DOA estimation method for conformal polarization-sensitive array based on virtual array extension technology

Abstract

The present invention discloses a conformal polarization sensitive array DOA estimation method based on virtual array extension technology, comprising determining a sparse non-uniform linear array from a conformal polarization sensitive array, constructing a first array flow pattern of the conformal polarization sensitive array and a second array flow pattern of the sparse non-uniform linear array; calculating a first covariance matrix according to the first array flow pattern and a spatial signal; calculating a second covariance matrix according to the second array flow pattern and the spatial signal; using the virtual array extension technology to expand the sparse non-uniform linear array to obtain a virtual uniform linear array, and constructing a third array flow pattern of the virtual uniform linear array; obtaining a virtual transformation matrix according to the second array flow pattern and the third array flow pattern; processing the second covariance matrix using the virtual transformation matrix to obtain a third covariance matrix; and performing DOA estimation according to the third covariance matrix and the first covariance matrix, thereby improving the estimation accuracy and obtaining a more accurate spatial signal angle measurement result, and the implementation is simple and low-cost.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and in particular relates to a method for estimating DOA (Direction of Arrival) of a conformal polarization-sensitive array based on a virtual array extension technology. Background Art

[0002] Conformal arrays are attached to the surface of a carrier, conforming to its structure. This arrangement maintains consistency with the carrier's shape, maximizing its aerodynamic performance, improving space utilization, and enhancing the stealth capabilities of the equipment carried. Conformal arrays are widely used on high-speed carriers such as aircraft, satellites, and missiles.

[0003] Since the carrier structure cannot be destroyed, the conformal array structure is sparse and irregular, the number of array elements is limited, and it does not have the good performance of regular arrays such as uniform circular arrays. The two-dimensional conformal array with discontinuous azimuth arrangement has the problem of poor DOA estimation accuracy and cannot perform direction finding tasks normally.

[0004] For irregular conformal polarization-sensitive arrays, the existing solutions to address the poor DOA estimation accuracy are divided into the following three categories: offline calibration and storage of amplitude and phase errors, installation of real-time correction hardware modules in the device, and increasing the number of array elements.

[0005] Among them, the offline calibration and storage of amplitude and phase errors has a long implementation cycle, and the amplitude and phase inconsistencies of the receiving channel vary greatly with increasing temperature. If all ambient temperatures of the carrier are to be covered, it will put huge pressure on the carrier's internal storage and increase the carrier hardware cost. In addition, the installation of a real-time correction hardware module in the carrier requires sufficient internal space. However, in actual engineering, the internal space of small aircraft is limited and it is impossible to install this module. Increasing the number of array elements in an irregular conformal polarization-sensitive array does not have good deambiguation capabilities due to the discontinuous space on the carrier where the array elements can be placed. In addition, adding array elements will also increase costs.

[0006] In summary, there is an urgent need for a DOA estimation method for conformal polarization-sensitive arrays with high estimation accuracy, simple implementation and low cost. Summary of the Invention

[0007] In order to solve the above problems existing in the prior art, the present invention provides a DOA estimation method for a conformal polarization-sensitive array based on a virtual array extension technology.

[0008] The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0009] The present invention provides a conformal polarization sensitive array DOA estimation method based on virtual array extension technology, comprising:

[0010] Determining a sparse non-uniform linear array from a conformal polarization-sensitive array, and constructing a first array flow pattern of the conformal polarization-sensitive array and a second array flow pattern of the sparse non-uniform linear array;

[0011] Calculate a first covariance matrix of received data of the conformal polarization sensitive array according to the first array flow pattern and spatial signal;

[0012] Calculate a second covariance matrix of the received data of the sparse non-uniform linear array according to the second array flow pattern and the spatial signal;

[0013] Expanding the sparse non-uniform linear array using a virtual array expansion technique to obtain a virtual uniform linear array, and constructing a third array flow pattern of the virtual uniform linear array;

[0014] Obtaining a virtual transformation matrix according to the second array flow pattern and the third array flow pattern;

[0015] Processing the second covariance matrix using the virtual transformation matrix to obtain a third covariance matrix of received data of the virtual uniform linear array;

[0016] DOA estimation is performed according to the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal.

