Conformal array joint angle-polarization parameter estimation method based on two-step least squares

Abstract

The application discloses a kind of based on two-step least square's conformal array angle-polarization parameter joint estimation method, belong to array signal processing technical field.The method of the present application includes: first, according to the establishment of received signal model conformal array model;Second, for several unknown signal source number, unknown angle and unknown polarization parameter incident signal, the angle parameter of all incident signals is estimated by first step least square method, and the number of signal sources is determined according to the number of peak values;Finally, using the polarization sensitivity of conformal array to space signal, select part of unobstructed element to construct observation equation, the polarization parameter of each incident signal is solved by second step least square method based on the estimated angle parameter.The based on two-step least square's conformal array angle-polarization parameter joint estimation method has the advantages of not needing to estimate signal source number in advance, high parameter estimation accuracy, simple and practical method and the like.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, and more specifically, relates to a method for joint estimation of conformal array angle-polarization parameters based on two-step least squares. Background Technology

[0002] Conformal array antenna elements are typically attached to the surface of a carrier, providing an aerodynamic shape consistent with the carrier. Compared to traditional linear and area arrays, conformal arrays offer advantages such as better concealment, wider detection range, relatively larger effective aperture, and relatively smaller radar cross-section (RCS), making them promising for applications in communications, airborne, missile-borne, and spaceborne systems. Direction of Arrival (DOA) estimation for conformal arrays, also known as angle estimation, is a classic problem in array signal processing. However, due to the curvature of the carrier, the orientation of each antenna element in a conformal array varies, resulting in different polarization responses to incoming signals. This inherently makes them sensitive to signal polarization. Because of the coupling between the angle and polarization information of the conformal array, DOA estimation performance is affected by polarization information. On the other hand, existing research shows that polarization information can effectively improve signal processing performance, for example, in applications such as space-time adaptive processing and anti-interference. However, polarization parameter estimation is the cornerstone of subsequent signal processing using polarization information. Therefore, joint estimation of angle and polarization parameters for conformal arrays is of paramount importance.

[0003] Currently, research on joint angle-polarization estimation for conformal arrays often extends traditional array parameter estimation methods. Existing methods include subspace-based algorithms, such as Multiple Signal Classification (MUSIC), and sparse recovery algorithms based on compressed sensing, such as Variational Sparse Bayesian Learning (VSBL). For subspace-based methods, it is often necessary to estimate the number of signal sources to construct signal and noise subspaces. However, in some scenarios, it is difficult to accurately estimate the number of signal sources, thus affecting subsequent parameter estimation. For sparse recovery algorithms, the large computational complexity and storage requirements, as well as the unavoidable off-grid problem, pose challenges to practical applications. Therefore, it is valuable to invent a joint angle-polarization parameter estimation algorithm for conformal arrays that does not require prior information about the number of signal sources, is simple and practical, and has high parameter estimation accuracy. Summary of the Invention

[0004] This invention provides a two-step least squares-based method for joint estimation of conformal array angle and polarization parameters, which enables joint estimation of array angle and polarization parameters without prior information on the number of signal sources, thereby improving the estimation accuracy of related parameters.

[0005] The technical solution adopted in this invention is as follows:

[0006] The two-step least squares conformal array angle-polarization parameter joint estimation method includes the following steps:

[0007] Step S1: Establish the received signal model based on the conformal array model. Specifically, the received signal model is as follows:

[0008]

[0009] Where Y represents the received signal data matrix (referred to as the received signal), K is the number of unknown signal sources, and θ k and γ represents the elevation and azimuth angles of the k-th signal. k and η k The polarization phase descriptor of the k-th signal, or simply the polarization parameter, γ k η represents the polarization angle. k Indicates polarization phase difference, Let N be the Gaussian white noise matrix, and N be the total number of elements. s The number of signal sampling points. e(γ k ,η k ) are the array manifold and spatial incoming signal matrix of the conformal array, respectively. diag(·) represents diagonal matrix operations. Let be the radiation pattern matrix composed of the radiation patterns of all array elements of the k-th signal. Let k be the spatial steering vector of the k-th signal. Let be the polarization Jones vector of the k-th signal. The specific signal form of the k-th signal;

[0010] Step S2: Estimate the angle parameters of all incident signals using the least squares method from the first step, and determine the number of signal sources based on the number of peaks in the response function;

[0011] Step S3: Select some unobstructed array elements to construct the observation equation;

[0012] Step S4: Based on the angle parameters of all incident signals estimated in step S2, and according to the observation equation constructed in step S3, obtain the polarization parameters of all incident signals through the second step least squares method.

