Direction and polarization joint estimation method based on time modulation array

Abstract

The invention belongs to the technical field of time modulation arrays, and relates to a direction and polarization joint estimation method based on a time modulation array, which comprises the following steps: establishing an alternating polarization time modulation array, obtaining a receiving signal of each array element, a time modulation function and a polarization vector of each array element, and further obtaining an actual receiving signal of each array element, establishing a linear relation among a harmonic component, a polarization parameter and an incident direction of a received signal of each sub-array; according to the linear relation, the relation between direction disturbance and direction function disturbance is obtained, a vector formed by subarray harmonic components is rewritten into a form containing a noise item, error disturbance between a truth value of a direction function and a corresponding estimator is obtained, and then a direction estimation value is obtained; according to the linear relation, the relation between the polarization matching coefficient of the array manifold vector estimation value and antenna polarization and radiation source polarization is obtained, and then the polarization estimation value is obtained. According to the invention, joint estimation of direction and polarization can be realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of time modulation array, in particular to a direction and polarization joint estimation method based on time modulation array. BACKGROUND

[0002] TMA (Time modulated array) is a new type of antenna array based on time modulation technology. By configuring multiple high-speed radio frequency switches at the back end of the array element and controlling the periodic on-off state, the array element has independent "intermittent sampling" time control capability, so as to regulate and control the radiation or receiving characteristics of the array antenna. Single-channel TMA also has the advantage of low cost, which only needs single-channel digital sampling. When using single-channel TMA to receive signals, in addition to the original signal, the periodic time modulation of the array element will produce several harmonic components, and the linear relationship between the fundamental frequency and the harmonic spectrum can be used to estimate the direction of the incident signal. Compared with the traditional multi-channel direction finding method, the single-channel TMA direction finding has the characteristics of simple structure, low cost and good phase consistency, and has been concerned in recent years.

[0003] In the prior art, the single-channel TMA direction finding method includes: using TMA with different lengths of baselines, long baseline provides larger array aperture to improve accuracy, and short baseline eliminates ambiguity solution, realizing high-precision and ambiguity-free direction finding. A wideband direction finding method is proposed for long-short baseline three-element single-channel TMA, which can solve the estimation ambiguity problem caused by the change of carrier frequency, and the strict mathematical relationship between direction finding bandwidth and baseline is discussed. The optimal linear unbiased estimator is used to effectively process the high-order harmonic component information of low signal-to-noise ratio, and the direction finding performance is improved.

[0004] However, when the antenna polarization is orthogonal or mismatched with the polarization of the incident signal, the estimation accuracy of the above-mentioned single-channel TMA direction finding method is significantly reduced, and the polarization parameters of the incident signal cannot be estimated. SUMMARY

[0005] Therefore, it is necessary to provide a direction and polarization joint estimation method based on time modulation array, which considers the polarization factors between the antenna and the incident signal, and can realize joint estimation of direction and polarization.

[0006] A direction and polarization joint estimation method based on time modulation array, comprising: acquiring a time modulation array, and setting two groups of alternately arranged polarization antennas, taking each polarization antenna as an array element, and taking each group of polarization antennas as a subarray to establish an alternating polarization time modulation array; Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained, thereby obtaining the actual received signal of each array element. Based on the actual received signal of each array element, a linear relationship is established between the harmonic components, polarization parameters, and incident direction of each sub-array received signal. Based on the linear relationship between the harmonic components of the received signal of each subarray, the polarization parameters, and the incident direction, the relationship between the directional disturbance and the directional function disturbance is obtained. The vector composed of the subarray harmonic components is rewritten into a form including a noise term to obtain the error disturbance between the true value of the directional function and the corresponding estimate. Based on the error disturbance between the true value of the directional function and the corresponding estimate, the estimated value of the direction is obtained. According to the linear relationship between the harmonic components of the received signal of each subarray, the polarization parameters and the incident direction, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and the radiation source polarization is obtained, and then the polarization estimate is obtained.

[0007] In one embodiment, obtaining a received signal of each array element, a time modulation function, and a polarization vector of each array element according to an alternating polarization time modulation array, and further obtaining an actual received signal of each array element, includes: According to the alternating polarization time modulation array, the received signal, time modulation function and polarization vector of each array element are obtained; Obtaining an initial representation of the actual received signal of each array element according to the received signal of each array element, the time modulation function, and the polarization vector of each array element; According to the initial representation of the actual received signal of each array element, the time domain expressions of the actual received signals of the two sub-arrays are obtained; The time modulation function is expanded into a series form and combined with the time domain expressions of the actual received signals of the two sub-arrays, the first k subharmonics; According to the first k The series form of the subharmonics and time modulation function is used to obtain the series decomposition form of the actual received signal of each subarray.

[0008] In one embodiment, obtaining a received signal of each array element, a time modulation function, and a polarization vector of each array element according to an alternating polarization time modulation array includes: ; ; ; Where, is the complex amplitude of the signal, is the incident signal polarization, are the amplitude and phase of the incident signal, is a unit imaginary number, is the incident signal frequency, is time, is the phase of the th element, is the th element, is the phase center distance between adjacent elements, is the signal incident angle, is the wavelength, is the relative amplitude representing the polarization state of the signal, is the relative phase representing the polarization state of the signal, is the transpose of is the time modulation function, is a positive integer, is the time modulation period, is the number of elements, is a set of integers; is the Jones vector of the polarization of the th element; According to the received signal of each element, the time modulation function, and the polarization vector of each element, an initial representation of the actual received signal of each element is obtained, including: ; In the formula, is the initial representation of the actual received signal of the th element, is the conjugate of ; According to the initial representation of the actual received signal of each element, a time domain expression of the actual received signals of the two subarrays is obtained, including: ; In the formula, is the received signal of the X-polarized subarray, is the received signal of the Y-polarized subarray, is the signal received by the n th element, is the signal received by the n th element; The time modulation function is expanded into a series form, and combined with the time domain expression of the actual received signals of the two subarrays, the second harmonic received by the two subarrays is obtained, including: k ; ; In the formula, is the second harmonic of the signal received by the th element, is the second harmonic of the signal received by thek the second harmonic component, the first harmonic received by the X-polarized subarray k the second harmonic, the first harmonic received by the Y-polarized subarray k the second harmonic, the conjugate of the polarization vector for X-polarization, the conjugate of the polarization vector for Y-polarization, the phase when the n is taken as 2 n -1, the phase when the n is taken as 2 n , the first harmonic received by the two subarrays and the series form of the time modulation function, the series decomposition form of the actual received signal of each subarray is obtained, including: k ; wherein, is the received signal of the X-polarized subarray, is the received signal of the Y-polarized subarray.

