Low-complexity super-resolution positioning method based on near-field FFT-MUSIC

Abstract

The present invention discloses a low-complexity super-resolution positioning method based on near-field FFT-MUSIC, which belongs to the field of wireless communication and signal processing. The method receives signals transmitted by signal sources at different positions through an antenna array, obtains their covariance matrix, estimates the number of spatial sources, and determines the noise subspace; performs a one-dimensional fast Fourier transform in the angular domain to obtain an angular range containing the true source direction information, and classifies the signal sources according to whether the angular range contains multiple peaks; further uses a one-dimensional far-field beamforming algorithm or a one-dimensional far-field MUSIC algorithm to perform a spectral peak search in the distance dimension to obtain a distance range based on the distance of the signal source; and performs a high-precision two-dimensional MUSIC spectral peak search within the angle-distance range to achieve the final determination of the source position. Thus, the method solves the problems of current near-field source positioning, such as the difficulty, high computational complexity, and the need to pair angle-distance parameters, and improves positioning accuracy and efficiency.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communication and signal processing, and in particular to a low-complexity super-resolution positioning method based on near-field FFT-MUSIC. Background Art

[0002] In the field of modern signal processing, high-resolution spatial source positioning is a key technology in array signal processing, and is widely used in radar perception, electronic countermeasures, biomedicine and other fields. With the increasing demand for spatial resolution and positioning accuracy, as well as the continuous development and evolution of high-frequency broadband signals and ultra-large-scale array technology, the complexity of signal processing has increased significantly. At the same time, in the research on spatial source positioning technology, it can be divided into far-field source positioning and near-field source positioning according to the distance between the source and the receiving array in space and the array aperture. In the far-field source positioning problem, the distance of the source is greater than the Rayleigh distance, that is, r>2D 2 / λ, where r is the distance between the signal source and the reference element of the array, D is the array aperture, and λ is the signal wavelength of the signal source. At this time, the signal reaching the array can be approximated as a uniform plane wave. The position of the spatial signal source is determined by the propagation direction of the electromagnetic wave of the signal source. Therefore, the far-field signal source positioning problem can be transformed into the estimation of the direction of arrival of the signal source. When the distance of the signal source satisfies When the source signal reaches the array, the wavefront takes the form of a spherical wave. At this point, the spatial source's position depends not only on the source's incoming wave direction but also on the distance between the source and the array. In the near-field source localization model, the distance to the far-field source can be considered infinite, making the far-field source a special case of the near-field source. However, due to the coupling between incoming wave direction and distance, near-field source localization requires a larger dimension of variables to be estimated, a more complex signal transmission model, and issues such as the inability of existing far-field localization methods to be directly applied.

[0003] In order to solve the above problems, many scholars have directly expanded the positioning algorithm of far-field signal sources and realized the joint estimation of the direction of arrival and distance of near-field signal sources. The signal source positioning methods in classic far-field scenarios mainly include beamforming technology based on spatial division multiple access and subspace algorithms. Among them, beamforming technology is widely used due to its low implementation complexity. However, the spatial resolution of the beamforming method is limited by the Rayleigh limit, that is, the half-power point beam width Improving angular resolution requires increasing the element spacing or the number of elements, which complicates system implementation. Directly applying these methods to near-field source localization results in insufficient resolution in both the angular and distance dimensions, and inaccurate parameter estimation. To increase angular resolution, subspace algorithms based on the orthogonality of the signal and noise subspaces can achieve spatial resolution exceeding the Rayleigh criterion. A classic example of this approach is the Multiple Signal Classification (MUSIC) algorithm. However, the computational complexity of these algorithms, due to the computation of the feature space, increases dramatically. While these algorithms offer high estimation accuracy, the two-dimensional angle-range spectral peak search makes the computational complexity much higher than that of far-field source localization. Subsequently, several researchers have proposed various algorithms, such as polynomial root-finding algorithms, maximum likelihood estimation algorithms, path tracing methods, weighted linear prediction methods, and the use of known cost function paths instead of path search, to further reduce the computational complexity. Consequently, algorithms based on spectral peak search exhibit high computational complexity, making their direct extension and application to the near field challenging. On the other hand, algorithms based on second-order statistics generally have low computational complexity because they do not require spectral peak searching. In recent years, many algorithms based on higher-order statistics have been proposed, but these algorithms often require parameter pairing due to the multiple matrix decomposition operations they require. How to effectively reduce computational complexity, avoid high-dimensional spectral peak searching and parameter pairing, and maximize the accuracy of parameter estimation is a key issue in near-field source parameter estimation and is of practical significance.