[0017] Optionally, determining a sparse non-uniform linear array from a conformal polarization-sensitive array includes:

[0018] Determine the horizontal axis of the conformal polarization sensitive array;

[0019] The array elements on the horizontal axis are formed into a sparse non-uniform linear array.

[0020] Optionally, performing DOA estimation according to the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal includes:

[0021] performing eigenvalue decomposition on the third covariance matrix, and then calculating the first spatial spectrum to obtain the azimuth angle of the spatial signal;

[0022] determining a second spatial spectrum of the conformal polarization-sensitive array according to the first covariance matrix;

[0023] The elevation angle of the spatial signal is searched for in the second spatial spectrum according to the azimuth angle of the spatial signal.

[0024] Optionally, the first array flow pattern is:

[0025]

[0026] Wherein, a(·) represents the conformal polarization sensitive array steering vector; the azimuth angle of the nth spatial signal is θ n Indicates; the pitch angle of the nth spatial signal is expressed as Indicates; the polarization auxiliary angle of the nth spatial signal is γ n The polarization phase difference of the nth spatial signal is represented by η n Indicates; n=1,2...N.

[0027] Optionally, the second array flow pattern is:

[0028]

[0029] The distance between the mth array element and the m-1th array element in the sparse non-uniform linear array is d m Indicates that m = 2...M sub ;M sub represents the total number of array elements in the sparse non-uniform linear array; the azimuth angle of the nth spatial signal is θ n represents; n=1,2...N; j represents an imaginary unit; e represents a natural base; λ represents the wavelength of the spatial signal; π represents pi.

[0030] Optionally, the third array flow pattern is:

[0031]

[0032] Wherein, d represents the element spacing in the virtual uniform linear array; the azimuth angle of the nth spatial signal is θ n represents; n=1,2...N; j represents an imaginary unit; e represents a natural base; λ represents the wavelength of the spatial signal; π represents pi; M v represents the total number of array elements in the virtual uniform linear array.

[0033] Optionally, the virtual transformation matrix is ​​calculated as follows:

[0034] B=(T H T) -1 / 2 T H ;

[0035] Wherein, B represents the virtual transformation matrix; A sub represents the second array flow pattern; A represents the first array flow pattern; A visual A represents the third array flow pattern; sub (θ) represents the second array flow pattern of the spatial signal with an azimuth angle of θ; A(θ) represents the first array flow pattern of the spatial signal with an azimuth angle of θ; A visual(θ) represents the third array manifold with the azimuth angle of the spatial signal being θ; θ represents the azimuth angle of the spatial signal; and the superscript H represents the matrix conjugate transpose.

[0036] Optionally, using the virtual transformation matrix to process the second covariance matrix to obtain a third covariance matrix of the received data of the virtual uniform linear array includes:

[0037]

[0038] Among them, R visual represents the third covariance matrix; R sub represents the second covariance matrix; σ n Represents the noise power corresponding to the nth spatial signal; n = 1, 2...N.

[0039] The present invention provides a conformal polarization-sensitive array DOA estimation method based on virtual array expansion technology. By using this technology to expand a sparse non-uniform linear array, a virtual uniform linear array is obtained. DOA estimation is then performed using the third covariance matrix of the received data from the virtual uniform linear array and the first covariance matrix of the received data from the conformal polarization-sensitive array. This improves the array's degrees of freedom and the accuracy of azimuth estimation, thereby increasing the accuracy of DOA estimation and achieving more precise spatial signal angle measurement results.

[0040] In addition, the conformal polarization-sensitive array DOA estimation method based on virtual array extension technology provided by the present invention does not increase hardware cost or damage the device structure, and is simple to implement and low-cost.

