigation interference suppression, and the heat map distribution and statistical characteristics of the multi-polarization interference suppression performance improvement effect are obtained.

[0063] The effect of improving the multi-polarization interference suppression performance increases with the decrease of the multi-polarization interference DOA range, and is basically consistent with the second eigenvalue distribution. The suppression effect of multi-polarization interference at low elevation angles is higher than that at high elevation angles.

[0064] Table 1 It can be seen from Table 1 that when the multi-polarization interference is less than the DOA range of [2°, 2°], the multi-polarization interference suppression performance is improved by up to 33.87 dB. When the multi-polarization interference is less than the DOA range of [10°, 10°], the multi-polarization interference suppression performance improvement effect is also greater than 20 dB overall, and the PDF of the polarization interference suppression performance improvement effect is relatively concentrated, and the std is stable between 4.62-7.77 dB. The mean and median are basically consistent, and the difference between the upper quartile and the lower quartile is also basically consistent, and does not fluctuate dramatically with the change of the multi-polarization interference DOA range. Therefore, it shows that the optimization algorithm not only has superior performance, but also has relatively stable performance and good robustness.

[0065] The convergence speed of P-GD (Projection gradient descent), P-Momentum (ProjectionMomentum), P-RMSprop (Projection Root Mean Square Propagation), P-ADAM (ProjectionADAM), QUSM-GD, and QUSM-ADAM algorithms in multi-polarization interference suppression performance optimization functions in different DOA ranges are compared. Among them, since the polarization factors directly iterated by GD, Momentum, RMSprop, and ADAM do not meet the constraints, the polarization factors are projected and scaled to meet the constant energy constraints, thereby obtaining the P-GD, P-Momentum, P-RMSprop, and P-ADAM algorithms.

[0066] The proposed algorithm has the best interference suppression effect and the fastest convergence speed. It only needs ten iterations to basically complete the convergence. The P-RMSprop, P-ADAM and QUSM-GD algorithms require an average of 30-40 iterations to converge stably. The P-GD and P-Momentum algorithms cannot converge within 50 iterations.

[0067] With the development of the field of electromagnetic wave polarization, multi-polarization interference suppression has become a new hot spot in the field of satellite navigation countermeasures. However, there is currently a lack of in-depth analysis and solutions for multi-polarization interference suppression. Therefore, this paper first constructs a multi-polarization interference reception model based on polarization decomposition and a multi-polarization interference suppression analysis model based on signal orthogonal subspace. The antenna array gain norm (AGN) and antenna array polarization equalization difference norm (APEDN) are introduced as performance evaluation indicators. Then, a multi-polarization interference suppression performance optimization function based on polarization equalization factor is constructed, and a multi-polarization interference suppression performance optimization algorithm based on QUSM-ADAM is proposed. Experimental results show that the algorithm proposed in this paper converges quickly and significantly improves the multi-polarization interference suppression performance. When the angle of arrival (DOA) range of multi-polarization interference is less than [10°, 10°], the average suppression effect is improved by more than 20dB. This study lays a theoretical foundation for the quantitative analysis and performance improvement of multi-polarization interference suppression of satellite navigation antenna arrays. It not only provides a new perspective in the field of satellite navigation polarization countermeasures, but also provides an effective solution for improving the polarization anti-interference capability of GNSS systems.

[0068] Reference Figure 3 In the embodiment of the present application, a computer device is also provided. The computer device may be a server, and its internal structure may be as follows: Figure 3As shown. The computer device includes a processor, a memory, a network interface and a database connected through a system bus. Among them, the processor designed by the computer is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The database of the computer device is used to store various polarization response vectors, etc. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, the satellite navigation polarization anti-interference method described in any of the above embodiments can be implemented.

[0069] Those skilled in the art will understand that Figure 3 The structure shown in is merely a block diagram of a portion of the structure related to the present application solution and does not constitute a limitation on the computer device to which the present application solution is applied.

[0070] An embodiment of the present application also provides a computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the satellite navigation polarization anti-interference method described in any of the above embodiments can be implemented.

[0071] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media provided in this application and used in the embodiments may include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0072] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, device, article or method including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, device, article or method. In the absence of further restrictions, an element defined by the sentence "includes a ..." does not exclude the existence of other identical elements in the process, device, article or method including the element.

[0073] The embodiments of the present application can acquire and process relevant data based on artificial intelligence technology. Artificial Intelligence (AI) is the theory, method, technology and application system that uses digital computers or machines controlled by digital computers to simulate, extend and expand human intelligence, perceive the environment, acquire knowledge and use knowledge to obtain the best results.

[0074] AI basic technologies generally include sensors, dedicated AI chips, cloud computing, distributed storage, big data processing technology, operation / interaction systems, mechatronics, etc. AI software technologies mainly include computer vision technology, robotics technology, biometrics technology, speech processing technology, natural language processing technology, and machine learning / deep learning.

[0075] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of the claims of the present invention.

Claims

1. A satellite navigation polarization anti-interference method, characterized in that: The method is implemented by a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner, wherein the first orthogonal feeding point and the second orthogonal feeding point of the antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator, the digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to the combiner, the combiner is connected to the radio frequency front end of the ground navigation receiver, the radio frequency front end is connected to the baseband processing unit of the ground navigation receiver, and the method is applied to the baseband processing unit, including: Acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; Calculating an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector; Constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; Solving the multi-polarization interference suppression performance optimization function based on a unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; The first analog domain polarization weight vector is input into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a first orthogonal feeding point, and the second analog domain polarization weight vector is input into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a second orthogonal feeding point for adjustment to obtain positioning information after anti-interference.

