A method for joint estimation of direction and polarization based on time modulation array

Abstract

The application belongs to the technical field of time modulation array, 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 the received signal of each array element, a time modulation function and the polarization vector of each array element, then obtaining the actual received signal of each array element, and establishing a linear relationship among the harmonic component of each subarray received signal, a polarization parameter and an incident direction; according to the linear relationship, obtaining the relationship between the direction disturbance and the direction function disturbance, rewriting the vector formed by the subarray harmonic component into a form containing a noise term, obtaining the error disturbance between the true value of the direction function and the corresponding estimation quantity, and then obtaining the estimation value of the direction; according to the linear relationship, obtaining 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, and then obtaining the estimation value of the polarization. The application can realize joint estimation of the direction and the polarization.

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, thereby regulating and controlling 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 generate 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 baselines provide larger array apertures to improve accuracy, and short baselines eliminate ambiguity solutions to achieve high-precision 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:

[0007] Obtain a time modulation array, and set two groups of alternately arranged polarization antennas, each polarization antenna as an array element, and each group of polarization antennas as a subarray to establish an alternating polarization time modulation array;

[0008] Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained, and then the actual received signal of each array element is obtained; 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 the received signal of each subarray.

[0009] Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the directional perturbation and the directional function perturbation is obtained. The vector formed by the harmonic components of the subarray is rewritten in the form of including a noise term to obtain the error perturbation between the true value of the directional function and the corresponding estimate. Based on the error perturbation between the true value of the directional function and the corresponding estimate, the estimated value of the direction is obtained.

[0010] Based on the linear relationship between the harmonic components of the received signal, polarization parameters, and incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and radiation source polarization is obtained, and thus the polarization estimate is obtained.

[0011] In one embodiment, 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, including:

[0012] Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained;

[0013] Based on the received signal, time modulation function, and polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained;

[0014] Based on the initial representation of the actual received signal of each array element, the time-domain expression of the actual received signal of the two subarrays is obtained;

[0015] Expanding the time modulation function into a series and combining it with the time-domain expressions of the actual received signals from the two subarrays, we obtain the first series received by the two subarrays. k Second harmonics;

[0016] According to the first received from the two subarrays 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.

[0017] In one embodiment, based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained, including:

[0018] ;

[0019] ;

[0020] ;

[0021] wherein, is the complex amplitude of the signal, is the polarization of the incident signal, is the amplitude and phase of the incident signal, is the imaginary unit, is the frequency of the incident signal, is time, is the phase of the th element, is the th element, is the phase center distance between adjacent elements, is the signal incidence 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;

[0022] 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:

[0023] ;

[0024] wherein, is the initial representation of the actual received signal of the th element, is the conjugate of ;

[0025] 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 sub-arrays is obtained, including:

[0026] ;

[0027] wherein, is the received signal of the X-polarized sub-array, is the received signal of the Y-polarized sub-array, is the 2 n- the signal received by the -th element, the signal received by the 2nd element, n the signal received by the -th element;

[0028] 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 sub-arrays, to obtain the 2nd harmonic received by the two sub-arrays, including: k

[0029]

[0030]

[0031] wherein, the 2nd harmonic component of the signal received by the -th element, the 2nd harmonic received by the X-polarized sub-array, k the 2nd harmonic received by the Y-polarized sub-array, the conjugate of the polarization vector of the X-polarization, k the conjugate of the polarization vector of the Y-polarization, the phase when the -th element in the -th element is taken as 2 k -1, the phase when the -th element in the -th element is taken as 2 ; n n n n

[0032] According to the 2nd harmonic received by the two sub-arrays and the series form of the time modulation function, the series decomposition form of the actual received signal of each sub-array is obtained, including: k

[0033]

[0034] wherein, the received signal of the X-polarized sub-array, the received signal of the Y-polarized sub-array.

[0035] In one embodiment, according to the actual received signal of each element, a linear relationship between the harmonic component of the received signal of each sub-array, the polarization parameter and the incident direction is established, including:

[0036]

[0037] wherein, the harmonic characteristic matrix of the X-polarized sub-array, the harmonic characteristic matrix of the Y-polarized sub-array, ​​​​​​​​​​​​​​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.

[0038] In one embodiment, according to the linear relationship between the received signal harmonic components, polarization parameters and incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained, and the vector composed of the subarray harmonic components is rewritten into a form containing noise terms, to obtain the error perturbation between the true value of the direction function and the corresponding estimator, including:

[0039] According to the linear relationship between the received signal harmonic components, polarization parameters and incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained:

[0040] ;

[0041] ;

[0042] ;

[0043] wherein, is the corresponding estimator of the true value of the direction function of the X-polarized subarray, is the corresponding estimator of the true value of the direction function of the Y-polarized subarray, is the estimator of the direction function, is the estimator of , is the first row of , is the first row of , is the estimator of , is the first row of , is the first row of , is the weighting coefficient, is the weighting value, is the estimator of and ;

[0044] The vector composed of the subarray harmonic components is rewritten into a form containing noise terms, to obtain the subarray harmonic component vector containing noise terms:

[0045] ;

[0046] wherein, is the generalized inverse matrix of the harmonic eigenvector matrix of the X polarized subarray, is the generalized inverse matrix of the harmonic eigenvector matrix of the Y polarized subarray, is the true value of the X polarized subarray direction function, is the estimate of the X polarized subarray direction function, is the true value of the Y polarized subarray direction function, is the estimate of the Y polarized subarray direction function, is the noise vector when extracting the harmonic estimate is the noise vector when extracting the harmonic estimate According to the relationship between the direction perturbation and the direction function perturbation and the subarray harmonic component vector containing the noise term, the error perturbation between the true value of the direction function and the corresponding estimate is obtained:

[0047]

[0048] ;

[0049] wherein, is the error perturbation between and , is the error perturbation between and , is the true value of the X polarized subarray direction function, is the true value of the Y polarized subarray direction function.