[0041] The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 1 is a flow chart of a method for estimating DOA of a conformal polarization-sensitive array based on virtual array extension technology provided by an embodiment of the present invention;

[0043] Figure 2 1 is a schematic structural diagram of a conformal polarization sensitive array provided by an embodiment of the present invention;

[0044] Figure 3 is a structural diagram of a virtual uniform linear array provided by an embodiment of the present invention;

[0045] Figure 4 This is a schematic diagram of the placement angle of a single dipole antenna;

[0046] Figure 5 It is a schematic diagram of the MUSIC spatial spectrum of the conformal polarization sensitive array;

[0047] Figure 6 It is a schematic diagram of the MUSIC spatial spectrum of a virtual uniform linear array;

[0048] Figure 7 This is a schematic diagram of the direction-finding error of the conformal polarization-sensitive array;

[0049] Figure 8 This is a schematic diagram of the direction-finding error of the conformal polarization-sensitive array after expansion based on the virtual array expansion technology. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0051] In order to solve the problems of low estimation accuracy, high cost and high implementation difficulty in the existing conformal polarization sensitive array DOA estimation method, the embodiment of the present invention provides a conformal polarization sensitive array DOA estimation method based on virtual array extension technology, see Figure 1 , Figure 1 1 is a flow chart of a method for DOA estimation of a conformal polarization-sensitive array based on virtual array extension technology provided by an embodiment of the present invention, which specifically includes the following steps:

[0052] Step S101 : determining a sparse non-uniform linear array from a conformal polarization-sensitive array, and constructing a first array flow pattern of the conformal polarization-sensitive array and a second array flow pattern of the sparse non-uniform linear array.

[0053] The structure of the conformal polarization sensitive array depends on the aerodynamic shape of the device it carries. The elements of the conformal polarization sensitive array are sparsely arranged in the position where the device can carry the elements. Figure 2 , Figure 2 Schematic diagram of the structure of the conformal polarization sensitive array provided by the embodiment of the present invention. Figure 2 In the paper, the conformal polarization-sensitive array is divided into two sub-arrays, where sub-array 1 is a sparse non-uniform linear array, and the other array elements except sub-array 1 constitute sub-array 2, which is an irregular sparse array.

[0054] An array flow pattern is a collection of steering vectors that is related to the array shape and the incoming spatial signal direction. Therefore, a conformal polarization-sensitive array's first array flow pattern can be constructed based on the spatial signal and a conformal polarization-sensitive array. A sparse non-uniform linear array's second array flow pattern can be constructed based on the spatial signal and a sparse non-uniform linear array.

[0055] Step S102 : calculating a first covariance matrix of received data of the conformal polarization-sensitive array according to the first array flow pattern and the spatial signal.

[0056] In an embodiment of the present invention, the position, number, and polarization direction of the array elements in the conformal polarization-sensitive array can be determined based on the first array flow pattern. Then, the first covariance matrix of the received data of the conformal polarization-sensitive array can be calculated based on the spatial signal.

[0057] The covariance matrix is ​​a Hermitian matrix in which each element represents the covariance between a pair of variables. The first covariance matrix can be used to represent the covariance between the received data of each element of the conformal polarization sensitive array, indicating the correlation between the received data of each element.

[0058] Step S103 : calculating a second covariance matrix of the received data of the sparse non-uniform linear array according to the second array flow pattern and the spatial signal.

[0059] Similarly, the position, number, and polarization direction of the array elements in the sparse non-uniform linear array can be determined based on the second array flow pattern. Then, the second covariance matrix of the received data of the sparse non-uniform linear array can be calculated based on the spatial signal.

[0060] The second covariance matrix can be used to represent the covariance between the data received by each array element of the sparse non-uniform linear array, indicating the correlation between the data received by each array element.