[0004] On the other hand, in recent years, some scholars have proposed algorithms to reduce the complexity of spectral peak search algorithms in order to address the problem of high computational complexity of spectral peak search. By decoupling the angle and distance parameters, the high-dimensional spectral peak search is converted into multiple one-dimensional spectral peak searches, which greatly reduces the complexity of the near-field source localization algorithm. However, these algorithms require that the array element spacing is no more than a quarter wavelength, and have limitations such as the inability to accurately estimate sources at different distances in the same direction, which restricts their application in practice. Therefore, there are still great challenges in the research of near-field source localization algorithms. Summary of the Invention

[0005] The present invention provides a low-complexity super-resolution positioning method based on near-field FFT-MUSIC. By combining the advantages of low complexity of fast Fourier transform with the super-resolution positioning capability of near-field two-dimensional MUSIC algorithm, the present invention solves the problems of great difficulty in near-field source positioning, high computational complexity of traditional positioning algorithms, and low positioning resolution. It greatly simplifies the near-field source positioning method and realizes super-resolution and low-complexity positioning.

[0006] The embodiment of the present invention provides a low-complexity super-resolution positioning method based on near-field FFT-MUSIC, comprising the following steps:

[0007] Step 1: Receive signals transmitted by signal sources at different locations through an antenna array, obtain the covariance matrix of the received signal and perform eigenvalue decomposition, estimate the number of spatial signal sources and determine the noise subspace based on the decomposed eigenvalues;

[0008] Step 2: performing a one-dimensional fast Fourier transform in the angle domain to obtain an angle range containing true source direction information, and classifying the signal source into a long-distance source and a short-distance source based on whether the angle range contains multiple peaks;

[0009] Step 3.1: For distant signal sources, a one-dimensional MUSIC algorithm is used in combination with the noise subspace to search the super-resolution distance dimension, and the distance value of the distant signal source is determined based on the spectrum peak.

[0010] Step 3.2: For close-range signal sources, perform far-field beamforming spectrum peak search based on the upper and lower bounds of the angular range, and determine the distance range of the close-range signal source based on a preset threshold.

[0011] Step 4.1, locate the distant signal source according to the angle and distance value of the distant signal source;

[0012] Step 4.2: Perform a two-dimensional MUSIC combined spectrum peak search within the angle and distance range to locate the close-range signal source;

[0013] Step 5: Check whether the number of estimated signal sources is equal to the actual number of signal sources. If there are signal sources that are not successfully estimated, expand the search range and repeat the spectrum peak search step in step 4.2.

[0014] Optionally, in one embodiment of the present invention, in step 1, obtaining a covariance matrix of the received signal and performing eigenvalue decomposition, estimating the number of spatial information sources and determining the noise subspace according to the decomposed eigenvalues, includes:

[0015] By performing eigendecomposition on the covariance matrix, we obtain K larger eigenvalues ​​and MK smaller eigenvalues. The number of signal sources in the space is estimated based on the K larger eigenvalues. Based on the orthogonal relationship between the noise subspace and the signal subspace, we obtain the noise subspace composed of the eigenvectors corresponding to the MK smaller eigenvalues.

[0016] Optionally, in one embodiment of the present invention, step 2 specifically includes:

[0017] A one-dimensional fast Fourier transform is performed in the angular domain, and combined with the covariance matrix, multiple angular clusters containing the signal directions of the source are obtained. The distant and close sources are distinguished according to the number of spectral peaks contained in the angular cluster. When only distant sources exist in the angular cluster, the number of spectral peaks in the angular cluster is 1; when only close sources exist in the angular cluster, the heights of the irregular spectral peaks in the angular cluster are approximately equal; when both close and distant sources exist in the angular cluster, the spectral peaks in the angular cluster show one or more outliers that are significantly higher than other spectral peaks.

[0018] Optionally, in one embodiment of the present invention, step 5 specifically includes:

[0019] When performing a two-dimensional MUSIC joint spectrum peak search within the angle and distance range, if the number of spectrum peaks obtained by the search is equal to the estimated number of spatial signal sources, all signal sources are located, and the angle and distance values ​​corresponding to the spectrum peaks are output. If the number of spectrum peaks obtained by the search is not equal to the estimated number of spatial signal sources, the distance range is expanded with a preset step size, and a two-dimensional MUSIC joint spectrum peak search is performed within the expanded angle and distance range until the number of spectrum peaks obtained by the search is equal to the estimated number of spatial signal sources.