[0050] In one embodiment, according to the error perturbation between the true value of the direction function and the corresponding estimate, the estimate of the direction is obtained, comprising:

[0051] 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;

[0052] According to the approximate expression of the error perturbation, the variance of the perturbation is obtained;

[0053] According to the variance of the perturbation, the error covariance matrix is obtained by using the least square method;

[0054] According to the error covariance matrix, the variance of the perturbation in the estimate is obtained;

[0055] According to the variance of the perturbation in the estimate, the optimal weight that minimizes the direction finding perturbation variance is obtained;

[0056] According to the optimal weight that minimizes the direction finding perturbation variance and the relationship between the direction perturbation and the direction function perturbation, the estimate of the direction is obtained.

[0057] ​​In one embodiment, a second order approximation is made according to the error disturbance between the true value of the direction function and the corresponding estimate, to obtain an error disturbance approximation expression, comprising:

[0058] ;

[0059] wherein, is the first row of , wherein, is the generalized inverse matrix of the harmonic characteristic matrix of the X polarization subarray, is the noise vector when extracting the harmonic estimate , is the phase when n in takes 3, is n when in takes N / 2, is the phase when n in takes ;

[0060] According to the error disturbance approximation expression, the variance of the disturbance is obtained, comprising:

[0061] ;

[0062] ;

[0063] wherein, 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 in n takes N-2;

[0064] According to the variance of the disturbance, the error covariance matrix is obtained by using the least square method, comprising:

[0065] ;

[0066] wherein, is the error covariance matrix, is a diagonal matrix;

[0067] According to the error covariance matrix, the variance of the disturbance in the estimate value is obtained, comprising:

[0068] ;

[0069] wherein, is a variance, is a direction function;

[0070] According to the variance of the disturbance in the estimated value, the optimal weight minimizing the variance of the direction-finding disturbance is obtained, comprising:

[0071] ;

[0072] wherein, is the optimal weight minimizing the variance of the direction-finding disturbance;

[0073] According to the optimal weight minimizing the variance of the direction-finding disturbance and the relationship between the direction disturbance and the direction function disturbance, the estimated value of the direction is obtained, comprising:

[0074] ;

[0075] wherein, is the estimated value of the direction.

[0076] In one embodiment, according to the linear relationship between the received signal harmonic component, the polarization parameter and the incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimated value and the antenna polarization and the polarization of the radiation source is obtained, and then the estimated value of the polarization is obtained, comprising:

[0077] According to the linear relationship between the received signal harmonic component, the polarization parameter and the incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimated value and the antenna polarization and the polarization of the radiation source is obtained:

[0078] ;

[0079] wherein, is the phase when in n is 1;

[0080] The estimated value of the polarization is obtained:

[0081] ;

[0082] wherein, is the conjugate transpose of , is the conjugate transpose of .

[0083] In one embodiment, the estimated value of the direction reaches the minimum when the polarizations of the two subarrays are orthogonal.

[0084] In one embodiment, the estimated value of the polarization reaches the minimum when the polarizations of the two subarrays are orthogonal.

[0085] The above-mentioned time-modulated array-based direction and polarization joint estimation method performs direction (angle) and polarization joint estimation based on a single-channel alternating polarization time-modulated array (AP-TMA), considers polarization factors in signal propagation and array configuration, can guarantee direction estimation accuracy when there is polarization mismatch between incident signals and a receiving array, and can obtain 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. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 FIG. 1 is a flowchart of a time-modulated array-based direction and polarization joint estimation method according to an embodiment;

[0087] Figure 2 FIG. 2 is a polarization parameter and incident direction joint estimation system configuration diagram according to an embodiment;

[0088] Figure 3 FIG. 3 is a root mean square error diagram of parameter estimation (incident angle ) under different signal-to-noise ratios and array element numbers according to an embodiment;

[0089] Figure 4 FIG. 4 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 according to an embodiment;

[0090] Figure 5 FIG. 5 is a root mean square error diagram of parameter estimation (incident angle ) of different single-polarization arrays in a full polarization domain according to an embodiment, where (a) is mode H and (b) is mode V;

[0091] Figure 6 FIG. 6 is a root mean square error diagram of parameter estimation (incident angle ) of different single-polarization arrays in a full polarization domain according to an embodiment, where (a) is mode L and (b) is mode R;

[0092] Figure 7 FIG. 7 is a root mean square error diagram of AP-TMA parameter estimation (incident angle ) in a full polarization domain according to an embodiment, where (a) is mode 1 and (b) is mode 2;

[0093] Figure 8 FIG. 8 is a root mean square error diagram of AP-TMA parameter estimation (incident angle Root Mean Square Error (RMSE) plot of polarization estimation (polarization amplitude ratio

[0094] Figure 9 Root Mean Square Error (RMSE) plot of polarization estimation (polarization amplitude ratio

[0095] Root Mean Square Error (RMSE) plot of polarization estimation (polarization amplitude ratio Figure 10 Root Mean Square Error (RMSE) plot of polarization estimation (polarization phase difference

[0096] Figure 11 Root Mean Square Error (RMSE) plot of polarization estimation (polarization phase difference

[0097] Root Mean Square Error (RMSE) plot of polarization estimation (polarization phase difference Figure 12 DETAILED DESCRIPTION

[0098] 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 not 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.