[0061] Step S104 : Expand the sparse non-uniform linear array using a virtual array expansion technology to obtain a virtual uniform linear array, and construct a third array flow pattern of the virtual uniform linear array.

[0062] Virtual array expansion technology involves using various techniques, including constructing a specific array structure model, mathematically processing the received signal source, and performing virtual array transformations, to achieve objectives such as expanding the original array aperture or increasing the number of elements. Applying various virtual array techniques, such as increasing the number of virtual elements, widening the array aperture, or transforming the array configuration, can significantly improve estimation accuracy, enhance array robustness, and achieve decoherence. Virtual array expansion technology can be used for the layout of large antenna arrays and the placement of irregular array antennas. Key methods for virtual array expansion include fourth-order cumulants, extrapolation, and interpolation.

[0063] See also Figure 3 , Figure 3 Figure 2 is a schematic diagram of the structure of a virtual uniform linear array provided by an embodiment of the present invention. Along the horizontal axis, a sparse non-uniform linear array is expanded by interpolation to obtain a virtual uniform linear array. The spacing between array elements in the virtual uniform linear array is equal, d, and the azimuth angle of the spatial signal is θ.

[0064] A third array flow pattern of a virtual uniform linear array can be constructed according to the spatial signal and the virtual uniform linear array.

[0065] Step S105 , obtaining a virtual transformation matrix according to the second array flow type and the third array flow type.

[0066] In the embodiment of the present invention, the second array flow pattern is an array flow pattern of a sparse non-uniform linear array, and the third array flow pattern is an array flow pattern of a virtual uniform linear array obtained by expanding the sparse non-uniform linear array. Therefore, based on the relationship between the second array flow pattern and the third array flow pattern, a virtual transformation matrix can be obtained.

[0067] Step S106: Process the second covariance matrix using the virtual transformation matrix to obtain a third covariance matrix of the received data of the virtual uniform linear array.

[0068] In this embodiment of the present invention, the second covariance matrix is ​​the covariance matrix of the received data of the sparse non-uniform linear array. Therefore, by processing the second covariance matrix according to the virtual transformation matrix obtained in step S105, the third covariance matrix of the received data of the virtual uniform linear array can be obtained.

[0069] The third covariance matrix of the received data of the virtual uniform linear array indicates the correlation between the received data of each array element in the virtual uniform linear array.

[0070] Step S107 : performing DOA estimation according to the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal.

[0071] In the embodiment of the present invention, after obtaining the third covariance matrix and the first covariance matrix, a MUSIC (Multiple Signal Classification) algorithm may be used to perform DOA estimation to obtain an angle measurement result of the spatial signal.

[0072] The MUSIC algorithm is based on subspace decomposition. It uses the eigenvalues ​​of the third covariance matrix and the first covariance matrix to obtain the noise subspace, and uses the orthogonality of the signal subspace and noise subspace to construct a spatial spectrum. By searching for spectral peaks, it estimates the direction of arrival of the spatial signal, including azimuth and elevation angles.

[0073] In this embodiment of the present invention, a virtual uniform linear array is obtained by expanding a sparse non-uniform linear array using virtual array expansion technology. DOA estimation is then performed using the third covariance matrix of the received data from the virtual uniform linear array and the first covariance matrix of the received data from the conformal polarization-sensitive array. This improves the array's degrees of freedom and the accuracy of azimuth estimation, thereby increasing the accuracy of DOA estimation and achieving more precise spatial signal angle measurement results.

[0074] In addition, the conformal polarization-sensitive array DOA estimation method based on virtual array extension technology provided by the embodiment of the present invention does not increase hardware cost or damage the device structure, and is simple to implement and low-cost.

[0075] In DOA estimation, the biggest difference from conventional DOA estimation algorithms is that the application of virtual array technology can improve the utilization efficiency of array element antennas and greatly improve the degree of freedom of the entire array.