[0020] Optionally, in one embodiment of the present invention, for a distant signal source, a one-dimensional MUSIC spectrum peak search function is constructed:

[0021]

[0022] Among them, v(r,β j ) is the near field direction vector, β j is the estimated angle value, U n is the noise subspace.

[0023] Optionally, in one embodiment of the present invention, for a short-range signal source, a range-dimensional beamforming spectrum peak search function constructed when performing a far-field beamforming spectrum peak search based on the upper and lower bounds of the angle range is:

[0024] P bf =v(r,θ) H Rv(r,θ)

[0025] Where v(r,θ) is the near-field direction vector, are the upper and lower bounds of the angle range, and R is the covariance matrix;

[0026] Determine the distance range of the close-range signal source based on the preset threshold, including:

[0027] According to the spectrum of the beamforming method, there are real angle distance values ​​(r k ,θ k) as the center, the energy diffusion characteristics in the angle-distance direction, the search angle range α i as well as At the true angle value θ k On both sides of the spectrum peak search function, the corresponding peak search function will have a local minimum, and according to the preset threshold, a value greater than the peak search function P is obtained. bf The distance range of the minimum threshold Γ is obtained to obtain the distance range of the close-range signal source.

[0028] The low-complexity super-resolution positioning method based on near-field FFT-MUSIC in the embodiment of the present invention has the following beneficial effects:

[0029] 1. This method can fully utilize the low accuracy of traditional fast Fourier transform angle estimation and the energy diffusion caused when estimating near-field signal sources. Based on low-complexity FFT and one-dimensional far-field distance search, cascaded super-resolution two-dimensional MUSIC (Multiple Signal Classification) spectrum peak search, it solves the problems of existing far-field positioning methods being unable to be directly applied to near-field scenarios and the high computational complexity of existing near-field positioning algorithms, greatly improving the accuracy and estimation efficiency of near-field signal source positioning.

[0030] 2. This method fully utilizes the different representations of near-field signal sources at different distances in the Fast Fourier Transform results, effectively distinguishing and locating near-field signal sources at different distances. This achieves compatibility in locating near-field and far-field signal sources, further reducing the complexity of the algorithm implementation.

[0031] 3. This method is applicable not only to general communications and array signal processing scenarios, but also to specialized applications, such as those involving multiple near- and far-field signal sources in similar signal directions. It has a wide range of applications and exhibits significant performance advantages in scenarios with densely distributed signal sources.

[0032] 4. Existing near-field positioning algorithms typically require constructing high-order statistics, thus requiring array element spacing to be no greater than a quarter wavelength. This method does not impose strict requirements on array element spacing, and can therefore be directly applied to most existing antenna equipment.

[0033] Additional aspects and advantages of the present invention will be set forth in part in the description which follows and, in part, will be obvious from the description which follows, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0035] Figure 1 A flowchart of a low-complexity super-resolution positioning method based on near-field FFT-MUSIC according to an embodiment of the present invention;

[0036] Figure 2 A schematic diagram of the execution process of a low-complexity super-resolution positioning method based on near-field FFT-MUSIC provided by an embodiment of the present invention;

[0037] Figure 3 A low-complexity super-resolution positioning scene graph based on near-field FFT-MUSIC provided by an embodiment of the present invention;

[0038] Figure 4 This is a rendering of the low-complexity super-resolution positioning algorithm based on near-field FFT-MUSIC provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0039] The following describes embodiments of the present invention in detail, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and are not to be construed as limiting the present invention.

[0040] Figure 1 The present invention provides a flowchart of a low-complexity super-resolution positioning method based on near-field FFT-MUSIC according to an embodiment of the present invention.

[0041] like Figure 1 As shown, the low-complexity super-resolution positioning method based on near-field FFT-MUSIC includes the following steps:

[0042] Step 1: Receive signals transmitted by signal sources at different locations through an antenna array, obtain the covariance matrix of the received signal and perform eigenvalue decomposition, estimate the number of spatial signal sources and determine the noise subspace based on the decomposed eigenvalues;

[0043] Step 2: performing a one-dimensional fast Fourier transform in the angle domain to obtain an angle range containing true source direction information, and classifying the signal source into a long-distance source and a short-distance source based on whether the angle range contains multiple peaks;

[0044] Step 3.1: For distant signal sources, a one-dimensional MUSIC algorithm is used in combination with the noise subspace to search the super-resolution distance dimension, and the distance value of the distant signal source is determined based on the spectrum peak.