[0009] In an embodiment, a linear relationship between the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray is established according to the actual received signal of each array element, including: ; wherein, is the harmonic eigenmatrix of the X-polarized subarray, is the harmonic eigenmatrix of the Y-polarized subarray, is the array manifold vector of the X-polarized subarray, is the array manifold vector of the Y-polarized subarray, is the vector composed of the harmonic components of the X-polarized subarray, is the vector composed of the harmonic components of the Y-polarized subarray.

[0010] In an embodiment, according to the linear relationship between the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the direction disturbance and the direction function disturbance is obtained, and the vector composed of the harmonic components of the subarray is rewritten into a form containing a noise term, and the error disturbance between the true value of the direction function and the corresponding estimated quantity is obtained, including: According to the linear relationship between the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the direction disturbance and the direction function disturbance is obtained: ; ;​ ; wherein, is the corresponding estimate of the true value of the directional function of the X polar subarray, is the corresponding estimate of the true value of the directional function of the Y polar subarray, is the estimate of the directional function, is the estimate of , is the estimate of , is the estimate of , is the estimate of , is the estimate of , is the estimate of , is the estimate of , is the estimate of , is the weighting coefficient, is the weighting value, is the estimate of and ; Rewrite the vector of the subarray harmonic components into the form containing noise terms, to obtain the vector of the subarray harmonic components containing noise terms: ; wherein, is the generalized inverse matrix of the harmonic characteristic matrix of the X polar subarray, is the generalized inverse matrix of the harmonic characteristic matrix of the Y polar subarray, is the estimate of , is the estimate of , is the noise vector when extracting the harmonic estimate , is the noise vector when extracting the harmonic estimate ; According to the relationship between the directional disturbance and the directional function disturbance and the vector of the subarray harmonic components containing noise terms, obtain the error disturbance between the true value and the corresponding estimate of the directional function: ; wherein, is the error disturbance between and , is the error disturbance between and , is the true value of the X-polarization subarray direction function, is the true value of the Y-polarization subarray direction function.

[0011] In one embodiment, obtaining an estimated value of the direction based on the error disturbance between the true value of the direction function and the corresponding estimated value includes: According to the error disturbance between the true value of the direction function and the corresponding estimated value, a second-order approximation is performed to obtain an approximate expression of the error disturbance; According to the error disturbance approximate expression, the variance of the disturbance is obtained; According to the variance of the disturbance, the least square method is used to obtain the error covariance matrix; According to the error covariance matrix, the variance of the disturbance in the estimate is obtained; According to the variance of the disturbance in the estimated value, the optimal weight that minimizes the variance of the direction finding disturbance is obtained; According to the optimal weight that minimizes the direction finding disturbance variance and the relationship between the direction disturbance and the direction function disturbance, the estimated value of the direction is obtained.

[0012] In one embodiment, a second-order approximation is performed based on the error disturbance between the true value of the direction function and the corresponding estimated value to obtain an approximate expression for the error disturbance, including: ; Where, for The first row of is the generalized inverse matrix of the harmonic characteristic matrix of the X-polarized subarray, is the extracted harmonic estimate The noise vector at time , For the time in n Take the phase of 3 o'clock, For the time in n When N / 2 is taken , For the time in n Pick The phase of time; According to the error disturbance approximate expression, the variance of the disturbance is obtained, including: ; ; Where, is the error disturbance The variance of is the error disturbance The variance of is the noise power, is the Euclidean norm, When When n When According to the variance of the disturbance, the error covariance matrix is obtained by using the least square method, comprising: Wherein, In the formula, The error covariance matrix is Diagonal matrix; According to the error covariance matrix, the variance of the disturbance in the estimated value is obtained, comprising: Wherein, In the formula, The variance is The direction function; According to the variance of the disturbance in the estimated value, the optimal weight for minimizing the variance of the direction disturbance is obtained, comprising: Wherein, In the formula, The optimal weight for minimizing the variance of the direction disturbance is According to the optimal weight for minimizing the variance of the direction disturbance and the relationship between the direction disturbance and the direction function disturbance, the estimated value of the direction is obtained, comprising: Wherein, In the formula, The estimated value of the direction is

[0013] In one embodiment, according to the linear relationship between the received signal harmonic component of each subarray, the polarization parameter and the incident direction, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and the polarization of the radiation source is obtained, and then the estimated value of the polarization is obtained, comprising: According to the linear relationship between the received signal harmonic component of each subarray, the polarization parameter and the incident direction, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and the polarization of the radiation source is obtained: Wherein, In the formula, When When n When The phase of 1 is taken; The estimated value of the polarization is obtained: Wherein, The conjugate transpose of The conjugate transpose of The conjugate transpose of The conjugate transpose of

[0014] ​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​In one embodiment, the estimate of the direction is minimized when the polarizations of the two sub-arrays are orthogonal.

[0015] In one embodiment, the estimate of the polarization is minimized when the polarizations of the two sub-arrays are orthogonal.

[0016] The above-mentioned joint estimation method of direction and polarization based on time modulated array is based on a single-channel alternating polarization time modulated array (AP-TMA) for joint estimation of direction (angle) and polarization. The polarization factors in signal propagation and array configuration are considered. When there is polarization mismatch between the incident signal and the receiving array, the direction estimation accuracy can be ensured, and the incident direction and polarization parameters of any polarized radiation source can be obtained. In addition, by extracting the multiple harmonic signals and using polarization projection weighting processing, the estimation accuracy of direction and polarization is improved, and the robust direction finding and polarization estimation performance is realized. BRIEF DESCRIPTION OF DRAWINGS