[0076] In one implementation, determining a sparse non-uniform linear array from a conformal polarization-sensitive array includes: determining a horizontal axis of the conformal polarization-sensitive array; and assembling array elements on the horizontal axis into a sparse non-uniform linear array.

[0077] See also Figure 2 The x-axis in the xoy coordinate system is the horizontal axis of the conformal polarization-sensitive array. The four array elements on this horizontal axis point in the same direction, forming a one-dimensional non-uniform linear array, denoted as sub-array 1, thus obtaining a sparse non-uniform linear array. The remaining four array elements are denoted as sub-array 2, thus obtaining an irregular sparse array.

[0078] Assume that there are N signal sources in space, i.e., spatial signals, incident on the conformal polarization sensitive array, and their two-dimensional wave arrival direction is θ n is the azimuth of the nth spatial signal, is the elevation angle of the nth spatial signal, and the coordinates of the array element in the conformal polarization sensitive array are (x m ,y m ,z m ),m=1,..,M, then the receiving signal models of the conformal polarization sensitive array and the sparse non-uniform linear array are:

[0079] X(t)=AS(t)+n(t);

[0080] X sub (t) = A sub S(t)+n(t);

[0081] Where X(t) represents the received signal model of the conformal polarization sensitive array; A represents the array flow type of the conformal polarization sensitive array, that is, the first array flow type; S(t) represents the spatial signal matrix; n(t) represents Gaussian white noise; X sub (t) represents the received signal model of the sparse non-uniform linear array; A sub represents the array flow pattern of the sparse non-uniform linear array, that is, the second array flow pattern; t represents time.

[0082] For a conformal polarization-sensitive array, the spatial phase factor caused by the nth spatial signal incident on the mth array element is:

[0083] u (m,n)=exp(-λ / 2πτ m );

[0084] Among them, u (m,n) represents the spatial phase factor caused by the nth spatial signal incident on the mth array element; λ represents the wavelength of the spatial signal; and π represents pi. The conformal polarization sensitive array is G=[g1,g2,...,g m ] T , represents the polarization reception characteristics of the array element, which is determined by the placement angle of the antenna. The superscript T indicates the transpose of the matrix.

[0085] In an embodiment of the present invention, the elements of the conformal polarization-sensitive array may all be incomplete electromagnetic vector sensors, which are only sensitive to the electric field component of the spatial signal, that is:

[0086] g m =[sinβ m cosα m ,sinβ m sinα m ,cosβ m ,0,0,0] T ;

[0087] Among them, g m represents the polarization receiving characteristic of the mth array element; β m represents the angle between the single dipole antenna and the z-axis; α m represents the angle between the projection of the single dipole antenna on the xoy plane and the x-axis; Figure 4 As shown, Figure 4 This is a schematic diagram of the placement angle of a single dipole antenna.

[0088] Since the conformal polarization sensitive array is distributed in the same plane, the angle between each array element and the z-axis is Right now Then g m =[cosα n ,sinα n ,0,0,0,0] T .

[0089] The spatial-polarization factor is:

[0090]

[0091] Among them, S ps represents the spatial-polarization factor; j represents the imaginary unit; e represents the natural base; h is a function with γ and η as variables; γ n represents the polarization auxiliary angle of the nth spatial signal; η n represents the polarization phase difference of the nth spatial signal; η∈[-π,π] represents the polarization state of the signal. Finally, the steering vector of the conformal polarization sensitive array is Has the following form:

[0092]

[0093] in, It represents the spatial phase factor caused by the nth spatial signal incident on the mth array element.

[0094] The array flow pattern of the conformal polarization sensitive array, that is, the first array flow pattern is:

[0095]

[0096] Where a(·) represents the steering vector of the conformal polarization sensitive array; the azimuth angle of the nth spatial signal is θ n Indicates; the pitch angle of the nth spatial signal is expressed as Indicates; the polarization auxiliary angle of the nth spatial signal is γ n The polarization phase difference of the nth spatial signal is represented by η n Indicates; n=1,2...N.