[0013] Further, step S2 specifically includes:

[0014] Step S201: Further simplify the expression, making the intermediate parameters Let the intermediate parameter e k =e(γ) k ,η k The received signal Y is simplified as follows:

[0015]

[0016] Step S202: Assuming the incident signal sources are independent of each other, the sample covariance matrix of the received signal Y can be expressed as:

[0017]

[0018] Among them, matrix Let I represent the noise power, and let I denote the identity matrix.

[0019] Step S203: Separate the k-th signal, treat the remaining K-1 signals and noise as interference signals, and re-represent the received signal Y as follows:

[0020]

[0021] Among them, intermediate parameters intermediate parameter e m =e(γ) m ,η m ), θ m and γ represents the elevation and azimuth angles of the m-th signal. m and η m This represents the polarization phase descriptor of the m-th signal. This represents the interference plus noise signal of the k-th signal;

[0022] Step S204: Add interference and noise to the signal j k The covariance matrix can be expressed as:

[0023]

[0024] Step S205: Obtain e k The least squares estimate is:

[0025]

[0026] According to the matrix inversion lemma It can be simplified to:

[0027]

[0028] Furthermore, it can be Simplify to

[0029]

[0030] in, Follow A k It changes with the changes, that is Follow θ and This represents the pitch and azimuth angles of the signal in the angular domain.

[0031] Step S206: Define the response function As shown below:

[0032]

[0033] Among them, intermediate parameters Traverse the angle domain, when When matched with the angle parameter of a certain incident signal, This will result in peak values, and the number of peak values ​​corresponds to the number of signal sources. Simultaneously, the position corresponding to the k-th peak value... This is the estimated value of the Jones vector of the polarization of the k-th incident signal. However, the polarization parameter estimation by one-step least squares has a large error, so it is necessary to solve for the polarization parameters of all incident signals by another one-step least squares method.

[0034] That is, traversing the angle domain based on the response function. The number of peaks determines the value of the number of signal sources K, and is based on the corresponding peak values. Determine the estimated angle of the angular parameters of each incident signal.

[0035] Furthermore, in step S3, the constructed observation equation is specifically as follows:

[0036]

[0037] in, This represents the received signal data matrix composed of the selected unobstructed array elements. This represents the Gaussian white noise matrix corresponding to the selected array element. Indicates the number of selected array elements, intermediate parameter This represents the radiation pattern matrix corresponding to the selected array element for the k-th signal. This represents the spatial steering vector corresponding to the selected array element for the k-th signal.

[0038] Furthermore, step S4 specifically includes:

[0039] The estimated angles of the K incident signal angle parameters obtained in step S2. Substituting into the observation equation, we get:

[0040]

[0041] make p k =p(γ) k ,η k ), will receive the signal data matrix Transformed into:

[0042]

[0043] make Will Transformed into:

[0044]

[0045] The least-squares estimate of the polarization Jones vector for all incident signals is obtained as follows:

[0046]

[0047] in, for The lth column, The polarization Jones vector estimation results for K incident signals;

[0048] Based on polarization Jones vector estimation results The estimated values ​​of the polarization parameters of K signals are obtained.

[0049] The technical solution provided by this invention brings at least the following beneficial effects:

[0050] Compared with existing conformal array angle-polarization parameter joint estimation techniques, this invention has the advantages of not requiring prior information on the number of signal sources, being simple and practical, and having high parameter estimation accuracy. Attached Figure Description

[0051] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0052] Figure 1 A flowchart illustrating the conformal array angle-polarization parameter joint estimation method based on two-step least squares provided in an embodiment of the present invention;

[0053] Figure 2 This is a schematic diagram of a hemispherical conformal array according to an embodiment of the present invention;

[0054] Figure 3 This is a simulation diagram of angle estimation in an embodiment of the present invention;

[0055] Figure 4 The following are curves showing the variation of the RMSE of parameter estimation with the signal-to-noise ratio in an embodiment of the present invention: (4-a) is the curve showing the variation of the angle parameter estimation error with the signal-to-noise ratio; (4-b) is the curve showing the variation of the polarization parameter estimation error with the signal-to-noise ratio under one-step least squares and two-step least squares.