[0017] Figure 1 It is a flowchart of the joint estimation method of direction and polarization based on time modulated array in one embodiment; Figure 2 It is a system configuration diagram of joint estimation of polarization parameters and incident direction in one embodiment; Figure 3 It is a root mean square error diagram of parameter estimation (incident angle ) under different signal-to-noise ratios and array element numbers in one embodiment; Figure 4 It is a root mean square error diagram of polarization estimation (polarization amplitude ratio and polarization phase difference ) under different signal-to-noise ratios and array element numbers in one embodiment; Figure 5 It is a root mean square error diagram of parameter estimation (incident angle ) of different single-polarization arrays in the full polarization domain in one embodiment, wherein (a) is mode H and (b) is mode V; Figure 6 It is a root mean square error diagram of parameter estimation (incident angle ) of different single-polarization arrays in the full polarization domain in one embodiment, wherein (a) is mode L and (b) is mode R; Figure 7 It is a root mean square error diagram of parameter estimation (incident angle ) of AP-TMA in the full polarization domain in one embodiment, wherein (a) is mode 1 and (b) is mode 2; Figure 8Root mean square error (RMSE) plots of AP-TMA parameter estimation (incidence angle ) in the full polarimetric domain for one embodiment, where (a) is mode HV and (b) is mode LR; Figure 9 Root mean square error (RMSE) plots of AP-TMA polarization estimation (polarization amplitude ratio ) in the full polarimetric domain for one embodiment, where (a) is mode 1 and (b) is mode 2; Figure 10 Root mean square error (RMSE) plots of AP-TMA polarization estimation (polarization amplitude ratio ) in the full polarimetric domain for one embodiment, where (a) is mode HV and (b) is mode LR; Figure 11 Root mean square error (RMSE) plots of AP-TMA polarization estimation (polarization phase difference ) in the full polarimetric domain for one embodiment, where (a) is mode 1 and (b) is mode 2; Figure 12 Root mean square error (RMSE) plots of AP-TMA polarization estimation (polarization phase difference ) in the full polarimetric domain for one embodiment, where (a) is mode HV and (b) is mode LR. DETAILED DESCRIPTION

[0018] In order to make the objects, technical solutions and advantages of the present application clearer, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and should not be used to limit the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of the present application.

[0019] In addition, the descriptions such as "first", "second" and the like in the present application are only for the purpose of description and should not be understood as indicating or implying the relative importance of the technical features or implicitly indicating the number of the technical features indicated. Therefore, the features limited by "first" and "second" can explicitly or implicitly include at least one of the features. In the description of the present application, the meaning of "multiple groups" is at least two groups, for example, two groups, three groups, etc., unless otherwise specifically limited.

[0020] In the present application, unless otherwise explicitly specified and limited, the terms "connection", "fixation" and the like shall be understood in a broad sense, for example, "fixation" can be fixed connection, or detachable connection, or integral; can be mechanical connection, or electrical connection, or physical connection, or wireless communication connection; can be directly connected, or indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship of two elements, unless otherwise explicitly limited. For those of ordinary skill in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0021] In addition, the technical solutions of various embodiments of the present application can be combined with each other, but it must be based on the fact that a person of ordinary skill in the art can realize it, when the combination of technical solutions appears contradictory or unachievable, it should be considered that the combination of technical solutions does not exist, nor is it within the scope of protection required by the present application.

[0022] The present application provides a direction and polarization joint estimation method based on time modulation array, as shown in the flowchart Figure 1 , in one embodiment, comprising: Step 101, obtaining a time modulation array, and setting two groups of alternately arranged polarized antennas, taking each polarized antenna as an array element, and taking each group of polarized antennas as a subarray, to establish an alternating polarization time modulation array.

[0023] In this step, as shown in the configuration diagram Figure 2 , a polarization parameter and incident direction joint estimation system is designed, and the alternating polarization time modulation array (AP-TMA) is composed of two groups of alternately arranged different polarized antennas; each group of co-polarized antennas is regarded as a subarray, and the polarization modes of the two subarrays need not be orthogonal but need to be different; when the polarization modes of the subarrays are orthogonal, the configuration can obtain optimal estimation performance; the subarrays of the array use two kinds of antennas with different polarizations, which are denoted as X-polarized subarray and Y-polarized subarray, and the corresponding polarization vectors are denoted as and , to introduce polarization dimension in TMA.

[0024] Step 102, according to the alternating polarization time modulation array, obtaining the received signal of each array element, the time modulation function and the polarization vector of each array element, and further obtaining the actual received signal of each array element; according to the actual received signal of each array element, establishing a linear relationship between the harmonic component of each subarray received signal, the polarization parameter and the incident direction.

[0025] Specifically: According to the alternating polarization time modulation array, the received signal of each array element, the time modulation function and the polarization vector of each array element are obtained; Obtaining an initial representation of the actual received signal of each array element according to the received signal of each array element, the time modulation function, and the polarization vector of each array element; According to the initial representation of the actual received signal of each array element, the time domain expressions of the actual received signals of the two sub-arrays are obtained; The time modulation function is expanded into a series form and combined with the time domain expressions of the actual received signals of the two sub-arrays, the first k subharmonics; According to the first k The series form of subharmonics and time modulation function is used to obtain the series decomposition form of the actual received signal of each sub-array; According to the actual received signal of each array element, a linear relationship between the harmonic component of each sub-array received signal, polarization parameters and incident direction is established.

[0026] More specifically: Assume that the total number of far-field sinusoidal plane waves incident on the array elements is The multi-antenna receiving signal is time-divided and received into a single receiving channel through the RF switch.

