A method for realizing angle super-resolution of non-uniform planar array tracking radar

Abstract

This application relates to a method for achieving super-resolution angle measurement in a non-uniform area array tracking radar. The method includes: performing first-level amplitude and phase correction and azimuth-dimensional digital beamforming on the non-uniform area array based on the amplitude ratio and phase difference of each element relative to a reference element, thus converting the non-uniform area array into an equivalent virtual non-uniform linear array; and performing second-level amplitude and phase correction on the virtual non-uniform linear array based on the amplitude ratio and phase difference of each equivalent element relative to a reference equivalent element. This application achieves super-resolution angle measurement by performing two-level amplitude and phase correction on the non-uniform area array, effectively converting the complex non-uniform area array into a simple virtual uniform linear array. Furthermore, based on this virtual uniform linear array, a computationally efficient maximum likelihood estimation algorithm based on observation geometry is applied.

Description

Technical Field

[0001] This application relates to the field of radar technology, and in particular to a method for achieving angular super-resolution for non-uniform array tracking radar. Background Technology

[0002] Radar is an important device in modern detection technology used to obtain information about the spatial distribution of targets. In practical applications, low-altitude targets fly at low altitudes and high speeds, and can conceal themselves in terrain environments, which greatly increases the difficulty of radar detection and stable tracking of targets.

[0003] Multipath propagation is a major factor affecting radar's performance in detecting and tracking low-altitude targets. When radar detects low-altitude targets, due to the strong multipath scattering components from land or sea, the radar's main beam receives reflected components from multiple paths when processing signals directly reflected from the target, thus creating a multipath problem. Direct and reflected signals are coherent signals. Although the different paths and slant ranges of the direct and reflected waves result in different phases and amplitudes, the difference in direction-of-arrival angle between the two sources is often less than the array's half-power beamwidth. Therefore, this slight difference and conventional angle estimation algorithms cannot separate multipath signals from direct signals, leading to a sharp increase in radar elevation angle measurement errors and even target tracking loss in the tracking loop.

[0004] In related technologies, to effectively distinguish between direct waves and multipath reflected waves, low elevation angle estimation algorithms are required to distinguish coherent signals and have high angular resolution in ultra-low altitude environments. Maximum likelihood estimation algorithms based on observation geometry, under certain conditions, can reach the Cramer-Rao bound in parameter estimation theory, making them an ideal high-precision angle measurement algorithm. However, in practical engineering applications, especially in area arrays, they face two challenges: First, the algorithm's performance heavily relies on an accurate array manifold model. Actual area arrays often suffer from non-uniform element arrangement due to design, manufacturing, and layout limitations, and even inconsistent amplitude and phase characteristics between elements, leading to a mismatch between the theoretical model and physical reality. Second, the maximum likelihood estimation algorithm has high computational complexity, making it difficult to guarantee real-time performance for area arrays.

[0005] Therefore, it is necessary to provide a new technical solution to improve one or more of the problems existing in the above solutions.

[0006] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this application is to provide an angular super-resolution implementation method for non-uniform array tracking radar, thereby overcoming, at least to some extent, one or more problems caused by the limitations and defects of related technologies.

[0008] According to a first aspect of the embodiments of this application, a method for achieving angular super-resolution for a non-uniform area array tracking radar is provided, the method comprising: Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, the radar non-uniform array is subjected to first-level amplitude and phase correction and azimuth digital beamforming to make the radar non-uniform array equivalent to a radar virtual non-uniform linear array. Based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, a two-stage amplitude and phase correction is performed on the radar virtual non-uniform linear array to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array. Based on the observation geometry of the radar virtual uniform linear array and the target, establish the geometric relationship between the target elevation angle and the multipath signal elevation angle; Based on the observed geometry, the attenuation factor matrix for signal propagation is obtained; The composite steering vector matrix is ​​obtained based on the geometric relationship and the attenuation factor matrix. Based on the composite steering vector matrix and the signal covariance matrix, the maximum likelihood estimation spectrum is obtained; Within a preset coarse search range, the maximum likelihood estimation spectrum is searched for spectral peaks to obtain a preliminary estimate of the target pitch angle. Using the preliminary estimate as the search center, a fine search range is set, and a spectral peak search is performed on the maximum likelihood estimation spectrum to obtain the optimal estimate of the target pitch angle.

[0009] In the embodiments of this application, the step of performing first-order amplitude and phase correction and azimuth-dimensional digital beamforming on the non-uniform radar array based on the amplitude ratio and phase difference of each element of the non-uniform radar array relative to the reference element, so as to convert the non-uniform radar array into a radar virtual non-uniform linear array, includes: The formulas for calculating the amplitude ratio and phase difference of each element of the non-uniform radar array relative to the reference element are as follows: (1) (2) In the formula, This represents the amplitude ratio of each element in a non-uniform radar array relative to a reference element. This represents the phase difference between each element of a non-uniform radar array and the reference element. The signals received by each element of a non-uniform radar array are... The signal received by the reference array element. This indicates the number of elements in a non-uniform radar array. This indicates the magnitude of the signal. Indicates the phase of the signal. This represents the phase of the signal received by each element of a non-uniform radar array. This indicates the phase of the signal received by the reference array element; Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, a first correction coefficient is obtained. Based on the first correction coefficient and the preset digital beam coefficient, digital beam synthesis of the radar non-uniform array in each direction dimension is completed, so as to convert the radar non-uniform array into an equivalent of a radar virtual non-uniform linear array.