[0099] In addition, the terms "first", "second", etc. used in the present application are only for the purpose of description, and cannot be understood as indicating or implying the relative importance of the indicated technical features or implicitly indicating the number of the indicated technical features. Therefore, the features defined with "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, such as two groups, three groups, etc., unless otherwise specifically limited.

[0100] ​​​In this application, unless otherwise expressly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0101] Furthermore, the technical solutions of the various embodiments of this application can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this application.

[0102] This application provides a method for joint estimation of direction and polarization based on a time-modulated array, such as... Figure 1 The flowchart shown, in one embodiment, includes:

[0103] Step 101: Obtain the time modulation array and set up two sets of alternately arranged polarized antennas, with each polarized antenna as an array element and each set of polarized antennas as a subarray, to establish an alternating polarization time modulation array.

[0104] In this step, such as Figure 2 The configuration diagram shown illustrates a joint estimation system for polarization parameters and incident direction. The alternating polarization time-modulated array (AP-TMA) consists of two sets of alternating antennas with different polarizations. Each set of antennas with the same polarization is considered a subarray. The polarizations of the two subarrays do not need to be orthogonal but must be different. This configuration achieves optimal estimation performance when the subarrays are orthogonal. The array subarrays use two types of antennas with different polarizations, denoted as the X-polarized subarray and the Y-polarized subarray, respectively, with their corresponding polarization vectors expressed as... and This is to introduce a polarization dimension in TMA.

[0105] Step 102: Based on the alternating polarization time modulation array, obtain the received signal, time modulation function and polarization vector of each array element, and then obtain the actual received signal of each array element; based on the actual received signal of each array element, establish the linear relationship between the harmonic components, polarization parameters and incident direction of the received signal of each subarray.

[0106] Specifically:

[0107] Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained;

[0108] According to the received signal of each array element, the time modulation function and the polarization vector of each array element, an initial representation of the actual received signal of each array element is obtained;

[0109] According to the initial representation of the actual received signal of each array element, a time domain expression of the actual received signal of two sub-arrays is obtained;

[0110] The time modulation function is expanded into a series form, and combined with the time domain expression of the actual received signal of two sub-arrays, the second harmonic received by two sub-arrays is obtained; k

[0111] According to the second harmonic received by two sub-arrays and the series form of the time modulation function, a series decomposition form of the actual received signal of each sub-array is obtained; k

[0112] According to the actual received signal of each array element, a linear relationship between the harmonic component of the received signal of each sub-array, the polarization parameter and the incident direction is established.

[0113] More specifically:

[0114] Suppose that a far-field sinusoidal plane wave is incident to an array with a total number of array elements , the multi-antenna received signal is received by a single receiving channel in time sharing through a radio frequency switch.

[0115] The polarization state is represented by a polarization descriptor containing a polarization amplitude ratio and a polarization phase difference , and according to the alternate 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, including:

[0116] ;

[0117] ;

[0118] ;

[0119] In the formula, is a signal complex amplitude, is an incident signal polarization, and constitute the received signal of the array element, is the amplitude and phase of the incident signal, is an imaginary unit, is an incident signal frequency, is time, is the phase of the th array element, is the ​​​an array element, is the phase center distance between adjacent array 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 (specifically: the time modulation function generated by the rapid switching of the antenna radio frequency switch after the signal arrives at the th array element), is a positive integer, is the time modulation period (also the switch modulation period), is the number of array elements, is a set of integers; is the Jones vector of the th array element polarization (i.e., the polarization vector of the th array element);

[0120] 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:

[0121] ;

[0122] In the formula, is the initial representation of the actual received signal of the th array element, is the conjugate of ;

[0123] The received signal can be separated in the time domain to obtain the signals of two polarization subarrays. According to the initial representation of the actual received signal of each array element, the time domain expression of the actual received signal of the two subarrays is obtained, including:

[0124] ;

[0125] In the formula, is the received signal of the X polarization subarray, is the received signal of the Y polarization subarray, is the signal received by the n th array element, is the signal received by the n th array element;

[0126] The time modulation function is expanded into a series form:

[0127] ;

[0128] In the formula, Let be the Fourier coefficient, representing the th... The first element receives the signal k Second harmonic components This indicates the angular frequency of the harmonic;

[0129] By performing harmonic analysis on the received signals from the two polarization subarrays, the target incident angle and polarization information can be solved using the linear relationship between the harmonic components. Combined with the time-domain expressions of the actual received signals from the two subarrays, the first harmonic received by the two subarrays can be obtained. k Second harmonic (i.e., angular frequency is) The components include:

[0130] ;

[0131] In the formula, The first received by the X-polarized subarray k Second harmonic The first received by the Y-polarized subarray k Second harmonic The polarization vector of X polarization conjugate, The polarization vector of Y polarization conjugate, For when In n Take 2 n The phase at -1 For when In n Take 2 n Phase of time;

[0132] According to the first received from the two subarrays k The series form of the second harmonics and the time modulation function is used to obtain the series decomposition form of the actual received signal of each subarray, including:

[0133] ;

[0134] In the formula, The received signal for the X-polarized subarray. The received signal is for the Y-polarized subarray;

[0135] Based on the actual received signal of each array element, establish a linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal of each subarray, including:

[0136] ;

[0137] Right now:

[0138] ;

[0139] ;

[0140] wherein, is the harmonic characteristic matrix (HCM) of the X-polarized subarray, determined by the Fourier coefficients of the time modulation function, is the harmonic characteristic matrix (HCM) of the Y-polarized subarray, determined by the Fourier coefficients of the time modulation function, is the array manifold vector of the X-polarized subarray (containing the polarization characteristics and angle information of the subarray), is the array manifold vector of the Y-polarized subarray (containing the polarization characteristics and angle information of the subarray), is the vector of the X-polarized subarray harmonic components, is the vector of the Y-polarized subarray harmonic components. Y is the vector of the Y-polarized subarray harmonic components.