[0097] Assume that the number of array elements of the sparse non-uniform linear array is M sub , then the second array flow pattern is:

[0098]

[0099] The distance between the mth element and the m-1th element in the sparse non-uniform linear array is d m Indicates that m = 2...M sub ;M sub represents the total number of array elements in the sparse non-uniform linear array; θ n represents the azimuth of the nth spatial signal; n = 1, 2...N; j represents the imaginary unit; e represents the natural base; λ represents the wavelength of the spatial signal; π represents pi.

[0100] In this embodiment of the present invention, a virtual array expansion technique is used to expand a sparse non-uniform linear array. The portion of the carrier that cannot accommodate array elements is ignored, and the length of the carrier that can accommodate array elements is measured to determine the position of the virtual array elements. The virtual uniform linear array is a scalar uniform linear array with an element spacing of d. The third array flow pattern is:

[0101]

[0102] Where d represents the element spacing in the virtual uniform linear array; θ nrepresents the azimuth of the nth spatial signal; n=1,2...N; j represents the imaginary unit; e represents the natural base; λ represents the wavelength of the spatial signal; π represents the circumference of the circle; M v Indicates the total number of array elements in the virtual uniform linear array.

[0103] At this time, the virtual transformation matrix T obtained directly is:

[0104]

[0105] A sub represents the second array flow pattern; A represents the first array flow pattern; A visual Indicates the third array flow pattern; A sub (θ) represents the second array flow pattern when the azimuth angle of the spatial signal is θ; A(θ) represents the first array flow pattern when the azimuth angle of the spatial signal is θ; A visual (θ) represents the third array manifold with the azimuth angle of the spatial signal being θ; θ represents the azimuth angle of the spatial signal.

[0106] According to the principle of virtual transformation technology, there is a transformation relationship between the received data of the virtual uniform linear array and the real space signal, namely:

[0107] x visual =T H x sub (t);

[0108] Among them, x visual represents the real space signal; x sub (t) represents the received data of the virtual uniform linear array.

[0109] Based on this, the second covariance matrix is ​​processed using the virtual transformation matrix to obtain the covariance matrix of the received data of the virtual uniform linear array:

[0110]

[0111] However, due to T H T≠I, so directly using the virtual transformation matrix T to calculate the covariance matrix of the virtual transformed data will turn white noise into colored noise, which will seriously affect the direction estimation performance. Where I represents the identity matrix.

[0112] Therefore, in the embodiment of the present invention, by whitening the noise, T is converted to:

[0113] B=(T H T) -1 / 2 T H ;

[0114] Wherein, B represents the virtual transformation matrix in the embodiment of the present invention.

[0115] Through the virtual transformation matrix B, the third covariance matrix is ​​obtained as:

[0116]

[0117] Among them, R visual represents the third covariance matrix; R sub represents the second covariance matrix; σ n Represents the noise power corresponding to the nth spatial signal; n = 1, 2...N.

[0118] In one implementation, performing DOA estimation based on the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal includes:

[0119] Performing eigenvalue decomposition on the third covariance matrix, and then calculating the first spatial spectrum to obtain the azimuth angle of the spatial signal;

[0120] determining a second spatial spectrum of the conformal polarization sensitive array according to the first covariance matrix;

[0121] The elevation angle of the spatial signal is searched for in the second spatial spectrum according to the azimuth angle of the spatial signal.

[0122] In the embodiment of the present invention, a spatial spectrum estimation algorithm, such as a MUSIC algorithm, may be used to perform DOA estimation based on the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal.

[0123] Specifically, the third covariance matrix is ​​subjected to eigenvalue decomposition, and the MUSIC algorithm is used to obtain the noise subspace. The first spatial spectrum is calculated and the azimuth angle is obtained through spectral peak search. The second spatial spectrum of the conformal polarization-sensitive array is then determined from the first covariance matrix. The column containing the azimuth angle in the second spatial spectrum of the conformal polarization-sensitive array is then searched for the elevation angle to obtain a two-dimensional DOA estimate.