[0010] In the embodiments of this application, the step of performing a two-stage amplitude and phase correction on the radar virtual non-uniform linear array based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, so as to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array, includes: The formulas for calculating the amplitude ratio and phase difference of each equivalent array element relative to the reference equivalent array element in the radar virtual non-uniform linear array are as follows: (3) (4) In the formula, This represents the amplitude ratio of each equivalent element in a radar virtual non-uniform linear array relative to a reference equivalent element. This represents the phase difference between each element of a radar virtual non-uniform linear array and a reference equivalent element. The signals received by each equivalent element of the radar's virtual non-uniform linear array are shown. The signal received by the reference equivalent array element. This indicates the number of elements in the radar's virtual non-uniform linear array. This represents the phase of the signal received by each element of the radar's virtual non-uniform linear array. This indicates the phase of the signal received by the reference equivalent array element; The process involves obtaining secondary correction coefficients based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, and then calibrating each equivalent array element of the radar virtual non-uniform linear array according to the secondary correction coefficients, so as to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

[0011] In the embodiments of this application, the observation geometry includes: the distance between the target and the radar, the radar antenna height, and the target flight altitude.

[0012] In embodiments of this application, establishing the geometric relationship between the target elevation angle and the multipath signal elevation angle based on the radar and target observation geometry includes: The geometric relationship between the target elevation angle and the multipath signal elevation angle is obtained based on the distance between the target and the radar, the radar antenna height, and the target flight altitude. The geometric relationship is as follows: (5) In the formula, Indicates the pitch angle of the multipath signal. Indicates the target pitch angle. Indicates the distance between the target and the radar. This indicates the height of the radar antenna.

[0013] In embodiments of this application, obtaining the attenuation factor matrix for signal propagation based on the observed geometry includes: The slant range of the multipath signal is obtained based on the distance between the target and the radar, the radar antenna height, and the target's flight altitude; wherein the formula for calculating the slant range of the multipath signal is as follows: (6) In the formula, Indicates the slant range of the multipath signal. Indicates the target flight altitude; Based on the slant range of the multipath signal and the slant range of the direct wave signal, the slant range difference between the direct wave signal and the multipath signal is obtained; wherein, the formula for calculating the slant range difference is as follows: (7) In the formula, Indicates the difference in slope distance; The signal propagation attenuation factor matrix is ​​obtained based on the slant range difference and reflection coefficient; wherein, the calculation formula for the attenuation factor matrix is ​​as follows: (8) In the formula, The attenuation factor matrix represents the signal propagation. The reflection coefficient is represented by j, which is an imaginary number. denoted by λ, where λ represents the wavelength of the electromagnetic wave, and T represents the transpose of the matrix.

[0014] In embodiments of this application, obtaining the composite steering vector matrix based on the geometric relationship and the attenuation factor matrix includes: The steering vector of the direct wave is obtained based on the pitch dimension adjacent subarray spacing and the target pitch angle; wherein, the calculation formula for the steering vector of the direct wave is as follows: (9) In the formula, The steering vector representing the direct wave; Based on the pitch dimension adjacent subarray spacing and the multipath signal pitch angle, the steering vector of the multipath signal is obtained; wherein, the calculation formula for the steering vector of the multipath signal is as follows: (10) In the formula, The steering vector representing a multipath signal; The composite steering vector matrix is ​​obtained based on the steering vector of the direct wave, the steering vector of the multipath signal, and the attenuation factor matrix; wherein the calculation formula for the composite steering vector matrix is ​​as follows: (11) In the formula, This represents the composite steering vector matrix.

[0015] In embodiments of this application, obtaining the maximum likelihood estimation spectrum based on the composite steering vector matrix and the signal covariance matrix includes: The formula for calculating the covariance matrix of the signal is as follows: (12) In the formula, Indicates a signal, This represents the conjugate transpose of the signal. The covariance matrix represents the signal; The formula for calculating the maximum likelihood estimation spectrum is as follows: (13) In the formula, (14) In the formula, Represents the maximum likelihood estimation spectrum. This represents the combined steering vector of the multipath signal and the direct wave. This represents the conjugate transpose of the composite guiding vector matrix. This indicates finding the trace of a matrix.

[0016] In embodiments of this application, the step of performing a spectral peak search on the maximum likelihood estimation spectrum within a preset coarse search range to obtain a preliminary estimate of the target pitch angle includes: The preset coarse search range is set based on the current beam pointing center and beamwidth, and the preset coarse search range is as follows: (15) In the formula, This indicates the preset coarse search range. This indicates that the current beam is pointing towards the center. Indicates beamwidth; The preliminary estimates are as follows: (16) In the formula, This represents a preliminary estimate. This indicates the elevation angle of the direct wave.