[0056] Figure 5 The following are curves showing the variation of the RMSE of parameter estimation with the number of snapshots in an embodiment of the present invention. (5-a) is the curve showing the variation of the angle parameter estimation error with the number of snapshots; (5-b) is the curve showing the variation of the polarization parameter estimation error with the number of snapshots under one-step least squares and two-step least squares. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0058] like Figure 1 As shown, this embodiment of the invention provides a method for joint estimation of conformal array angle-polarization parameters based on two-step least squares, the specific implementation steps of which include:

[0059] S1: Establish the received signal model based on the conformal array model.

[0060] Common conformal arrays include cylindrical conformal arrays, conical conformal arrays, and hemispherical conformal arrays. The embodiments of this invention use... Figure 2 Taking the hemispherical conformal array shown as an example, a conformal array model is established. Figure 2 As shown, the radius of the hemispherical conformal array is R, the vertex of the hemisphere is located on the positive Z-axis of the global Cartesian coordinate system, and the center of the sphere coincides with the origin O. Array elements are placed on the hemisphere along concentric rings, with the largest ring having a radius of R. The largest ring is located in the XOY plane, and the arc length between adjacent rings is l1 = 0.5λ, where λ is the signal wavelength. The spacing between adjacent array elements on the same ring is l2 = 0.5λ. One adjacent array element is placed along the tangent of the ring, denoted by "o"; the other is placed along the parallel of the ring, denoted by "x". Assume the hemispherical conformal array has N array elements, and the coordinates of the nth array element in the global Cartesian coordinate system are d. n =[x n ,y n ,z n ] T For K far-field narrowband signals, their normalized incident direction vector is: Where θ is the pitch angle. It is the azimuth angle.

[0061] The spatial steering vector of the k-th signal can be expressed as:

[0062]

[0063] The received signal model can be specifically represented as:

[0064]

[0065] Where K is the number of unknown signal sources; This is the polarization spatial steering vector for the k-th signal; Let N be the specific signal form of the k-th signal. s N is the number of signal sampling points; N is the Gaussian white noise matrix; This represents the pattern matrix composed of the pattern patterns of all array elements of the k-th signal; Let be the polarization Jones vector of the k-th signal; for ease of description, let

[0066]

[0067] S2: Construct the first step of the least squares method to estimate the angular parameters of all incident signals, and obtain the number of signal sources based on the number of peaks in the response function. Specifically:

[0068] S201: Further simplify the expression, making Let e k =e(γ) k ,η k The received signal is simplified to...

[0069]

[0070] S202: Assuming the incident signal sources are independent of each other, the sample covariance matrix of the received signal Y can be expressed as:

[0071]

[0072] in, Let I represent the noise power and I denote the identity matrix.

[0073] S203: Separate the k-th signal, treat the remaining K-1 signals and noise as interference signals, and re-represent the received signal Y as follows:

[0074]

[0075] S204: Interference plus noise signal j k The covariance matrix can be expressed as

[0076]

[0077] S205: Obtain e k The least squares estimate is

[0078]

[0079] According to the matrix inversion lemma It can be simplified to

[0080]

[0081] Furthermore, it can be Simplify to

[0082]

[0083] in, Follow A k It changes with the changes, that is Follow It changes with the changes.

[0084] S206: Define the response function As shown below

[0085]

[0086] in, Traverse the angle domain, when When matched with the angle parameter of a certain incident signal, This will result in peak values, and the number of peak values ​​corresponds to the number of signal sources. Simultaneously, the position corresponding to the k-th peak value... This is the estimated value of the Jones vector of the polarization of the k-th incident signal. However, the polarization parameter estimation in one-step least squares has a large error, so it is necessary to solve for the polarization parameters of all incident signals by another one-step least squares method.

[0087] S3: Based on the polarization sensitivity of the conformal array to the incident signal, a subset of array elements are selected to construct the observation equation. Specifically:

[0088]

[0089] in, The received signal data matrix formed by the selected array elements; The number of selected array elements.

[0090] S4: Based on the estimated angle parameters in step S2, the polarization parameters of all incident signals are solved using the least squares method in the second step. For the K estimated angles... Combining the observation equations, we have

[0091]

[0092] To simplify the expression, let p k =p(γ) k ,η k ),

[0093] The least-squares estimate of the polarization Jones vector of all incident signals is obtained as follows:

[0094]

[0095] in, for The lth column; The above equation represents the polarization Jones vector estimation results for K incident signals. Since the spatial orientation and position of each element in the conformal array are different, the above equation... The fact that the column must be of full rank indicates that least squares must have a solution. Further, we obtain the estimated polarization parameters of the K signals. Specifically, the polarization parameters of the k-th signal are:

[0096]

[0097]

[0098] Here, angle(·) represents the phase angle operation.