[0124] The number of virtual array elements that can be carried is determined according to the carrier length, the virtual uniform linear array that needs virtual transformation is determined by adding virtual array elements, and the array flow pattern of the virtual uniform linear array is constructed, where the array element spacing of the virtual uniform linear array is λ / 2, and λ is the wavelength of the spatial signal.

[0125] In embodiments of the present invention, any irregular conformal polarization-sensitive array that meets the conditions for disassembly can employ the methods provided by these embodiments to improve DOA estimation accuracy. Furthermore, if hardware storage space permits, offline storage of amplitude and phase errors can also improve DOA estimation accuracy. Furthermore, even for non-polarization-sensitive arrays, the methods provided by these embodiments can be employed to process these irregular arrays, thereby improving DOA estimation accuracy.

[0126] In addition, the virtual array expansion technology is used locally on the array. The expanded virtual array is not limited to a uniform array and can be adjusted according to actual needs.

[0127] A simulation experiment is conducted based on the conformal polarization sensitive array DOA estimation method based on the virtual array extension technology provided by the embodiment of the present invention. The structure of the conformal polarization sensitive array used in the simulation experiment is shown in FIG. Figure 2 The conformal polarization-sensitive array is arranged in a bilaterally symmetrical triangular structure. Due to the carrier shape, no array elements can be placed in the center. The x-axis subarray was virtually expanded to 30 elements. The simulation simulated a signal source with a direction of arrival of (30°, 35°) and a signal frequency of 9 GHz. Amplitude and phase errors were added to simulate channel amplitude and phase mismatches at high temperatures.

[0128] See also Figure 5 and Figure 6 , Figure 5 This is a schematic diagram of the MUSIC spatial spectrum of the conformal polarization sensitive array. Figure 6 Figure 1 is a schematic diagram of the MUSIC spatial spectrum of a virtual uniform linear array. The simulation results show that the spatial spectrum generated by the original array has a high pseudo-peak value, which affects direction finding accuracy. By combining the azimuth direction finding results of the one-dimensional virtual linear array with the spectrum peak search, an accurate DOA estimation result is obtained. Here, peak / power represents the spatial spectrum peak; yaw angle represents the azimuth angle; and pitch angle represents the elevation angle.

[0129] Under the above simulation conditions, 100 Monte Carlo simulations were performed to statistically analyze the direction-finding errors of the conformal polarization-sensitive array before and after expansion using the virtual array expansion technology. Figure 7 and Figure 8 The direction finding error includes the azimuth error and the elevation error. Figure 7 This is a schematic diagram of the direction finding error of the conformal polarization sensitive array. Figure 8 This is a schematic diagram of the direction-finding error of the conformal polarization-sensitive array after expansion based on the virtual array expansion technology.

[0130] It should be noted that the terms "first," "second," and the like are used to distinguish similar objects and are not necessarily used to describe a particular order or precedence. It should be understood that the terms used in this manner are interchangeable where appropriate, so that the embodiments of the present invention described herein can be implemented in sequences other than those illustrated or described herein. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present invention. Instead, they are merely examples of devices and methods consistent with some aspects of the present invention.

[0131] In the description of this specification, the reference terms "one embodiment," "some embodiments," "example," "specific example," or "some examples" mean that the specific features or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0132] Although the present invention is described herein in conjunction with various embodiments, in the process of implementing the claimed invention, those skilled in the art can understand and implement other variations of the disclosed embodiments by viewing the drawings and the disclosed content. In the description of the present invention, the word "comprising" does not exclude other components or steps, "one" or "a" does not exclude multiple situations, and "multiple" means two or more, unless otherwise clearly and specifically defined. In addition, certain measures are recorded in different embodiments, but this does not mean that these measures cannot be combined to produce good results.