2. The satellite navigation polarization anti-interference method according to claim 1, characterized in that: The step of calculating the antenna array gain norm and the antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector and the second horizontal polarization response vector comprises: set up in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; According to the formula and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, , represents the vertically polarized signal of the nth antenna, represents the horizontal polarization signal of the nth antenna, represents the horizontal polarization signal of the ith antenna, represents the horizontal polarization signal of the jth antenna, represents the vertical polarization signal of the jth antenna, represents the vertically polarized signal of the i-th antenna.

3. The satellite navigation polarization anti-interference method according to claim 2, characterized in that: The step of constructing a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm comprises: A multi-polarization interference suppression performance optimization function is constructed based on the antenna array gain norm and the antenna array polarization equalization difference norm. ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

4. The satellite navigation polarization anti-interference method according to claim 3, characterized in that: The step of solving the multi-polarization interference suppression performance optimization function based on the unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point includes: Calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it to the Riemann gradient on the Stiefel manifold ;in Representation Matrix exist The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; set up ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential, represents the upper triangular matrix in QR decomposition, Represents the transpose of the upper triangular matrix in the QR decomposition; Determine the initial value , and calculate on ; Combined step size parameter , calculate along Direction geodesic equation, update iterative value ; judge Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; The preset convergence condition will be reached It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

5. The satellite navigation polarization anti-interference method according to claim 1, characterized in that: The antenna array of the ground navigation receiver is a seven-element satellite navigation antenna array.

6. The satellite navigation polarization anti-interference method according to claim 1, characterized in that: The antenna is a microstrip antenna.

7. A satellite navigation polarization anti-interference device, characterized in that: The invention comprises a ground navigation receiver, a digitally controlled amplitude modulator, a digitally controlled phase modulator and a combiner, wherein the first orthogonal feeding point and the second orthogonal feeding point of the antenna of the ground navigation receiver are respectively connected to the digitally controlled amplitude modulator and the digitally controlled phase modulator, the digitally controlled amplitude modulator and the digitally controlled phase modulator are connected to the combiner, the combiner is connected to the radio frequency front end of the ground navigation receiver, the radio frequency front end is connected to the baseband processing unit of the ground navigation receiver, and the baseband processing unit comprises: An acquisition module, configured to acquire a first vertical polarization response vector and a first horizontal polarization response vector of the first orthogonal feeding point, and a second vertical polarization response vector and a second horizontal polarization response vector of the second orthogonal feeding point; A calculation module, configured to calculate an antenna array gain norm and an antenna array polarization equalization difference norm according to the first vertical polarization response vector, the first horizontal polarization response vector, the second vertical polarization response vector, and the second horizontal polarization response vector; A construction module, used to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm; A solving module, used for solving the multi-polarization interference suppression performance optimization function based on a unitary Stiefel manifold constraint to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point; An input module is used to input the first analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a first orthogonal feeding point, and to input the second analog domain polarization weight vector into a digitally controlled amplitude modulator and a digitally controlled phase modulator connected to a second orthogonal feeding point for adjustment to obtain positioning information after anti-interference.

8. The satellite navigation polarization anti-interference device according to claim 7, characterized in that: The computing module comprises: Set up submodules for setting in, , are respectively the first vertical polarization response vector and the first horizontal polarization response vector of the first orthogonal feeding point, and are respectively a second vertical polarization response vector and a second horizontal polarization response vector of a second orthogonal feeding point, and N represents the number of antennas; The norm calculation submodule is used to calculate the and formula Calculate the antenna array gain norm and the antenna array polarization balance difference norm; where n represents the nth antenna, represents the antenna array gain norm, represents the antenna array polarization balance difference norm, , represents the azimuth, represents the pitch angle, H represents the conjugate transpose, , represents the vertically polarized signal of the nth antenna, represents the horizontal polarization signal of the nth antenna, represents the horizontal polarization signal of the ith antenna, represents the horizontal polarization signal of the jth antenna, represents the vertical polarization signal of the jth antenna, represents the vertically polarized signal of the i-th antenna.

9. The satellite navigation polarization anti-interference device according to claim 8, characterized in that: The building blocks include: A construction submodule is used to construct a multi-polarization interference suppression performance optimization function based on the antenna array gain norm and the antenna array polarization equalization difference norm. ;in, is the polarization weight vector of the first simulation domain, Contains both amplitude and phase information. is the polarization weight vector of the second simulation domain.

10. The satellite navigation polarization anti-interference device according to claim 9, characterized in that: The solution module comprises: A gradient calculation submodule is used to calculate the gradient of the multi-polarization interference suppression performance optimization function in the Euclidean space and project it onto the Riemann gradient on the Stiefel manifold. ;in Representation Matrix exist The projection of represents the Riemann gradient, In Euclidean space The derivative of a point, ; Setting submodule, used to set ,in , , Indicates Iteration , Indicates Iteration ; represents QR decomposition, represents the matrix exponential, represents the upper triangular matrix in QR decomposition, Represents the transpose of the upper triangular matrix in the QR decomposition; Determine the submodule, used to determine the initial value , and calculate on ; Geodesic equation calculation submodule, used to combine step size parameters , calculate along Geodesic equation of direction, update iterative value ; Inventory submodule, used to judge Whether the convergence condition is met, if not, then Iterate as a new starting point until the preset convergence condition is reached; The vector calculation submodule is used to achieve the preset convergence conditions It is proposed to obtain a first analog domain polarization weight vector of the first orthogonal feeding point and a second analog domain polarization weight vector of the second orthogonal feeding point.

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