[0027] Polarization Amplitude Ratio Polarization phase difference Polarization descriptor of Characterize the polarization state and obtain the received signal, time modulation function, and polarization vector of each element based on the alternating polarization time modulation array, including: ; ; ; Where, is the complex amplitude of the signal, is the incident signal polarization, and The received signal of the array element is constituted. are the amplitude and phase of the incident signal, is the imaginary unit, is the incident signal frequency, For time, For the The phase of the array element, For the Array elements, is the distance between the phase centers of adjacent array elements, is the signal incident angle, is the wavelength, To characterize the relative amplitude of the signal polarization state, To characterize the relative phase of the signal polarization state, for The transpose of is the time modulation function (specifically: the signal reaches the After the array elements are formed, the time modulation function generated by the rapid switching of the antenna RF switch) is a positive integer, is the time modulation period (also the switching modulation period), is the number of array elements, is a set of integers; For the The Jones vector of the polarization of the array element (i.e. polarization vector of each array element); The normalized complex voltage received by the antenna is defined as At this time, according to the received signal of each array element, the time modulation function and the polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained, including: ; Where, For the The initial representation of the actual received signal of each array element, for conjugation of; The received signal can be separated in the time domain to obtain the signals of the two polarization sub-arrays. Based on the initial representation of the actual received signal of each array element, the time domain expressions of the actual received signals of the two sub-arrays are obtained, including: ; Where, is the received signal of the X-polarization subarray, is the received signal of the Y-polarization subarray, For the 2nd n -The signal received by 1 array element, For the 2nd n The signal received by each array element; Expand the time modulation function into a series form: ; Where, is the Fourier coefficient, indicating the The array element receives the signal k Subharmonic components, represents the angular frequency of the harmonic; By performing harmonic analysis on the received signals of the two polarization arrays, the linear relationship between the harmonic components can be used to solve the target incident angle and polarization information. Combined with the time domain expression of the actual received signals of the two sub-arrays, the second polarization information received by the two sub-arrays can be obtained. k Subharmonics (i.e., angular frequencies of of the amount), including: ; where, is the 2nd harmonic received by the X-polarized subarray, k is the 2nd harmonic received by the Y-polarized subarray, is the conjugate of the polarization vector of X-polarization k is the conjugate of the polarization vector of Y-polarization is the phase when in takes 2 -1, is the phase when in n takes 2 n -1, is the phase when in n takes 2 n ; According to the 2nd harmonic received by the two subarrays and the series form of the time modulation function, the series decomposition form of the actual received signal of each subarray is obtained, including: k ; ; where, is the received signal of the X-polarized subarray, is the received signal of the Y-polarized subarray; According to the actual received signal of each array element, a linear relationship between the harmonic component, polarization parameter and incident direction of the received signal of each subarray is established, including: ; i.e.: ; ; where, is the harmonic characteristic matrix (HCM) of the X-polarized subarray, which is determined by the Fourier coefficient generated by the time modulation function, is the harmonic characteristic matrix (HCM) of the Y-polarized subarray, which is determined by the Fourier coefficient generated by the time modulation function, is the array manifold vector of the X-polarized subarray (including the polarization characteristics and angle information of the subarray), is the array manifold vector of the Y-polarized subarray (including the polarization characteristics and angle information of the subarray), is the vector composed of the harmonic components of the X-polarized subarray, is the vector composed of the harmonic components of the Y-polarized subarray. Y

[0028] In this step, signal modeling is performed, and finally a model describing the array manifold vector, array harmonic component and time modulation prior information is obtained.​

[0029] In step 103, according to the linear relationship between the harmonic component of the received signal, the polarization parameter and the incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained, the vector composed of the harmonic components of the subarrays is rewritten into a form containing a noise term, and the error perturbation between the true value of the direction function and the corresponding estimate is obtained; and according to the error perturbation between the true value of the direction function and the corresponding estimate, the estimate of the direction is obtained.

[0030] Specifically, According to the linear relationship between the harmonic component of the received signal, the polarization parameter and the incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained, the vector composed of the harmonic components of the subarrays is rewritten into a form containing a noise term, and the error perturbation between the true value of the direction function and the corresponding estimate is obtained; According to the error perturbation between the true value of the direction function and the corresponding estimate, a second-order approximation is performed to obtain an approximate expression of the error perturbation; According to the approximate expression of the error perturbation, the variance of the perturbation is obtained; According to the variance of the perturbation, the error covariance matrix is obtained by using the least square method; According to the error covariance matrix, the variance of the perturbation in the estimate is obtained; According to the variance of the perturbation in the estimate, the optimal weight that minimizes the variance of the direction finding perturbation is obtained; According to the optimal weight that minimizes the variance of the direction finding perturbation and the relationship between the direction perturbation and the direction function perturbation, the estimate of the direction is obtained.

[0031] More specifically, For AP-TMA, when the polarization factor must be strictly considered to avoid the energy of the received signal of a certain subarray in the single-polarization TMA or AP-TMA caused by polarization mismatch being reduced to near zero, thereby avoiding significantly reducing the received signal-to-noise ratio (SNR). The polarization state of two subarrays is considered in the present application, the estimate is corrected to a weighted result suitable for the polarization of the subarray, so as to maintain the robustness of the angle estimation under any polarization condition and improve the estimation accuracy.

[0032] Definition is the theoretical value of and Although and are in a nonlinear relationship, when the signal-to-noise ratio is not extremely low, it can be considered that the perturbation of is proportional to the perturbation of According to the linear relationship between the harmonic component of the received signal, the polarization parameter and the incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained: ; ; ; wherein, is the corresponding estimate of the directional function true value of the X polarized subarray, is the corresponding estimate of the directional function true value of the Y polarized subarray, is the estimate of the directional function (obtained by weighting the estimates of the two subarrays ), is the estimate of , is the first row (of the row) of , is the first row of , is the estimate of , is the first row of , is the first row of , is the weighting coefficient, is the weighting value, the sum of the weighting coefficients is constrained to 1 to guarantee unbiased estimate, is the estimate of and ; ; Considering the signal-to-noise ratio of the received signal, the vector composed of the subarray harmonic components is rewritten in the form containing noise terms, and the subarray harmonic component vector containing noise terms is obtained: ; wherein, ; ; wherein, is the generalized inverse matrix of the harmonic eigenmatrix of the X polarized subarray, is the generalized inverse matrix of the harmonic eigenmatrix of the Y polarized subarray, is the estimate of , is the estimate of , is the noise vector when extracting the harmonic estimate , is the noise vector when extracting the harmonic estimate , and representative frequency The noise components in the received signals of the X-polarized subarray and the Y-polarized subarray are zero-mean random variables with equal power for real and imaginary parts and independent and identically distributed, and are noise matrices composed of perturbations on the harmonics of the received signals of the subarrays, respectively; According to the relationship between the directional perturbation and the directional function perturbation and the harmonic component vectors of the subarrays containing noise terms, the error perturbation between the true value of the directional function and the corresponding estimator is obtained: ; wherein, is the error perturbation between and , is the error perturbation between and , is the true value of the directional function of the X-polarized subarray, is the true value of the directional function of the Y-polarized subarray; Since the noise on each harmonic is much smaller than the harmonic amplitude, according to the error perturbation between the true value of the directional function and the corresponding estimator, a second-order approximation is performed to obtain an approximate expression of the error perturbation, including: ; wherein, is the first row of , is the generalized inverse matrix of the harmonic characteristic matrix of the X-polarized subarray, is the noise vector when extracting the harmonic estimate , is the phase when in n takes 3, is when n in takes N / 2, is the phase when in n takes N+1; According to the approximate expression of the error perturbation, the variance of the perturbation is obtained, including: ; ; wherein, is the variance of the error perturbation , is the variance of the error perturbation , is the noise power, is the Euclidean norm, is when is the phase of n when N-2; is the variance of and are independent and identically distributed, according to the variance of the disturbance, the error covariance matrix is obtained by using the least square method, including: ; wherein, is the error covariance matrix, is a diagonal matrix; According to the error covariance matrix, the variance of the disturbance in the estimated value is obtained, including: ; wherein, is the variance, is the direction function, is the disturbance between the observation value and the true value ; According to the variance of the disturbance in the estimated value, the optimal weight which minimizes the variance of the direction finding disturbance is obtained, including: (1) When the final angle estimation is a weighted combination of the results of two sub-arrays, and the weight is determined by the power ratio of the polarization projection of the incident signal on the sub-array, the estimated disturbance of direction finding reaches the minimum, which is called polarization projection weighting; Therefore, in the actual signal processing, the actual optimal weight which minimizes the variance of the direction finding disturbance is obtained: ; wherein, is the actual optimal weight which minimizes the variance of the direction finding disturbance; According to the relationship between the actual optimal weight which minimizes the variance of the direction finding disturbance and the disturbance of the direction and the disturbance of the direction function, the estimated value of the direction is obtained, including: ; wherein, is the estimated value of the direction.