[0141] In this step, signal modeling is performed, and finally a model describing the array manifold vector, array harmonic components, and time modulation prior information is obtained.

[0142] In step 103, according to the linear relationship between the received signal harmonic components, polarization parameters, and incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained, and the vector of the subarray harmonic components is rewritten into a form containing a noise term, to obtain the error perturbation between the true value of the direction function and the corresponding estimate; according to the error perturbation between the true value of the direction function and the corresponding estimate, the estimate of the direction is obtained.

[0143] Specifically:

[0144] According to the linear relationship between the received signal harmonic components, polarization parameters, and incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained, and the vector of the subarray harmonic components is rewritten into a form containing a noise term, to obtain the error perturbation between the true value of the direction function and the corresponding estimate;

[0145] 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;

[0146] According to the approximate expression of the error perturbation, the variance of the perturbation is obtained;

[0147] According to the variance of the perturbation, a least squares method is used to obtain the error covariance matrix;

[0148] According to the error covariance matrix, the variance of the perturbation in the estimate is obtained;

[0149] According to the variance of the perturbation in the estimate, the optimal weight that minimizes the direction finding perturbation variance is obtained;

[0150] Based on the optimal weights that minimize the variance of the direction-finding perturbation and the relationship between the direction perturbation and the direction function perturbation, the estimated value of the direction is obtained.

[0151] More specifically:

[0152] For AP-TMA, when When polarization is used, it is essential to strictly consider polarization factors to avoid a sudden drop in the received signal energy of a subarray in a single-polarization TMA or AP-TMA to near zero due to polarization mismatch, thereby preventing a significant reduction in the received signal-to-noise ratio (SNR). This application considers the polarization states of two subarrays and corrects the estimated value to a weighted result adapted to the subarray polarization, in order to maintain the robustness of angle estimation under arbitrary polarization conditions and improve the estimation accuracy.

[0153] definition for and The theoretical value, although and The relationship is non-linear, but when the signal-to-noise ratio is not extremely low, it can be considered... disturbance and The perturbation is proportional to the direction function perturbation. Based on the linear relationship between the harmonic components of the received signal, polarization parameters, and incident direction of each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained:

[0154] ;

[0155] ;

[0156] ;

[0157] In the formula, This is the corresponding estimator of the true value of the direction function of the X-polarization subarray. This is the corresponding estimator of the true value of the direction function of the Y-polarization subarray. The direction function estimator (obtained by weighting the estimates of the two subarrays) (estimated quantity) for The estimated value, for The OK( Each element has OK), for The OK, for The estimated value, for The OK, Let be the first row, be the weighting coefficient, be the weighting value, and the sum of the weighting coefficients is constrained to 1 to ensure unbiased estimation, be and the estimated values of the two theoretical values;

[0158] 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 to obtain the subarray harmonic component vector containing noise terms:

[0159] ;

[0160] wherein,

[0161] ;

[0162] ;

[0163] In the formula, 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 estimated value of is the estimated value of is the noise vector when extracting the harmonic estimate is the noise vector when extracting the harmonic estimate is the noise vector when extracting the harmonic estimate is the noise vector when extracting the harmonic estimate is the noise vector when extracting the harmonic estimate and represent the noise components in the X-polarized subarray and the Y-polarized subarray received signals at frequency These noise components are zero-mean random variables with equal power and independent and identically distributed , and are noise matrices composed of disturbances on each harmonic of the subarray received signals, respectively;

[0164] According to the relationship between the direction disturbance and the direction function disturbance and the subarray harmonic component vector containing noise terms, the error disturbance between the true value of the direction function and the corresponding estimate is obtained:

[0165] ;

[0166] In the formula, is the error disturbance between and , is the error perturbation between the true value of the X-polarized subarray directional function, the true value of the Y-polarized subarray directional function;

[0167] 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 estimate, a second-order approximation is made to obtain an error perturbation approximate expression, including:

[0168] ;

[0169] wherein, is the first row of , wherein, 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 takes 3, n is when in n takes N / 2, , is the phase when in n takes N+1;

[0170] According to the error perturbation approximate expression, the variance of the perturbation is obtained, including:

[0171] ;

[0172] ;

[0173] wherein, is the variance of the error perturbation , is the variance of the error perturbation , is the noise power, is the Euclidean norm, is the phase when in n takes N-2;

[0174] Since and are independent and identically distributed, according to the variance of the perturbation, the least squares method is used to obtain the error covariance matrix, including:

[0175] ;

[0176] wherein,​ is the error covariance matrix, is a diagonal matrix;

[0177] According to the error covariance matrix, the variance of the disturbance in the estimated value is obtained, comprising:

[0178]

[0179] wherein, is the variance, is the direction function, is the observation value and the true value disturbance;

[0180] According to the variance of the disturbance in the estimated value, the optimal weight minimizing the variance of the direction finding disturbance is obtained, comprising:

[0181] (1)

[0182] 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 the direction finding reaches the minimum, which is called polarization projection weighting; therefore, in the actual signal processing, the actual optimal weight minimizing the variance of the direction finding disturbance is obtained:

[0183]

[0184] wherein, is the actual optimal weight minimizing the variance of the direction finding disturbance;

[0185] According to the actual optimal weight minimizing the variance of the direction finding disturbance and the relationship between the direction disturbance and the direction function disturbance, the estimated value of the direction is obtained, comprising:

[0186]

[0187] wherein, is the estimated value of the direction.