[0017] In the embodiments of this application, the step of setting a fine search range with the preliminary estimate as the search center and performing a spectral peak search on the maximum likelihood estimation spectrum to obtain the optimal estimate of the target pitch angle includes: The precise search range is as follows: (17) In the formula, Indicates the scope of the fine search; The optimal estimate is as follows: (18) In the formula, This represents the optimal estimate.

[0018] The technical solutions provided by the embodiments of this application may include the following beneficial effects: In one embodiment of this application, the above method, through two-stage amplitude and phase correction of the radar non-uniform array, transforms the complex radar non-uniform array into a simple virtual uniform linear array, providing reliable system conditions for the implementation of the maximum likelihood estimation method. The two-stage amplitude and phase correction systematically addresses non-ideal factors such as channel inconsistency and element position deviation in actual radar systems, enhancing the robustness and engineering feasibility of the method. Based on the radar virtual uniform linear array, a computationally efficient maximum likelihood estimation algorithm based on observation geometry is applied to obtain the optimal estimate of the target elevation angle, thus achieving super-resolution angle measurement. This application simplifies the maximum likelihood estimation algorithm based on observation geometry, transforming a two-dimensional search into a one-dimensional search, significantly reducing the computational load.

[0019] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and do not limit this application. Attached Figure Description

[0020] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0021] Figure 1This schematically illustrates a flowchart of the steps of an angular super-resolution implementation method for a non-uniform array tracking radar according to an exemplary embodiment of this application. Figure 2 This schematic diagram illustrates the geometric relationship between the target pitch angle and the multipath signal pitch angle in an exemplary embodiment of this application. Figure 3 This schematically illustrates the observation geometry of the target and the uniform linear array in an exemplary embodiment of this application; Figure 4 The schematic diagram illustrates the search results for the maximum likelihood estimation spectral peak value when only first-level amplitude and phase correction is performed in an exemplary embodiment of this application, with a target slant range of 3000m. Figure 5 The schematic illustration shows the maximum likelihood estimation spectral peak search results when performing two-stage amplitude and phase correction in an exemplary embodiment of this application, with a target slant distance of 3000m. Figure 6 The schematic diagram illustrates the search results for the maximum likelihood estimation spectral peak when only first-level amplitude and phase correction is performed in an exemplary embodiment of this application, with a target slant range of 5000m. Figure 7 The illustration shows the search results for the maximum likelihood estimation spectral peak when performing two-stage amplitude and phase correction in an exemplary embodiment of this application with a target slant distance of 5000m. Detailed Implementation

[0022] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided to make this application more comprehensive and complete, and to fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0023] Furthermore, the accompanying drawings are merely illustrative of this application and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0024] This example implementation provides an angular super-resolution method for non-uniform area array tracking radar. (Reference) Figure 1 As shown, the method may include steps S101 to S108.

[0025] In step S101: Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, the radar non-uniform array is subjected to first-level amplitude and phase correction and azimuth-dimensional digital beamforming, so as to convert the radar non-uniform array into a radar virtual non-uniform linear array.

[0026] Step S102: Based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, perform two-stage amplitude and phase correction on the radar virtual non-uniform linear array to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

[0027] Step S103: Based on the observation geometry of the radar virtual uniform linear array and the target, establish the geometric relationship between the target elevation angle and the multipath signal elevation angle.

[0028] Step S104: Obtain the attenuation factor matrix for signal propagation based on the observation geometry.

[0029] Step S105: Obtain the composite steering vector matrix based on the geometric relationship and the attenuation factor matrix.

[0030] Step S106: Obtain the maximum likelihood estimation spectrum based on the composite steering vector matrix and the signal covariance matrix.

[0031] Step S107: Perform a peak search on the maximum likelihood estimation spectrum within a preset coarse search range to obtain a preliminary estimate of the target pitch angle.

[0032] Step S108: Using the preliminary estimate as the search center, set the fine search range, perform spectral peak search on the maximum likelihood estimation spectrum, and obtain the optimal estimate of the target pitch angle.

[0033] In one embodiment of this application, the above method, through two-stage amplitude and phase correction of the radar non-uniform array, transforms the complex radar non-uniform array into a simple virtual uniform linear array, providing reliable system conditions for the implementation of the maximum likelihood estimation method. The two-stage amplitude and phase correction systematically addresses non-ideal factors such as channel inconsistency and element position deviation in actual radar systems, enhancing the robustness and engineering feasibility of the method. Based on the radar virtual uniform linear array, a computationally efficient maximum likelihood estimation algorithm based on observation geometry is applied to obtain the optimal estimate of the target elevation angle, thus achieving super-resolution angle measurement. This application simplifies the maximum likelihood estimation algorithm based on observation geometry, transforming a two-dimensional search into a one-dimensional search, significantly reducing the computational load.