[0033] In this step, by adaptively processing the estimation results of each sub-array according to the polarization projection (i.e. polarization projection weighting), the optimal angle estimation can be realized.

[0034] Step 104, according to the linear relationship between the harmonic component of the signal received by each sub-array, the polarization parameter and the incident direction, the relationship between the polarization matching coefficient of the array flow vector estimation value and the antenna polarization and the polarization of the radiation source is obtained, and then the estimated value of the polarization is obtained.

[0035] Specifically: According to the linear relationship between the received signal harmonic components, polarization parameters and incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimation and the antenna polarization and the radiation source polarization is obtained: ; In the formula, is the phase of 1, n is the phase of 1, is the vector containing the polarization matching coefficient, is the vector containing the polarization matching coefficient; The radiation source polarization can be obtained from the polarization matching coefficient and the polarization characteristics of the alternate polarization array, that is, the estimation of the polarization is obtained: ; In the formula, is the conjugate transpose of , is the conjugate transpose of .

[0036] In this embodiment, the estimation of the direction reaches the minimum when the polarizations of the two subarrays are orthogonal, and the estimation of the polarization reaches the minimum when the polarizations of the two subarrays are orthogonal.

[0037] Specifically: According to the relationship between the direction disturbance and the direction function disturbance, the error disturbance between the true value and the corresponding estimation of the direction function, and the variance of the disturbance, the disturbance of the incident angle estimation when the polarization projection is weighted can be expressed as: ; The variance of the disturbance is proportional to: ; The mean value (that is, the integral in the full polarization domain) of on the full polarization domain can be expressed as , is a function of the antenna polarization and ; By applying the inequality, it can be obtained that: (2) iff is a constant, that is, When the polarization is constructed as an orthogonal basis, the equation is established; Therefore, the relationship between the polarization of the two subarrays and the mean value of the angle estimation disturbance variance can be calculated:​​ ; This shows that when the polarizations of the two sub-arrays are orthogonal, the direction finding disturbance reaches the minimum, i.e. the estimated value of the direction has the optimal performance.

[0038] From the estimated value of the polarization, using two different polarization types of units, according to the projection of the radiation source on the two polarizations to infer its polarization state, considering the existence of noise, the actual polarization estimation can be expressed as: (3) wherein, and respectively represent the disturbance of the external radiation source caused by noise on the X polarization and Y polarization projection values, both are independent and identically distributed, and the variance is , the polarization estimation error can be expressed as: ; Since is a vector composed of random variables, the expectation of the square of its Euclidean norm is used to quantify the fluctuation amplitude: ; Therefore, we can get: ; This shows that when the polarizations of the two sub-arrays are orthogonal, the polarization estimation disturbance reaches the minimum, i.e. the estimated value of the polarization has the optimal performance.

[0039] It should be noted that the derivation of formula (1) (2) (3) is as follows.

[0040] Formula (1): The relationship between the HCMs of the two different sub-arrays and can be expressed by matrix row transformation: ; In the formula, is a diagonal matrix, and satisfies: ; From this we can get: ; The relationship between its row vectors is: ; The variance of the disturbance can be expressed as: ; Since the modulus of the diagonal elements is 1, we can get: ; Then, the optimal weights that minimize the variance of the disturbance can be solved as .

[0041] Equation (2): For any real number , consider the integral: ; When is and , we have: ; That is: ; Thus, we obtain a variant of the estimate of the polarization: ; The equality holds if and only if for any and , we have , that is , where C is a constant; If the equality holds, then: ; This shows that when the polarizations of the two sub-arrays are orthogonal, the average disturbance in the direction finding process is minimized.

[0042] Equation (3): According to the estimated value of the polarization and the harmonic component vector of the sub-array containing the noise term, when considering the harmonic noise, the manifold vector and will produce corresponding errors: ; The simplified expression is shown in the representation of the actual polarization estimate: ; It can be seen that and are independent and identically distributed random variables; since and are linear combinations of independent and identically distributed complex Gaussian random variables, they still maintain the independent and identically distributed characteristics.

[0043] The above-mentioned time modulation array-based direction and polarization joint estimation method is based on a single-channel alternating polarization time modulation array (AP-TMA) to perform direction (angle) and polarization joint estimation, considers polarization factors in signal propagation and array configuration, can ensure direction estimation accuracy when there is polarization mismatch between the incident signal and the receiving array, and can obtain the incident direction and polarization parameters of an arbitrary polarized radiation source. In addition, by extracting a multi-harmonic signal and using polarization projection weighting processing, the direction and polarization estimation accuracy is improved, and robust direction finding and polarization estimation performance is achieved.