[0188] In this step, by adaptively processing the estimated results of each sub-array according to the polarization projection (i.e. polarization projection weighting), the optimal angle estimation can be realized.

[0189] 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 stream vector estimated value and the antenna polarization and the polarization of the radiation source is obtained, and then the estimated value of the polarization is obtained.

[0190] Specifically:

[0191] ​​​According to the linear relationship between the received signal harmonic component, polarization parameter and incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimation value and the antenna polarization and the radiation source polarization is obtained:

[0192] ;

[0193] wherein, is the phase of when n is 1, is the vector containing the polarization matching coefficient, is the vector containing the polarization matching coefficient;

[0194] The radiation source polarization can be obtained from the polarization matching coefficient and the polarization characteristics of the alternate polarization array, i.e. the estimation value of the polarization is obtained:

[0195] ;

[0196] wherein, is the conjugate transpose of , is the conjugate transpose of .

[0197] In the embodiment, the estimation value of the direction reaches the minimum when the polarizations of the two subarrays are orthogonal, and the estimation disturbance of the polarization reaches the minimum when the estimation value of the polarization reaches the minimum when the polarizations of the two subarrays are orthogonal.

[0198] Specifically:

[0199] According to the relationship between the direction disturbance and the disturbance of the direction function, the error disturbance between the true value of the direction function and the corresponding estimation value and the variance of the disturbance, the disturbance of the incident angle estimation when the polarization projection is weighted can be expressed as:

[0200] ;

[0201] The variance of the disturbance is proportional to:

[0202] ;

[0203] The mean value (i.e. the integral in the full polarization domain) of on the full polarization domain can be expressed as , is the function of the antenna polarization and ;

[0204] By applying the inequality, it can be obtained that:​

[0205] (2)

[0206] iff is constant, i.e. The equation holds when the polarizations constitute an orthogonal basis.

[0207] Thus the mean of the variance of the angle estimation perturbation can be calculated in terms of the polarization of the two subarrays:

[0208] .

[0209] This shows that when the polarizations of the two subarrays are orthogonal, the direction of arrival perturbation reaches a minimum, i.e. the estimate of the direction has optimal performance.

[0210] From the estimate of the polarization, using two different polarized elements, the polarization state of the source can be inferred from its projections on the two polarizations. Considering the existence of noise, the actual polarization estimate can be expressed as:

[0211] (3)

[0212] where and represent the perturbations of the projections of the external source on the X polarization and Y polarization respectively due to noise, which are independent and identically distributed with variance The polarization estimation error can be expressed as:

[0213] .

[0214] Since is a vector composed of random variables, the expectation of the square of its Euclidean norm is used to quantify the fluctuation amplitude:

[0215] .

[0216] Therefore we have:

[0217] .

[0218] This shows that when the polarizations of the two subarrays are orthogonal, the polarization estimation perturbation reaches a minimum, i.e. the estimate of the polarization has optimal performance.

[0219] It should be noted that the derivation of the formulas (1), (2), and (3) is as follows.

[0220] Formula (1):

[0221] The relationship between the HCMs of the two different subarrays and can be expressed by matrix row transformation:

[0222] ;

[0223] wherein, is a diagonal matrix, and satisfies:

[0224] ;

[0225] Thus we have:

[0226] ;

[0227] The relation between the row vectors is:

[0228] ;

[0229] The variance of the perturbation can be expressed as:

[0230] ;

[0231] Since the modulus of the diagonal elements of is 1, we have:

[0232] ;

[0233] Then the optimal weight that minimizes the variance of the perturbation can be solved as:

[0234] .

[0235] Equation (2):

[0236] For any real number , consider the integral:

[0237] ;

[0238] When is and , we have:

[0239] ;

[0240] That is:

[0241] ;

[0242] Thus we get the variant of the estimate of polarization:

[0243] ;

[0244] The equation holds if and only if for any and , it satisfies , that is, where C is a constant;

[0245] If the equation is established, then:

[0246] ;

[0247] This shows that when the two sub-arrays are polarized orthogonally, the average disturbance in the direction finding process is minimized.

[0248] Equation (3):

[0249] According to the sub-array harmonic component vector containing the noise term and the estimated value of the polarization, when considering the harmonic noise, the manifold vector and will generate corresponding errors:

[0250] ;

[0251] The simplified expression is shown in the representation of the actual polarization estimation:

[0252] ;

[0253] It can be seen that, and 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.

[0254] The above direction and polarization joint estimation method 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 a polarization mismatch between the incident signal and the receiving array, the direction estimation accuracy can be guaranteed, and the incident direction and polarization parameters of any polarized radiation source can be obtained. In addition, by extracting multiple harmonic signals and using polarization projection weighting processing, the estimation accuracy of direction and polarization is improved, and robust direction finding and polarization estimation performance is achieved.

[0255] Specifically:

[0256] 1) A joint estimation method based on a new AP-TMA architecture is proposed. By changing the polarization of the array elements (without increasing the hardware cost), the polarization mismatch problem in TMA direction finding is solved, the angle-polarization parameters of any polarized signal are robustly estimated, and the spatial-polarization domain perception ability of TMA is enhanced.