[0034] Below, we will refer to Figures 2 to 7 The steps of the method described above in this example embodiment will be explained in more detail.

[0035] In step S101, the amplitude ratio of each element of the radar non-uniform array relative to the reference element can be calculated using the signals received by each element of the radar non-uniform array and the signals received by the reference element. The specific calculation process is described in the following embodiments. The phase difference of each element of the radar non-uniform array relative to the reference element can be calculated using the phase of the signals received by each element of the radar non-uniform array and the phase of the signals received by the reference equivalent element. The specific calculation process is described in the following embodiments. Using the amplitude ratio of each element of the radar non-uniform array relative to the reference element and the phase difference of each element of the radar non-uniform array relative to the reference element, first-order amplitude and phase correction and azimuth-dimensional digital beamforming can be performed on the radar non-uniform array to convert it into a radar virtual non-uniform linear array.

[0036] Furthermore, step S101 includes the following: The formulas for calculating the amplitude ratio and phase difference of each element in a non-uniform radar array relative to the reference element are as follows: (1) (2) In the formula, This represents the amplitude ratio of each element in a non-uniform radar array relative to a reference element. This represents the phase difference between each element of a non-uniform radar array and the reference element. The signals received by each equivalent element of a non-uniform radar array are... The signal received by the reference array element. This indicates the number of elements in a non-uniform radar array. This indicates the magnitude of the signal. Indicates the phase of the signal. This represents the phase of the signal received by each element of a non-uniform radar array. This indicates the phase of the signal received by the reference array element; Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, a first correction coefficient is obtained. Based on the first correction coefficient and the preset digital beam coefficient, digital beam synthesis of the radar non-uniform array in each direction is completed, so as to convert the radar non-uniform array into an equivalent of a radar virtual non-uniform linear array.

[0037] It is understandable that the amplitude ratio of each element of the non-uniform radar array relative to the reference element can be calculated using formula (1), and the phase difference of each element of the non-uniform radar array relative to the reference element can be calculated using formula (2). The first-order correction coefficients are obtained using the amplitude ratios and phase differences of each element of the non-uniform radar array relative to the reference element. The first-order correction coefficients are then used to balance the signal amplitude and phase of each element to the amplitude and phase of the reference element, thus completing the first-order amplitude-phase correction.

[0038] Based on the actual geometric positions of each element in the radar non-uniform array, digital beamforming weights pointing to a specific azimuth angle are calculated. A weighted sum of digital beamforming values ​​is then applied to each row of the radar non-uniform array, thus achieving an equivalence between the radar non-uniform array and a virtual non-uniform linear array. Specifically, the actual geometric position refers to the subarray coordinates of each element in the radar non-uniform array. The specific azimuth angle refers to the azimuth angle at which the beam is pointed.

[0039] In step S102, based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, a second-level amplitude and phase correction is performed on the radar virtual non-uniform linear array to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

[0040] The reference equivalent array element is an arbitrarily selected equivalent array element within the virtual non-uniform linear array. By comparing the signals received by each equivalent array element in the radar virtual non-uniform linear array with the signals received by the reference equivalent array element, the amplitude ratio of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element can be calculated. The specific calculation process is described in the following embodiments. Similarly, by comparing the signals received by each equivalent array element in the radar virtual non-uniform linear array with the signals received by the reference equivalent array element, the phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element can be calculated. The specific calculation process is described in the following embodiments.

[0041] By using the amplitude ratio of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element and the phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, a two-stage amplitude and phase correction can be performed on the radar virtual non-uniform linear array, thereby achieving equivalence from the radar virtual non-uniform linear array to the radar virtual uniform linear array.

[0042] In one embodiment, step S102 includes the following: The formulas for calculating the amplitude ratio and phase difference of each equivalent element in a radar virtual non-uniform linear array relative to the reference equivalent element are as follows: (3) (4) In the formula, This represents the amplitude ratio of each equivalent element in a radar virtual non-uniform linear array relative to a reference equivalent element. This represents the phase difference between each element of a radar virtual non-uniform linear array and a reference equivalent element. The signals received by each equivalent element of the radar's virtual non-uniform linear array are shown. The signal received by the reference equivalent array element. This indicates the number of elements in the radar's virtual non-uniform linear array. This represents the phase of the signal received by each element of the radar's virtual non-uniform linear array. This indicates the phase of the signal received by the reference equivalent array element; Based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, the secondary correction coefficients are obtained. The equivalent array elements of the radar virtual non-uniform linear array are then calibrated according to the secondary correction coefficients to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

[0043] It is understandable that the amplitude ratio of each equivalent element in the radar virtual non-uniform linear array relative to the reference equivalent element can be calculated using formula (3), and the phase difference of each equivalent element in the radar virtual non-uniform linear array relative to the reference equivalent element can be calculated using formula (4). Secondary correction coefficients are generated using the amplitude ratio of each equivalent element in the radar virtual non-uniform linear array relative to the reference equivalent element and the phase difference of each equivalent element in the radar virtual non-uniform linear array relative to the reference equivalent element. Secondary amplitude and phase correction can be performed using these secondary correction coefficients to achieve equivalence between the radar virtual non-uniform linear array and the radar virtual uniform linear array, that is, to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

[0044] This application achieves a two-stage amplitude and phase correction for a non-uniform radar array, effectively transforming the complex array into a simple virtual uniform linear array, thus providing reliable system conditions for the implementation of the maximum likelihood estimation method. The two-stage amplitude and phase correction systematically addresses non-ideal factors in practical radar systems, such as channel inconsistency and element position deviations, enhancing the method's robustness and engineering feasibility.