[0044] Specifically, 1) A joint estimation method based on a new AP-TMA architecture is proposed, which solves the polarization mismatch problem in TMA direction finding by changing the polarization mode of the array elements (without increasing hardware cost), realizes robust estimation of the angle-polarization parameters of an arbitrary polarized signal, and enhances the spatial-polarization domain perception ability of TMA.

[0045] 2) It is proposed that the TMA direction finding result is equivalent to the uniformly weighted combination of the angle estimation of multiple sub-arrays inside the array, and the optimal estimation is the polarization projection weighting of the estimation values of two different polarization sub-arrays in the AP-TMA.

[0046] 3) An optimal configuration criterion for the polarization of the AP-TMA dual-subarray antenna is proposed, and the two sub-arrays only need to satisfy the polarization orthogonal condition without specific polarization combination, which provides practical guidance for expanding the application of AP-TMA.

[0047] It should be understood that, although Figure 1 The steps in the flowchart are displayed in sequence according to the direction of the arrows, but these steps are not necessarily executed in sequence according to the direction of the arrows. Unless otherwise specified in this article, the execution of these steps has no strict order limitation, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps in the flowchart can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution order of these sub-steps or stages is not necessarily sequential, but can be executed with at least part of other steps or sub-steps or stages of other steps.

[0048] In a specific embodiment, the method proposed in the present application is verified by simulation, and the signal-to-noise ratio, the number of array elements The influence of the polarization of the incident signal on the measurement accuracy is studied, and the TMA and the AP-TMA are compared. This embodiment relates to various polarization configurations of the AP-TMA, each configuration being represented by the abbreviations in Table 1. Modes H, V, L and R represent four single-polarization TMAs of horizontal, vertical, left-handed circular and right-handed circular polarization, respectively; modes HV and LR are two AP-TMAs composed of polarization-orthogonal subarrays; modes 1 and 2 are two AP-TMAs with non-orthogonal polarization subarrays. The specific configurations are shown in Table 1.

[0049] Table 1: Mode abbreviations corresponding to AP-TMAs with different polarization configurations

[0050] Table 2: Some simulation parameters

[0051] A. Estimation accuracy under different signal-to-noise ratios and array element numbers The characteristics of the received signal after time modulation of the radio frequency signal entering mode HV under different signal-to-noise ratios and array element numbers are studied by simulation. The polarization parameters and the angle of the incident signal are estimated by using the linear relationship between the -4th to +4th harmonic components, and the performance is evaluated by using the root mean square error (RMSE). After fast Fourier transform (FFT), the three parameters of the incident signal, i.e. the polarization amplitude ratio, the polarization phase difference and the incident angle, can be estimated by using the harmonic characteristic matrix of the array and the harmonic components of the received signal.

[0052] Table 2 lists the main simulation parameters, which are used in the subsequent simulations unless otherwise specified. The polarization state of the incident signal is represented by the polarization descriptor , and the polarization descriptor is , i.e. left-handed circular polarization. The received signal is sampled for 1000 points, and the received performance under different signal-to-noise ratios and array element numbers is evaluated by 1000 Monte Carlo simulations, and the RMSE of the estimated parameters is calculated.

[0053] As shown in Figure 3 and Figure 4 , with the increase of the signal-to-noise ratio, the RMSE of the incident angle estimation and the polarization parameter estimation decreases to different degrees. The angle estimation error decreases with the increase of the array element number, because more array elements expand the array aperture, which is one of the key factors affecting the measurement accuracy. However, the estimation accuracy of the two polarization parameters does not significantly improve with the increase of the array elements, because the total number of sampling points is fixed in the simulation. The increase of the array elements leads to the decrease of the sampling points of a single array element, while the polarization projection energy of each subarray remains unchanged. Therefore, the polarization parameter estimation accuracy of the method of the present application almost only depends on the signal-to-noise ratio, but The RMSE of AP-TMA slightly decreases with the increase of array elements, because the angle and polarization phase difference information are coupled, and the estimation accuracy of angle is improved, the estimation accuracy of polarization is also improved.

[0054] B. Direction finding accuracy in full polarization domain The incident signals of different polarizations are simulated, and the signal-to-noise ratio is set to 10 dB, and the number of array elements is 8. The linear relationship between the -2th to +2th harmonic components is used to estimate the incident angle after the time modulation of the incident signals of different polarizations entering the AP-TMA, and the performance is evaluated by the RMSE. In order to show the direction finding accuracy of the AP-TMA, four kinds of single-polarization TMAs, mode H, mode V, mode L and mode R, are compared. The parameters and vary in the range of 0° to 90° and 0° to 360° respectively, i.e. the full polarization domain, which represents all polarization states of the incident signals. The signals with a signal-to-noise ratio of 10 dB (before polarization projection) are input into the AP-TMA with different polarization settings, and the RMSE of 1000 direction finding results is taken.

[0055] As shown in Figure 5 and Figure 6 , for the four different polarization settings of the single-polarization TMA, when the polarization is matched, the RMSE reaches the minimum value of 0.045°. When there is a polarization mismatch, the direction finding RMSE rises sharply, and obviously the single-polarization TMA cannot achieve stable estimation performance for arbitrary polarization incident signals. In addition, due to the polarization mismatch, the single-polarization TMA may fail in some areas of the full polarization domain and cannot perform angle estimation.

[0056] As shown in Figure 7 , the overall RMSE of the angle estimation of the non-orthogonal polarization AP-TMA is better than that of the single-polarization TMA, but it still shows a large error for specific polarization incident signals, which is caused by the non-orthogonal polarization of the two sub-arrays. When the array receives an arbitrary polarization incident signal, the received energy will fluctuate significantly due to the difference in signal polarization.

[0057] As shown in Figure 8 , the RMSE of mode HV and mode LR remains stable in the full polarization domain, and the error values of the two modes are always between 0.06° and 0.065°. This is because the polarization of the sub-array in both cases forms an orthogonal polarization basis, which ensures that the total received energy is constant in any case.

[0058] The above simulation shows that for arbitrary polarization incident signals, the direction finding performance of the AP-TMA is better than that of the single-polarization TMA. The use of two sub-arrays with orthogonal polarization bases can significantly improve the direction finding robustness and achieve higher accuracy.

[0059] C. Polarization estimation accuracy in full polarization domain The simulation is also performed for an incident signal with arbitrary polarization, and the parameter settings remain the same as before.