[0099] In the simulation, it is assumed that K = 3 independent narrowband signals are incident on a hemispherical conformal array in the far field, with carrier frequencies of 150MHz, 200MHz, and 250MHz, and corresponding angle-polarization parameters of [missing information]. and When the signal-to-noise ratio is 20dB, the number of snapshots N s =2600, Figure 3 The angle estimation results are given. Without loss of generality, Figure 4 The number of snapshots N is given. s When Q = 2600, under 200 Monte Carlo experiments, the RMSE curve of the parameter estimation method of this invention as a function of signal-to-noise ratio (SNR) is shown. The RMSE is defined as follows:

[0100]

[0101]

[0102] Figure 5The present invention provides the RMSE of parameter estimation for the method of the present invention as a function of the number of snapshots N under the condition of Q=200 Monte Carlo experiments with a signal-to-noise ratio (SNR) of -5dB. s The variation curve is shown. Simulation results show that the angle parameter estimation method of this invention is almost unaffected by the number of snapshots, and the parameter estimation error is small with high resolution. Simultaneously, the relevant analysis in step S206 is verified; the two-step least squares method effectively reduces the polarization parameter estimation error compared to the one-step least squares method.

[0103] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0104] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A two-step least squares based joint angle-polarization parameter estimation method for conformal arrays, characterized in that, The method comprises the following steps: Step S1, establishing a received signal model according to a conformal array model; where Y denotes the conformal array received signal data matrix, K is the unknown number of signal sources, θ k and denote the elevation and azimuth angle of the kth signal, γ k and η k denote the polarization angle and polarization phase difference of the polarization phase descriptor of the kth signal, is a Gaussian white noise matrix, N is the total number of array elements, N s is the number of signal sampling points, e(γ k ,η k ) respectively denote the array manifold of the conformal array and the matrix of the spatial wave signals, diag(·) is the diagonal matrix operation, corresponds to the directivity matrix composed of the directivity pattern of all array elements of the kth signal, denotes the spatial domain steering vector of the kth signal, is the polarization Jones vector of the kth signal, is the specific signal form of the kth signal; Step S2, estimating angle parameters of all incident signals through a first-step least square method, and determining a number of signal sources according to a number of peak values of a response function; Step S3, selecting part of unshielded array elements to construct an observation equation; Step S4, based on the angle parameters of all incident signals estimated in step S2, according to the observation equation constructed in step S3, obtaining polarization parameters of all incident signals through a second-step least square method.

2. The method of claim 1, wherein, The step S2 specifically comprises: Step S201: Let an intermediate variable Let an intermediate variable e k = e(γ k ,η k ), simplify Y to: Step S202, expressing a sample covariance matrix of Y as: where the matrix is the noise power, and I denotes the identity matrix. Step S203, separating out a kth signal, regarding the remaining K-1 signals and noise as interference signals, and re-expressing Y as: where the intermediate variable The intermediate variable e m = e(γ m , η m ), θ m and denotes the elevation and azimuth angle of the m-th signal, γ m and η m denote the polarization phase descriptors of the m-th signal, denotes the interference plus noise signal of the k-th signal; Step S204: adding an interference noise signal j k The covariance matrix of the interference noise signal j is represented as: Step S205: Obtain e k The least square estimate of e is: According to the matrix inversion lemma, we have which simplifies to: Step S206: Defining a response function wherein the intermediate variable θ and denote the elevation and azimuth angle of the signal in the angular domain; traversing the angular domain, determining the value of the number of signal sources K based on the number of peaks of the response function and determining the estimated angles of the angular parameters of the incident signals based on the angles corresponding to each peak ​ 3. The method of claim 1, wherein, In the step S3, the constructed observation equation is specifically: wherein, represents the received signal data matrix of selected unoccluded elements, represents the Gaussian white noise matrix corresponding to the selected elements, represents the number of selected elements, the intermediate variable represents the steering matrix of the kth signal corresponding to the selected elements, represents the spatial domain steering vector of the kth signal corresponding to the selected elements.

4. The method of claim 3, wherein, The step S4 specifically comprises: the estimated angle of the angle parameter of the K incident signals estimated in step S2 Substituting into the observation equation, we get: Let p k = p(γ k ,η k ), the received signal data matrix is transformed to: Let will be transformed into: The least square estimation of the polarization Jones vector of all incident signals is: wherein is the first column of is the polarization Jones vector estimate of the K incident signals; Based on the polarization Jones vector estimation result The polarization parameter estimates for the K signals are obtained.

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