[0045] In step S103, the geometric relationship between the target's elevation angle and the multipath signal's elevation angle can be established through the radar and target observation geometry. This geometric relationship is used to subsequently obtain the signal propagation attenuation factor matrix. Furthermore, the observation geometry includes: the distance between the target and the radar, the radar antenna height, and the target's flight altitude.

[0046] In one embodiment, step S103 includes the following: refer to Figure 2 and Figure 3 Based on the geometric relationships between the distance between the target and the radar, the radar antenna height, the target elevation angle, and the multipath signal elevation angle, the geometric relationships are as follows: (5) In the formula, Indicates the pitch angle of the multipath signal. Indicates the target pitch angle. Indicates the distance between the target and the radar. This indicates the height of the radar antenna.

[0047] It is understandable that by observing the distance between the target and the radar and the height of the radar antenna in the geometry, the geometric relationship shown in formula (5) can be obtained. The geometric relationship facilitates the subsequent acquisition of the composite steering vector matrix.

[0048] In step S104, the attenuation factor matrix of signal propagation is obtained according to the observation geometry. The attenuation factor matrix is ​​used to obtain the composite steering vector matrix in the subsequent process.

[0049] Furthermore, step S104 includes the following: The slant range of the multipath signal is obtained based on the distance between the target and the radar, the radar antenna height, and the target's flight altitude. The formula for calculating the slant range of the multipath signal is as follows: (6) In the formula, Indicates the slant range of the multipath signal. Indicates the target flight altitude; Based on the slant range of the multipath signal and the slant range of the direct wave signal, the slant range difference between the direct wave signal and the multipath signal is obtained; the formula for calculating the slant range difference is as follows: (7) In the formula, This represents the slant range difference between the direct wave signal and the multipath signal; The attenuation factor matrix for signal propagation is obtained based on the slant range difference and the reflection coefficient; the formula for calculating the attenuation factor matrix is ​​as follows: (8) In the formula, The attenuation factor matrix represents the signal propagation. The reflection coefficient is represented by j, which is an imaginary number. denoted by λ, where λ represents the wavelength of the electromagnetic wave, and T represents the transpose of the matrix.

[0050] It is understandable that the slant range of the multipath signal can be obtained by using the distance between the target and the radar, the radar antenna height, and the target's flight altitude. Specifically, the slant range of the multipath signal can be obtained using formula (6). The slant range difference between the direct wave signal and the multipath signal can be obtained by using the slant range of the direct wave signal and the slant range of the multipath signal. Specifically, the slant range difference between the direct wave signal and the multipath signal can be obtained using formula (7). Then, the signal propagation attenuation factor matrix can be obtained based on the slant range difference and the reflection coefficient. Specifically, the attenuation factor matrix can be obtained using formula (8). The attenuation factor matrix facilitates the subsequent obtaining of the composite steering vector matrix.

[0051] In step S105, a composite steering vector matrix is ​​obtained based on geometric relationships and the attenuation factor matrix. This composite steering vector matrix is ​​used to subsequently obtain the maximum likelihood estimation spectrum. The composite steering vector matrix constructed using geometric relationships and the attenuation factor matrix can capture both the spatial orientation and propagation attenuation information of the source. Applying it to the subsequent calculation of the maximum likelihood estimation spectrum can effectively compensate for the spectral estimation error caused by incomplete modeling in traditional steering vectors, further improving the angular resolution, estimation accuracy, and anti-interference capability of the maximum likelihood estimation spectrum.

[0052] Furthermore, step S105 includes the following: The steering vector of the direct wave is obtained based on the pitch dimension adjacent subarray spacing and the target pitch angle; the formula for calculating the steering vector of the direct wave is as follows: (9) In the formula, The steering vector representing the direct wave; The steering vector of the multipath signal is obtained based on the pitch dimension adjacent subarray spacing and the multipath signal pitch angle; the formula for calculating the steering vector of the multipath signal is as follows: (10) In the formula, The steering vector representing a multipath signal; Based on the steering vector of the direct wave, the steering vector of the multipath signal, and the attenuation factor matrix, the composite steering vector matrix is ​​obtained; the calculation formula for the composite steering vector matrix is ​​as follows: (11) In the formula, This represents the composite steering vector matrix.