[0060] like Figure 9 As shown, for non-orthogonal polarization AP-TMA estimation The RMSE of mode 1 is poor due to the sub-array polarization orthogonality, which causes the RMSE to fluctuate violently in the full polarization domain, ranging from a minimum of 0.125° to a maximum of 0.527°. However, mode 2 benefits from better sub-array polarization orthogonality, and the RMSE fluctuation is smaller, ranging from 0.145° to 0.365° in the polarization domain.

[0061] like Figure 10 As shown, the HV and LR modes The estimated RMSE remains robust in the full polarization domain, with an error range between 0.175° and 0.185°.

[0062] like Figure 11 and Figure 12 As shown, AP-TMA was used to Estimation is made when the polarization amplitude ratio When approaching 0° and 90°, the RMSE will rise sharply. This is because the relative amplitude difference between the horizontal and vertical polarization components is too large, resulting in a sharp drop in the signal-to-noise ratio of the phase information of the smaller polarization component after polarization projection, making it difficult to obtain phase information, thus significantly reducing the RMSE when the polarization is close to horizontal or vertical. The estimation accuracy is improved, but this has little effect on the overall information of the polarization parameters. When it is close to 0° or 90°, The importance of the information represented by the AP-TMA is reduced, so it is believed that the AP-TMA remains robust in the full polarization domain. Estimated performance.

[0063] like Figure 11 As shown, for non-orthogonal polarization AP-TMA The root mean square error (RMSE) of mode 1 fluctuates dramatically in the entire polarization domain, with the RMSE below 0.5° in only a small area. The orthogonality of the two subarrays in mode 2 is better, and the RMSE fluctuation is smaller, with the RMSE below 0.5° in most areas, indicating that its direction finding performance is more robust.

[0064] like Figure 12 As shown in Figure 2, the AP-TMA of the orthogonal polariton array has a RMSE of less than 0.5° in most areas, showing robust Estimated performance.

[0065] The above simulations verify the effectiveness of the proposed method. AP-TMA expands the sensing capabilities of traditional TMA in the polarization dimension. By adopting a subarray design with orthogonal polarization bases, it achieves robust polarization estimation and reduces the root mean square error of the measurement.

[0066] In summary, the application proposes a new method of realizing joint estimation of direction and polarization by using single-channel AP-TMA. By combining AP-TMA with polarization projection weighting, the method effectively solves the direction finding failure problem of traditional single-channel TMA in the case of polarization mismatch, and realizes robust polarization and angle estimation of arbitrary polarized incident signals. When the polarization modes of the subarrays are orthogonal, the system performance is optimal. Simulation further verifies the effectiveness of the method proposed in the application. Compared with the traditional method, the direction finding robustness of the application is significantly improved, and the polarization estimation capability is added. The application provides a cost-effective solution for the practical application of single-channel TMA.

[0067] The contents not described in detail in the specification belong to the prior art known to those skilled in the art.

[0068] The technical features of the above embodiments can be combined in any manner. To make the description concise, all possible combinations of the technical features in the above embodiments are not described, but as long as the combinations of the technical features do not exist contradictions, they should be considered as the scope of the present application.

[0069] The above embodiments only express several implementation manners of the application, and the description is specific and detailed, but it should not be understood as a limitation on the scope of the application. It should be pointed out that for those skilled in the art, without departing from the concept of the application, some modifications and improvements can be made, which are all within the protection scope of the application. Therefore, the protection scope of the application should be subject to the appended claims.

Claims

1. A method for joint direction and polarization estimation based on time modulation array, characterized in that, The method comprises the following steps: An alternating polarization time modulation array is obtained, and two groups of polarization antennas are arranged alternately, each polarization antenna being an array element, and each group of polarization antennas being a subarray, so as to establish the alternating polarization time modulation array; According to the alternating polarization time modulation array, the received signal, the time modulation function and the polarization vector of each array element are obtained, and then the actual received signal of each array element is obtained; According to the actual received signal of each array element, a linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray is established; According to the linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the direction disturbance and the direction function disturbance is obtained, the vector formed by the harmonic components of the subarrays is rewritten into a form containing noise items, and the error disturbance between the true value of the direction function and the corresponding estimation is obtained; and according to the error disturbance between the true value of the direction function and the corresponding estimation, the estimation value of the direction is obtained; According to the linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimation value and the antenna polarization and the polarization of the radiation source is obtained, and then the estimation value of the polarization is obtained.

2. The method of claim 1, wherein, According to the alternating polarization time modulation array, the received signal, the time modulation function and the polarization vector of each array element are obtained, and then the actual received signal of each array element is obtained, which comprises the following steps: According to the alternating polarization time modulation array, the received signal, the time modulation function and the polarization vector of each array element are obtained; According to the received signal, the time modulation function and the polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained; According to the initial representation of the actual received signal of each array element, the time domain expression of the actual received signal of two subarrays is obtained; The time modulation function is expanded into a series form and combined with the time domain expressions of the actual received signals of the two sub-arrays, the first k subharmonics; The actual received signal of each subarray is obtained according to the second harmonic and the series form of the time modulation function. k The actual received signal of each subarray is obtained according to the second harmonic and the series form of the time modulation function.

3. The method of claim 2, wherein, According to the alternating polarization time modulation array, the received signal, the time modulation function and the polarization vector of each array element are obtained, which comprises the following steps: ； ； ； wherein, is the signal complex amplitude, is the incident signal polarization, is the amplitude and phase of the incident signal, is the imaginary unit, is the incident signal frequency, is time, is the phase of the th element, is the th element, is the distance between the phase centers of adjacent elements, is the signal incidence angle, is the wavelength, is the relative amplitude characterizing the signal polarization state, is the relative phase characterizing the signal polarization state, is the transpose of ; is the time modulation function, is a positive integer, is the time modulation period, is the number of elements, is a set of integers; is the Jones vector of the th element polarization; According to the received signal, the time modulation function and the polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained, which comprises the following steps: ； Where, For the The initial representation of the actual received signal of each array element, for conjugation of; According to the initial representation of the actual received signal of each array element, the time domain expression of the actual received signal of two subarrays is obtained, which comprises the following steps: ； wherein is the received signal of the X polarized subarray, is the received signal of the Y polarized subarray, is the signal received by the 2 n -1 element, is the signal received by the 2 n -1 element. The time modulation function is expanded into a series form, and the time domain expression of the actual received signals of the two sub-arrays is combined to obtain the second harmonic received by the two sub-arrays, including: k second harmonic, including: ； ； Where, For the The array element receives the signal k Subharmonic components, The first received by the X-polarization subarray k subharmonics, The first k subharmonics, is the conjugate of the polarization vector of X polarization, is the conjugate of the polarization vector of Y polarization, For the time in n Take 2 n Phase at -1, For the time in n Take 2 n The phase of time; The actual received signal of each subarray is obtained in a series form according to the second harmonic and the series form of the time modulation function, and includes: k a series decomposition form of the actual received signal of each subarray ； wherein is the received signal of the X polarized subarray, is the received signal of the Y polarized subarray.