[0257] 2) The TMA direction finding result is equivalent to the uniformly weighted combination of multiple subarray angle estimates inside the array. The optimal estimation is the polarization projection weighted estimation of two different polarization subarrays in AP-TMA.

[0258] 3) The optimal configuration criterion of AP-TMA dual-subarray antenna polarization is proposed. The two subarrays only need to satisfy the polarization orthogonal condition without specific polarization combination, which provides practical guidance for the expansion of AP-TMA application.

[0259] It should be understood that, although Figure 1 The steps in the flowchart of the method are displayed in sequence according to the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other orders. Moreover, Figure 1 At least part of the steps in the method can include multiple sub-steps or multiple stages, which are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in rotation or alternation with other steps or sub-steps or stages of other steps.

[0260] In a specific embodiment, the method proposed in the application is verified by simulation, and the influence of signal-to-noise ratio, array element number and incident signal polarization on measurement accuracy is analyzed, and TMA and AP-TMA are compared. The embodiment relates to various polarization settings of AP-TMA, and each configuration is represented by the abbreviation in Table 1. Modes H, V, L and R represent four single-polarized TMAs of horizontal, vertical, left circular and right circular 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.

[0261] Table 1: Mode abbreviations of AP-TMA with different polarization configurations

[0262]

[0263] Table 2: Part of the simulation parameters

[0264]

[0265] A. Estimation accuracy under different signal-to-noise ratios and array element numbers

[0266] The characteristics of the received signal under different SNR and array element number conditions are studied by simulating the time modulation of the RF signal entering the mode HV. The linear relationship between the -4th to +4th harmonic components is used to estimate the polarization parameters and angle of the incident signal, and the performance is evaluated by 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, are estimated by using the harmonic characteristic matrix of the array and the harmonic components of the received signal.

[0267] The main simulation parameters are listed in Table 2, and the subsequent simulation is not specially mentioned. The polarization state of the incident signal is represented by the polarization descriptor , and the polarization descriptor is , i.e. left circular polarization. The received signal is sampled for 1000 points, and the received performance under different SNR and array element number conditions is evaluated by 1000 Monte Carlo simulations, and the RMSE of the estimated parameters is calculated.

[0268] As shown in Figure 3 and Figure 4 , with the increase of the SNR, 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 precision. However, the estimation precision of the two polarization parameters does not significantly improve with the increase of the array element number, because the total sampling points are fixed in the simulation. The increase of the array element number leads to the decrease of the sampling points of the single array element, and the polarization projection energy of each subarray remains unchanged. Therefore, the polarization parameter estimation precision of the method almost only depends on the SNR, but the RMSE of slightly decreases with the increase of the array element number, because the angle and the polarization phase difference information are coupled, and when the angle estimation precision improves, the estimation precision of also improves.

[0269] B. Direction finding precision in full polarization domain

[0270] The incident signals of different polarizations are simulated, and the SNR is set to 10 dB and the array element number 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 AP-TMA, and the performance is evaluated by the RMSE. In order to show the direction finding precision of the AP-TMA, four single-polarization TMAs, i.e. mode H, mode V, mode L and mode R, are compared. The variation ranges of the parameters and are 0° to 90° and 0° to 360° respectively, i.e. the full polarization domain, which represents all the incident signals of different polarizations. The signals with the SNR 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.

[0271] like Figure 5 and Figure 6 As shown, for four different polarization settings, the RMSE reaches its lowest value of 0.045° when polarization is matched. When polarization mismatch exists, the direction-finding RMSE increases sharply, clearly indicating that a single-polarization TMA cannot achieve robust estimation performance for incident signals of arbitrary polarization. Furthermore, due to polarization mismatch, a single-polarization TMA may fail in certain regions of the full polarization domain, making angle estimation impossible.

[0272] like Figure 7 As shown, the overall RMSE of angle estimation by the non-orthogonal polarization AP-TMA is better than that of the single-polarization TMA, but it still exhibits a large error for incident signals with specific polarizations. This is due to the non-orthogonality of the polarizations of the two subarrays. When the array receives incident signals with arbitrary polarizations, the received energy will fluctuate significantly due to the difference in signal polarization.

[0273] like Figure 8 As shown, the RMSE of modes HV and LR remains robust across the entire polarization domain, with the error values ​​for both modes consistently between 0.06° and 0.065°. This is because the subarray polarization in both cases constitutes an orthogonal polarization basis, ensuring a constant total received energy under all conditions.

[0274] The simulations above show that, for arbitrary polarization incident signals, the direction-finding performance of the AP-TMA is superior to that of the single-polarization TMA. Using two subarrays with orthogonal polarization bases can significantly improve direction-finding robustness and achieve higher accuracy.

[0275] C. Accuracy of polarization estimation within the entire polarization domain

[0276] The simulation was also performed for an incident signal with arbitrary polarization, and the parameter settings remained the same as before.

[0277] like Figure 9 As shown, for non-orthogonal polarization AP-TMA estimation The RMSE of Mode 1 is poor due to the poor polarization orthogonality of the subarray, resulting in drastic fluctuations in the RMSE across the entire polarization domain, ranging from a minimum of 0.125° to a maximum of 0.527°; while Mode 2 benefits from better subarray polarization orthogonality, resulting in smaller RMSE fluctuations, ranging from 0.145° to 0.365° within the polarization domain.