[0053] It is understandable that the steering vector of the direct wave can be obtained through formula (9), and the steering vector of the direct wave is used to obtain the composite steering vector matrix, as shown in the figure. The pitch dimension adjacent subarray spacing is represented by d. The steering vector of the multipath signal can be obtained through formula (10), and the steering vector of the multipath signal is used to obtain the composite steering vector matrix. Through the steering vector of the direct wave, the steering vector of the multipath signal and the attenuation factor matrix, the composite steering vector matrix can be obtained. The composite steering vector matrix can be obtained through formula (11), realizing the dimensionality reduction processing of the maximum likelihood estimation angle super-resolution algorithm.

[0054] In step S106, the maximum likelihood estimation spectrum is obtained based on the composite steering vector matrix and the covariance matrix of the signal.

[0055] Furthermore, step S106 includes the following: The formula for calculating the covariance matrix of a signal is as follows: (12) In the formula, Indicates a signal, This represents the conjugate transpose of the signal. The covariance matrix represents the signal; The formula for calculating the maximum likelihood estimation spectrum is as follows: (13) (14) In the formula, Represents the maximum likelihood estimation spectrum. This represents the combined steering vector of the multipath signal and the direct wave. This represents the conjugate transpose of the composite guiding vector matrix. This indicates finding the trace of a matrix.

[0056] Understandably, by constructing the maximum likelihood spectrum function from the signal's covariance matrix, compared to traditional subspace-based spectrum estimation algorithms such as MUSIC and CAPON, this application can still maintain sharp spectral peak characteristics and high angular resolution under harsh conditions of low snapshot number and low signal-to-noise ratio. It can effectively suppress spurious peak interference and significantly improve the accuracy and reliability of angle estimation.

[0057] In step S107, the maximum likelihood estimation spectrum is searched for spectral peaks within a preset coarse search range to obtain a preliminary estimate of the target pitch angle.

[0058] Furthermore, step S107 includes the following: The preset coarse search range is set based on the current beam pointing center and beamwidth. The preset coarse search range is as follows: (15) In the formula, This indicates the preset coarse search range. This indicates that the current beam is pointing towards the center. Indicates beamwidth; The preliminary estimates are as follows: (16) In the formula, This represents a preliminary estimate. This indicates the elevation angle of the direct wave.

[0059] Understandably, by performing a peak search on the maximum likelihood estimation spectrum within a preset coarse search range, a preliminary estimate of the target pitch angle can be quickly obtained. This significantly reduces the computational load of the global traversal search while ensuring a certain level of estimation accuracy, thereby improving the real-time performance and computational efficiency of pitch angle estimation.

[0060] In step S108, the preliminary estimate is used as the search center, the fine search range is set, and the peak value of the maximum likelihood estimation spectrum is searched to obtain the optimal estimate of the target pitch angle.

[0061] In one embodiment, step S108 includes the following: The scope of the fine search is as follows: (17) In the formula, Indicates the scope of the fine search; The optimal estimate is as follows: (18) In the formula, This represents the optimal estimate.

[0062] Understandably, this application employs a pre-defined coarse search range to perform spectral peak search on the maximum likelihood estimation spectrum. This quickly determines the approximate location of the target's pitch angle, obtaining a preliminary estimate, effectively reducing the massive computational load caused by global traversal, and improving the real-time performance of angle estimation. Then, a fine search range is set centered on the preliminary pitch angle estimate, further performing spectral peak search on the maximum likelihood estimation spectrum. This enables precise angle optimization within a smaller range, significantly reducing computational load while significantly improving the estimation accuracy of the target pitch angle, achieving fast and high-precision angle estimation. Through this two-stage search strategy of "coarse positioning + fine search," the algorithm's computational complexity is significantly reduced while ensuring high accuracy and reliability of pitch angle estimation, balancing estimation efficiency and accuracy, and improving the system's angle detection performance in complex environments.

[0063] To verify the angular super-resolution implementation method for non-uniform array tracking radar provided in this application, this application illustrates the method through the following experimental data.

[0064] The relevant parameters of the measured data are as follows: The radar antenna height is 3m, the target flight altitude (i.e., the target's flight altitude relative to the center of the radar array) is 40m, and the signal-to-noise ratio is 30dB. For the angle measurement results (i.e., the optimal estimate of the target's elevation angle), please refer to [link to relevant documentation]. Figure 4-7 . Figure 4 This is the search result for the maximum likelihood estimation spectral peak value when only first-level amplitude and phase correction is performed and the target slant distance is 3000m, provided by an embodiment of the present invention. Figure 5 This is the search result for the maximum likelihood estimation spectral peak value when performing two-stage amplitude and phase correction and targeting a slant distance of 3000m, provided by an embodiment of the present invention. Figure 6 This is the search result for the maximum likelihood estimation spectral peak value when only first-level amplitude and phase correction is performed and the target slant distance is 5000m, provided by an embodiment of the present invention. Figure 7 This is the maximum likelihood estimation spectral peak search result provided by an embodiment of the present invention for performing two-stage amplitude and phase correction with a slant range of 5000m. Here, the target slant range is the straight-line distance between the target and the radar. The target echo includes direct waves and multipath echoes; the direct wave slant range is equal to the target slant range, while the multipath signal slant range is not equal to the target slant range.