4. The method of claim 3, wherein, According to the actual received signal of each array element, a linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray is established, which comprises the following steps: ； wherein is the harmonic eigenvector matrix of the X polarized subarray, is the harmonic eigenvector matrix of the Y polarized subarray, is the array manifold vector of the X polarized subarray, is the array manifold vector of the Y polarized subarray, is the vector of harmonic components of the X polarized subarray, is the vector of harmonic components of the Y polarized subarray.

5. The method of claim 1 to 4, wherein, According to the linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the direction disturbance and the direction function disturbance is obtained, the vector formed by the harmonic components of the subarrays is rewritten into a form containing noise items, and the error disturbance between the true value of the direction function and the corresponding estimation is obtained, which comprises the following steps: According to the linear relationship among the harmonic component, the polarization parameter and the incident direction of the received signal of each subarray, the relationship between the direction disturbance and the direction function disturbance is obtained: ； ； ； wherein is a corresponding estimate of the true value of the directional function of the X polarimetric subarray, is a corresponding estimate of the true value of the directional function of the Y polarimetric subarray, is a directional function estimate, is an estimate of , an estimate of , an estimate of , the first row of , the first row of , the first row of , the first row of , an estimate of , an estimate of , the first row of , the first row of , the first row of , the first row of , the first row of , the first row of , a weighting coefficient, , a weighting value, , an estimate of , an estimate of , an estimate of , an estimate of The vector formed by the harmonic components of the subarrays is rewritten into a form containing noise items, and the subarray harmonic component vector containing noise items is obtained: ； Where, is the generalized inverse matrix of the harmonic characteristic matrix of the X-polarization subarray, is the generalized inverse matrix of the harmonic characteristic matrix of the Y-polarized array, for The estimated value of for The estimated value of To extract harmonics estimate The noise vector at time , To extract harmonics estimate The noise vector at time ; According to the relationship between the direction disturbance and the direction function disturbance and the subarray harmonic component vector containing the noise term, an error disturbance between the true value of the direction function and the corresponding estimation is obtained: ； wherein is the true value of the X polar subarray directional function, is the true value of the Y polar subarray directional function, is the error perturbation between the true value and the measured value, is the true value of the X polar subarray directional function, is the true value of the Y polar subarray directional function, is the error perturbation between the true value and the measured value, is the true value of the X polar subarray directional function, is the true value of the Y polar subarray directional function.

6. The method of claim 5, wherein, According to the error disturbance between the true value of the direction function and the corresponding estimation, an estimation value of the direction is obtained, including: According to the error disturbance between the true value of the direction function and the corresponding estimation, a second-order approximation is performed to obtain an approximate expression of the error disturbance; According to the approximate expression of the error disturbance, a variance of the disturbance is obtained; According to the variance of the disturbance, a least square method is used to obtain an error covariance matrix; According to the error covariance matrix, a variance of the disturbance in the estimation value is obtained; According to the variance of the disturbance in the estimation value, an optimal weight minimizing the direction finding disturbance variance is obtained; According to the optimal weight minimizing the direction finding disturbance variance and the relationship between the direction disturbance and the direction function disturbance, the estimation value of the direction is obtained.

7. The method of claim 6, wherein, According to the error disturbance between the true value of the direction function and the corresponding estimation, a second-order approximation is performed to obtain an approximate expression of the error disturbance, including: ； Where, for The first row of is the generalized inverse matrix of the harmonic characteristic matrix of the X-polarized subarray, is the extracted harmonic estimate The noise vector at time , For the time in n Take the phase of 3 o'clock, For the time in n When N / 2 is taken , For the time in n Take the phase at N+1; According to the approximate expression of the error disturbance, a variance of the disturbance is obtained, including: ； ； wherein is the variance of the error disturbance is the variance of the error disturbance is the variance of the error disturbance is the variance of the error disturbance is the noise power, is the Euclidean norm, is the phase when is the phase when n is the phase when According to the variance of the disturbance, a least square method is used to obtain an error covariance matrix, including: ； wherein is the error covariance matrix, is a diagonal matrix; According to the error covariance matrix, a variance of the disturbance in the estimation value is obtained, including: ； wherein is the variance, is the directional function; According to the variance of the disturbance in the estimation value, an optimal weight minimizing the direction finding disturbance variance is obtained, including: ； wherein optimal weight for minimizing the direction-finding disturbance variance; According to the optimal weight minimizing the direction finding disturbance variance and the relationship between the direction disturbance and the direction function disturbance, the estimation value of the direction is obtained, including: ； In the formula, is an estimate of the direction.

8. The method of claim 1 to 4, wherein, According to the linear relationship between the received signal harmonic component of each subarray, the polarization parameter and the incident direction, a relationship between the polarization matching coefficient of the array manifold vector estimation value and the antenna polarization and the polarization of the radiation source is obtained, and then an estimation value of the polarization is obtained, including: According to the linear relationship between the received signal harmonic component of each subarray, the polarization parameter and the incident direction, a relationship between the polarization matching coefficient of the array manifold vector estimation value and the antenna polarization and the polarization of the radiation source is obtained: ； wherein is when in n phase 1 An estimation value of the polarization is obtained: ； wherein is the conjugate transpose of is the conjugate transpose of is the conjugate transpose of is the conjugate transpose of 9. The method of claim 1 to 4, wherein, The direction estimation disturbance reaches the minimum when the polarization of the two subarrays is orthogonal.

10. The method of claim 1 to 4, wherein, The polarization estimation disturbance reaches the minimum when the polarization of the two subarrays is orthogonal.

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