[0133] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A conformal polarization sensitive array DOA estimation method based on virtual array extension technology, characterized in that: include: Determining a sparse non-uniform linear array from a conformal polarization-sensitive array, and constructing a first array flow pattern of the conformal polarization-sensitive array and a second array flow pattern of the sparse non-uniform linear array; Calculate a first covariance matrix of received data of the conformal polarization sensitive array according to the first array flow pattern and spatial signal; Calculate a second covariance matrix of the received data of the sparse non-uniform linear array according to the second array flow pattern and the spatial signal; Expanding the sparse non-uniform linear array using a virtual array expansion technique to obtain a virtual uniform linear array, and constructing a third array flow pattern of the virtual uniform linear array; Obtaining a virtual transformation matrix according to the second array flow pattern and the third array flow pattern; Processing the second covariance matrix using the virtual transformation matrix to obtain a third covariance matrix of received data of the virtual uniform linear array; DOA estimation is performed according to the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal.

2. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: Determine sparse non-uniform linear arrays from conformal polarization-sensitive arrays, including: Determine the horizontal axis of the conformal polarization sensitive array; The array elements on the horizontal axis are formed into a sparse non-uniform linear array.

3. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: Performing DOA estimation according to the third covariance matrix and the first covariance matrix to obtain an angle measurement result of the spatial signal includes: performing eigenvalue decomposition on the third covariance matrix, and then calculating the first spatial spectrum to obtain the azimuth angle of the spatial signal; determining a second spatial spectrum of the conformal polarization-sensitive array according to the first covariance matrix; The elevation angle of the spatial signal is searched for in the second spatial spectrum according to the azimuth angle of the spatial signal.

4. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: The first array flow pattern is: Wherein, a(·) represents the steering vector of the conformal polarization sensitive array; the azimuth angle of the nth spatial signal is θ n Indicates; the pitch angle of the nth spatial signal is expressed as Indicates; the polarization auxiliary angle of the nth spatial signal is γ n The polarization phase difference of the nth spatial signal is represented by η n Indicates; n=1,2...N.

5. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: The second array flow pattern is: The distance between the mth array element and the m-1th array element in the sparse non-uniform linear array is d m Indicates that m = 2...M sub ;M sub represents the total number of array elements in the sparse non-uniform linear array; the azimuth angle of the nth spatial signal is θ n represents; n=1,2...N; j represents an imaginary unit; e represents a natural base; λ represents the wavelength of the spatial signal; π represents pi.

6. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: The third array flow pattern is: Wherein, d represents the element spacing in the virtual uniform linear array; the azimuth angle of the nth spatial signal is θ n represents; n=1,2...N; j represents an imaginary unit; e represents a natural base; λ represents the wavelength of the spatial signal; π represents pi; M v represents the total number of array elements in the virtual uniform linear array.

7. The conformal polarization sensitive array DOA estimation method according to claim 1, wherein: The virtual transformation matrix is ​​calculated as follows: B=(T H T) -1 / 2 T H ; Wherein, B represents the virtual transformation matrix; A sub represents the second array flow pattern; A represents the first array flow pattern; A visual Represents the third array flow pattern; A sub (θ) represents the second array flow pattern of the spatial signal with an azimuth angle of θ; A(θ) represents the first array flow pattern of the spatial signal with an azimuth angle of θ; A visual (θ) represents the third array manifold with the azimuth angle of the spatial signal being θ; θ represents the azimuth angle of the spatial signal; and the superscript H represents the matrix conjugate transpose.

8. The conformal polarization sensitive array DOA estimation method according to claim 7, wherein: Processing the second covariance matrix using the virtual transformation matrix to obtain a third covariance matrix of received data of the virtual uniform linear array includes: Among them, R sub represents the second covariance matrix; σ n Represents the noise power corresponding to the nth spatial signal; n = 1, 2...N.

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