[0278] like Figure 10 As shown, mode HV and mode LR The estimated RMSE remains robust across the fully polarized domain, with an error range between 0.175° and 0.185°.

[0279] like Figure 11 and Figure 12 As shown, AP-TMA is used to... When the polarization amplitude ratio The RMSE sharply increases when the polarization approaches 0° and 90°, because the relative amplitude difference between the horizontal and vertical polarization components is too large, which causes the phase information of the smaller polarization component to sharply decrease in signal-to-noise ratio after polarization projection, and it is difficult to obtain the phase information, thereby significantly reducing the estimation accuracy, but this has little effect on the overall information of the polarization parameters. When the polarization approaches 0° or 90°, the importance of the information represented decreases, and therefore it is considered that the AP-TMA maintains a stable estimation performance in the full polarization domain.

[0280] As Figure 11 shown, for the non-orthogonal polarization AP-TMA, the RMSE of mode 1 fluctuates sharply in the entire polarization domain, and the RMSE is less than 0.5° only in a small part of the area; the orthogonality of the two subarrays of mode 2 is better, and the RMSE fluctuates less, and the RMSE is less than 0.5° in most areas, indicating that its direction finding performance is more stable.

[0281] As Figure 12 shown, the AP-TMA of the orthogonal polarization subarray has an RMSE less than 0.5° in most areas, and has a stable estimation performance.

[0282] The above simulation verifies the effectiveness of the method of the present application. The AP-TMA extends the perception ability of the traditional TMA in the polarization dimension, and through the design of the subarray with an orthogonal polarization base, it realizes stable polarization estimation and reduces the root mean square error of the measurement.

[0283] In summary, the present application proposes a new method for realizing joint estimation of direction and polarization by using a single-channel AP-TMA. By combining the AP-TMA with polarization projection weighting, the direction finding failure problem of the traditional single-channel TMA in the case of polarization mismatch is effectively solved, and stable polarization and angle estimation of an arbitrary polarized incident signal is realized, and the system performance is optimal when the polarization mode of the subarray is orthogonal. The simulation further verifies the effectiveness of the method proposed in the present application. Compared with the traditional method, the direction finding robustness of the present application is significantly improved, and the polarization estimation capability is added, which provides a cost-effective solution for the practical application of single-channel TMA.

[0284] The contents not described in detail in the specification belong to the prior art known to those skilled in the art.

[0285] Any technical features in the above embodiments can be combined, and for the sake of brevity, not all possible combinations are described above, however, as long as the combinations of technical features do not contradict each other, they shall be considered within the scope of the present disclosure.

[0286] The above embodiments only express several implementation manners of the present application, and the description is relatively specific and detailed, but it shall not be understood as a limitation on the scope of the present application. It should be noted that, for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present application, and these shall be within the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the appended claims.

Claims

1. A method for joint estimation of direction and polarization based on a time-modulated array, characterized in that, include: Obtain the time modulation array and set up two sets of alternately arranged polarized antennas, with each polarized antenna as an array element and each set of polarized antennas as a subarray, to establish an alternately polarized 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, and then the actual received signal of each array element is obtained. Based on the actual received signal of each array element, establish a linear relationship between the harmonic components, polarization parameters and incident direction of the received signal of each subarray. Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the directional perturbation and the directional function perturbation is obtained. The vector formed by the harmonic components of the subarray is rewritten in the form of including a noise term to obtain the error perturbation between the true value of the directional function and the corresponding estimate. Based on the error perturbation between the true value of the directional function and the corresponding estimate, the estimated value of the direction is obtained. Based on the linear relationship between the harmonic components of the received signal, polarization parameters, and incident direction of each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and radiation source polarization is obtained, and thus the polarization estimate is obtained.

2. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 1, characterized in that, Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained, and thus the actual received signal of each array element is obtained, including: Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained; Based on the received signal, time modulation function, and polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained; Based on the initial representation of the actual received signal of each array element, the time-domain expression of the actual received signal of the two subarrays is obtained; Expanding the time modulation function into a series and combining it with the time-domain expressions of the actual received signals from the two subarrays, we obtain the first series received by the two subarrays. k Second harmonics; According to the first received from the two subarrays 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.

3. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 2, characterized in that, Based on the alternating polarization time modulation array, the received signal, time modulation function, and polarization vector of each array element are obtained, including: In the formula, For the complex amplitude of the signal, Polarization of the incident signal The amplitude and phase of the incident signal, The imaginary unit, The incident signal frequency, For time, For the first The phase of each array element, For the first Each array element, The distance between the phase centers of adjacent array elements. The angle of incidence of the signal. For wavelength, To characterize the relative amplitude of the signal polarization state, To characterize the relative phase of the signal polarization state, for transpose; For time modulation function, It is a positive integer. For time modulation period, The number of array elements. It is a set of integers; For the first Jones vectors polarized by each array element; Based on the received signal, time modulation function, and polarization vector of each array element, the initial representation of the actual received signal of each array element is obtained, including: In the formula, For the first The initial representation of the actual received signal of each array element. for The conjugate; 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 subarrays are obtained, including: In the formula, The received signal for the X-polarized subarray. The received signal for the Y-polarized subarray. For the 2nd n -1 array element receives the signal, For the 2nd n The signal received by each array element; Expanding the time modulation function into a series and combining it with the time-domain expressions of the actual received signals from the two subarrays, we obtain the first series received by the two subarrays. k Subharmonics include: In the formula, For the first The first element receives the signal. k Second harmonic components The first received by the X-polarized subarray k Second harmonic The first received by the Y-polarized subarray k Second harmonic The conjugate of the polarization vector of X polarization. The conjugate of the polarization vector of Y polarization. For when In n Take 2 n The phase at -1 For when In n Take 2 n Phase of time; According to the first received from the two subarrays k The series form of the second harmonics and the time modulation function is used to obtain the series decomposition form of the actual received signal of each subarray, including: In the formula, The received signal for the X-polarized subarray. This is the received signal for the Y-polarized subarray.

4. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 3, characterized in that, Based on the actual received signal of each array element, establish a linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal of each subarray, including: In the formula, Let X be the harmonic characteristic matrix of the X-polarization subarray. The harmonic characteristic matrix of the Y-polarization subarray is... Let X be the array manifold vector of the X-polarization subarray. Let be the array manifold vector of the Y-polarization subarray. The vector formed by the harmonic components of the X-polarized subarray. It is a vector composed of the harmonic components of the Y-polarized subarray.

5. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 4, characterized in that, Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the direction perturbation and the direction function perturbation is obtained. The vector formed by the subarray harmonic components is then rewritten in a form including a noise term, yielding the error perturbation between the true value and the corresponding estimate of the direction function, including: Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the directional perturbation and the directional function perturbation is obtained: In the formula, This is the corresponding estimator of the true value of the direction function of the X-polarization subarray. This is the corresponding estimator of the true value of the direction function of the Y-polarization subarray. For the direction function estimator, for The estimated value, for The OK, for The +1 line, for The estimated value, for The OK, for The +1 line, These are weighting coefficients. For weighted values, for and Estimates of these two theoretical values; Rewriting the vector formed by the subarray harmonic components into a form that includes noise terms yields the subarray harmonic component vector containing noise terms: In the formula, Let be the generalized inverse matrix of the harmonic characteristic matrix of the X-polarization subarray. Let be the generalized inverse matrix of the harmonic characteristic matrix of the Y-polarization subarray. for The estimated value, for The estimated value, To extract harmonic estimates The noise vector at that time, To extract harmonic estimates The noise vector at that time; Based on the relationship between the direction perturbation and the direction function perturbation, and the subarray harmonic component vector containing the noise term, the error perturbation between the true value of the direction function and the corresponding estimate is obtained: In the formula, for and Error disturbance between for and Error disturbance between Let be the truth value of the direction function of the X-polarization subarray. Let be the true value of the direction function of the Y-polarization subarray.

6. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 5, characterized in that, Based on the error perturbation between the true value of the direction function and the corresponding estimator, the estimated value of the direction is obtained, including: Based on the error perturbation between the true value of the direction function and the corresponding estimator, a second-order approximation is performed to obtain an approximate expression for the error perturbation; The variance of the disturbance is obtained based on the approximate expression for the error disturbance. Based on the variance of the disturbance, the least squares method is used to obtain the error covariance matrix; Based on the error covariance matrix, the variance of the disturbance in the estimated value is obtained; Based on the variance of the perturbation in the estimated values, the optimal weights that minimize the variance of the direction-finding perturbation are obtained. Based on the optimal weights that minimize the variance of the direction-finding perturbation and the relationship between the direction perturbation and the direction function perturbation, the estimated value of the direction is obtained.

7. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 6, characterized in that, Based on the error perturbation between the true value of the direction function and the corresponding estimator, a second-order approximation is performed to obtain an approximate expression for the error perturbation, including: In the formula, for The first line, in which, It is the generalized inverse matrix of the harmonic characteristic matrix of the X-polarization subarray. It is to extract harmonic estimation The noise vector at that time, For when In n Take the phase at time 3. For when In n When taking N / 2 , For when In n Take the phase at N+1; Based on the approximate expression for the error disturbance, the variance of the disturbance is obtained, including: In the formula, For error disturbance variance For error disturbance variance For noise power, For the Euclidean norm, For when In n Take the phase at N-2; Based on the variance of the disturbance, the least squares method is used to obtain the error covariance matrix, which includes: In the formula, Let be the error covariance matrix. It is a diagonal matrix; Based on the error covariance matrix, the variance of the disturbance in the estimated value is obtained, including: In the formula, For variance, It is a direction function; Based on the variance of the perturbation in the estimated values, the optimal weights that minimize the variance of the direction-finding perturbation are obtained, including: In the formula, The optimal weights that minimize the variance of the direction-finding disturbance; Based on the optimal weights that minimize the variance of the direction-finding perturbation and the relationship between the direction perturbation and the direction function perturbation, the estimated value of the direction is obtained, including: In the formula, This is an estimate of the direction.

8. The method for joint estimation of direction and polarization based on a time-modulated array according to claim 7, characterized in that, Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and radiation source polarization is obtained, thus yielding the polarization estimate, including: Based on the linear relationship between the harmonic components, polarization parameters, and incident direction of the received signal in each subarray, the relationship between the polarization matching coefficient of the array manifold vector estimate and the antenna polarization and radiation source polarization is obtained: In the formula, For when In n Take the phase of 1; The estimated values ​​of polarization are obtained: In the formula, for The conjugate transpose of . for The conjugate transpose of .

9. A method for joint estimation of direction and polarization based on a time-modulated array according to any one of claims 1 to 4, characterized in that, The perturbation of the direction estimate is minimized when the polarizations of the two subarrays are orthogonal.

10. A method for joint estimation of direction and polarization based on a time-modulated array according to any one of claims 1 to 4, characterized in that, The polarization estimate perturbation is minimized when the polarizations of the two subarrays are orthogonal.

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