[0065] When the target's flight altitude is 40m and its slant distance is 3000m, the target's true pitch angle is calculated to be 0.71°. Figure 5 When only level one amplitude and phase correction is performed, the peak value is 0.68°. Figure 6 The peak search result for the two-stage amplitude and phase correction is 0.71°. Calculating the target's true pitch angle at a flight altitude of 40m relative to the radar array center and a slant range of 5000m, the target's actual pitch angle is 0.42°. Figure 5 When only level one amplitude and phase correction is performed, the peak value is 0.46°. Figure 6 When performing two-stage amplitude and phase correction, the peak search result is 0.43°.

[0066] Comparison Figure 4 and Figure 5 , Figure 6 and Figure 7 The following conclusions can be drawn: The angle super-resolution implementation method for non-uniform array tracking radar proposed in this application can enable non-uniform arrays to achieve angle super-resolution with low computational complexity and high angle measurement accuracy.

[0067] This application solves the problem of poor tracking accuracy caused by the significant multipath effect in ultra-low altitude environments. It completes the engineering implementation of the maximum likelihood estimation angle super-resolution algorithm based on observation geometry on tracking radar, effectively reducing the angle measurement error caused by multipath effect and greatly improving the tracking accuracy in ultra-low altitude environments.

[0068] It should be noted that although the steps of the method in this application are described in a specific order in the accompanying drawings, this does not require or imply that these steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps. Furthermore, it is readily understood that these steps may be executed synchronously or asynchronously, for example, in multiple modules / processes / threads.

[0069] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A method for achieving angular super-resolution in a non-uniform area array tracking radar, characterized in that, The method includes: Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, the radar non-uniform array is subjected to first-level amplitude and phase correction and azimuth digital beamforming to make the radar non-uniform array equivalent to a radar virtual non-uniform linear array. Based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, a two-stage amplitude and phase correction is performed on the radar virtual non-uniform linear array to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array. Based on the observation geometry of the radar virtual uniform linear array and the target, establish the geometric relationship between the target elevation angle and the multipath signal elevation angle; Based on the observed geometry, the attenuation factor matrix for signal propagation is obtained; The composite steering vector matrix is ​​obtained based on the geometric relationship and the attenuation factor matrix. Based on the composite steering vector matrix and the signal covariance matrix, the maximum likelihood estimation spectrum is obtained; Within a preset coarse search range, the maximum likelihood estimation spectrum is searched for spectral peaks to obtain a preliminary estimate of the target pitch angle. Using the preliminary estimate as the search center, a fine search range is set, and a spectral peak search is performed on the maximum likelihood estimation spectrum to obtain the optimal estimate of the target pitch angle.

2. The method for achieving angular super-resolution for non-uniform area array tracking radar according to claim 1, characterized in that, The step of performing first-order amplitude and phase correction and azimuth-dimensional digital beamforming on the non-uniform radar array based on the amplitude ratio and phase difference of each element relative to the reference element, so as to convert the non-uniform radar array into a virtual non-uniform radar linear array, includes: The formulas for calculating the amplitude ratio and phase difference of each element of the non-uniform radar array relative to the reference element are as follows: （1） （2） In the formula, This represents the amplitude ratio of each element in a non-uniform radar array relative to a reference element. This represents the phase difference between each element of a non-uniform radar array and the reference element. The signals received by each element of a non-uniform radar array are... The signal received by the reference array element. This indicates the number of elements in a non-uniform radar array. This indicates the magnitude of the signal. Indicates the phase of the signal. This represents the phase of the signal received by each element of a non-uniform radar array. This indicates the phase of the signal received by the reference array element; Based on the amplitude ratio and phase difference of each element of the radar non-uniform array relative to the reference element, a first correction coefficient is obtained. Based on the first correction coefficient and the preset digital beam coefficient, digital beam synthesis of the radar non-uniform array in each direction dimension is completed, so as to convert the radar non-uniform array into an equivalent of a radar virtual non-uniform linear array.

3. The method for achieving angular super-resolution in a non-uniform area array tracking radar according to claim 2, characterized in that, The step of performing a two-stage amplitude and phase correction on the radar virtual non-uniform linear array based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, so as to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array, includes: The formulas for calculating the amplitude ratio and phase difference of each equivalent array element relative to the reference equivalent array element in the radar virtual non-uniform linear array are as follows: （3） （4） In the formula, This represents the amplitude ratio of each equivalent element in a radar virtual non-uniform linear array relative to a reference equivalent element. This represents the phase difference between each element of a radar virtual non-uniform linear array and a reference equivalent element. The signals received by each equivalent element of the radar's virtual non-uniform linear array are... The signal received by the reference equivalent array element. This indicates the number of elements in the radar's virtual non-uniform linear array. This represents the phase of the signal received by each element of the radar's virtual non-uniform linear array. This indicates the phase of the signal received by the reference equivalent array element; The process involves obtaining secondary correction coefficients based on the amplitude ratio and phase difference of each equivalent array element in the radar virtual non-uniform linear array relative to the reference equivalent array element, and then calibrating each equivalent array element of the radar virtual non-uniform linear array according to the secondary correction coefficients, so as to convert the radar virtual non-uniform linear array into a radar virtual uniform linear array.

4. The method for achieving angular super-resolution in a non-uniform area array tracking radar according to claim 1, characterized in that, The observation geometry includes: the distance between the target and the radar, the radar antenna height, and the target's flight altitude.

5. The method for achieving angular super-resolution in a non-uniform area array tracking radar according to claim 4, characterized in that, The step of establishing the geometric relationship between the target elevation angle and the multipath signal elevation angle based on the radar and target observation geometry includes: Based on the geometric relationship between the distance between the target and the radar, the radar antenna height, the target elevation angle, and the multipath signal elevation angle, the geometric relationship is as follows: （5） In the formula, Indicates the pitch angle of the multipath signal. Indicates the target pitch angle. Indicates the distance between the target and the radar. This indicates the height of the radar antenna.

6. The method for achieving angular super-resolution for non-uniform area array tracking radar according to claim 5, characterized in that, The step of obtaining the signal propagation attenuation factor matrix based on the observed geometry includes: The slant range of the multipath signal is obtained based on the distance between the target and the radar, the radar antenna height, and the target's flight altitude; wherein the formula for calculating the slant range of the multipath signal is as follows: （6） In the formula, Indicates the slant range of the multipath signal. Indicates the target flight altitude; Based on the slant range of the multipath signal and the slant range of the direct wave signal, the slant range difference between the direct wave signal and the multipath signal is obtained; wherein, the formula for calculating the slant range difference is as follows: （7） In the formula, Indicates the difference in slope distance; The signal propagation attenuation factor matrix is ​​obtained based on the slant range difference and reflection coefficient; wherein, the calculation formula for the attenuation factor matrix is ​​as follows: （8） In the formula, The attenuation factor matrix represents the signal propagation. The reflection coefficient is represented by j, which is an imaginary number. denoted by λ, where λ represents the wavelength of the electromagnetic wave, and T represents the transpose of the matrix.

7. The method for achieving angular super-resolution for non-uniform area array tracking radar according to claim 6, characterized in that, The process of obtaining the composite steering vector matrix based on the geometric relationship and the attenuation factor matrix includes: The steering vector of the direct wave is obtained based on the pitch dimension adjacent subarray spacing and the target pitch angle; wherein, the calculation formula for the steering vector of the direct wave is as follows: （9） In the formula, The steering vector representing the direct wave; Based on the pitch dimension adjacent subarray spacing and the multipath signal pitch angle, the steering vector of the multipath signal is obtained; wherein, the calculation formula for the steering vector of the multipath signal is as follows: （10） In the formula, The steering vector representing a multipath signal; The composite steering vector matrix is ​​obtained based on the steering vector of the direct wave, the steering vector of the multipath signal, and the attenuation factor matrix; wherein the calculation formula for the composite steering vector matrix is ​​as follows: （11） In the formula, This represents the composite steering vector matrix.

8. The method for achieving angular super-resolution in a non-uniform area array tracking radar according to claim 7, characterized in that, The step of obtaining the maximum likelihood estimation spectrum based on the composite steering vector matrix and the signal covariance matrix includes: The formula for calculating the covariance matrix of the signal is as follows: （12） In the formula, Indicates a signal, This represents the conjugate transpose of the signal. The covariance matrix represents the signal; The formula for calculating the maximum likelihood estimation spectrum is as follows: （13） （14） In the formula, Represents the maximum likelihood estimation spectrum. This represents the combined steering vector of the multipath signal and the direct wave. This represents the conjugate transpose of the composite guiding vector matrix. This indicates finding the trace of a matrix.

9. The method for achieving angular super-resolution for non-uniform area array tracking radar according to claim 8, characterized in that, The step of performing a spectral peak search on the maximum likelihood estimation spectrum within a preset coarse search range to obtain a preliminary estimate of the target pitch angle includes: The preset coarse search range is set based on the current beam pointing center and beamwidth, and the preset coarse search range is as follows: （15） In the formula, This indicates the preset coarse search range. This indicates that the current beam is pointing towards the center. Indicates beamwidth; The preliminary estimates are as follows: （16） In the formula, This represents a preliminary estimate. This indicates the elevation angle of the direct wave.

10. The method for achieving angular super-resolution in a non-uniform area array tracking radar according to claim 9, characterized in that, The process of using the preliminary estimate as the search center, setting a fine search range, and performing a spectral peak search on the maximum likelihood estimation spectrum to obtain the optimal estimate of the target pitch angle includes: The precise search range is as follows: （17） In the formula, Indicates the scope of the fine search; The optimal estimate is as follows: （18） In the formula, This represents the optimal estimate.

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