[0045] Step 3.2: For close-range signal sources, perform far-field beamforming spectrum peak search based on the upper and lower bounds of the angular range, and determine the distance range of the close-range signal source based on a preset threshold.

[0046] Step 4.1, locate the distant signal source according to the angle and distance value of the distant signal source;

[0047] Step 4.2: Perform a two-dimensional MUSIC combined spectrum peak search within the angle and distance range to locate the close-range signal source;

[0048] Step 5: Check whether the number of estimated signal sources is equal to the actual number of signal sources. If there are signal sources that are not successfully estimated, expand the search range and repeat the spectrum peak search step in step 4.2.

[0049] The method of the present invention is based on the low computational complexity of the fast Fourier transform, and converts the angle-distance two-dimensional joint estimation of the traditional near-field positioning method into a one-dimensional search in the angle and distance dimensions. Since a single spectrum peak cannot be obtained when the fast Fourier transform is used to estimate the angle of the near-field signal, there is an energy leakage problem and only the angle range cluster can be determined. The number of spectrum peaks in the angle cluster is greater than 1 to distinguish between the closer and farther sources, and they are located separately, further reducing the computational complexity. For the close source, a two-dimensional small-scale super-resolution MUSIC spectrum peak search is performed to achieve high-precision estimation and automatic matching of the angle-distance parameters.

[0050] In one embodiment of the present invention, in step 1, obtaining the covariance matrix of the received signal and performing eigenvalue decomposition, estimating the number of spatial information sources and determining the noise subspace based on the decomposed eigenvalues, includes:

[0051] By performing eigendecomposition on the covariance matrix, we can obtain K larger eigenvalues ​​and MK smaller eigenvalues. We can estimate the number of sources in the space based on the K larger eigenvalues. Based on the orthogonal relationship between the noise subspace and the signal subspace, we can obtain the noise subspace U consisting of the eigenvectors corresponding to the MK smaller eigenvalues. n .

[0052] In one embodiment of the present invention, step 2 specifically includes:

[0053] A one-dimensional fast Fourier transform is performed in the angular domain, and combined with the covariance matrix, multiple angular clusters containing the signal directions of the source are obtained. The distant and close sources are distinguished according to the number of spectral peaks contained in the angular cluster. When only distant sources exist in the angular cluster, the number of spectral peaks in the angular cluster is 1; when only close sources exist in the angular cluster, the heights of the irregular spectral peaks in the angular cluster are approximately equal; when both close and distant sources exist in the angular cluster, the spectral peaks in the angular cluster show one or more outliers that are significantly higher than other spectral peaks.

[0054] Angle clustering occurs when the incoming wave direction of a near-field source cannot be directly determined using a Fast Fourier Transform (FFT). This results in an energy diffusion effect. This is manifested as irregular peaks within a certain range of the angle search spectrum centered on the actual source direction, making it difficult to accurately estimate the source direction. When the sources are located in similar directions, their irregular peaks overlap, further complicating estimation. Consequently, only a rough angle range, or angle cluster, can be determined.

[0055] The actual number of signal sources contained in an angle cluster is unknown. Due to the differences in angle cluster morphology caused by the positional differences of the signal sources within the angle cluster, the signal sources can be divided into two categories with different distances and located separately. Specifically, when only long-distance signal sources exist in a certain angle cluster, the number of spectral peaks in the angle cluster is 1, so the angle value can be directly obtained using the fast Fourier transform. However, when close-range signal sources exist within the angle cluster, the angle cluster will exhibit irregular energy diffusion regardless of whether long-distance sources are also present. When only close-range signal sources exist, the heights of the irregular spectral peaks in the angle cluster are approximately equal. If there are also distant signal sources within the angle range, the spectral peaks in the angle cluster will exhibit one or more outliers that are significantly higher than the other spectral peaks.

[0056] The distance ranges obtained in step 3.2, i.e., the distance clusters, correspond one-to-one to the angle ranges obtained in step 2, i.e., the angle clusters. The approximate range of the distance parameter, i.e., the distance cluster, is determined based on the distance of the signal source. Specifically, for the case where only distant sources exist, a one-dimensional MUSIC search is performed in the super-resolution distance dimension, and the distance value of the distant source is determined based on the spectrum peak. For the angle clusters where close sources exist, a one-dimensional distance beamforming search is performed on the upper and lower bounds of the angle clusters, and the range of the distance cluster is determined based on the threshold. If a signal source at a greater distance also exists within the range of the angle cluster, the angle value of the distant signal source is obtained by searching for outliers. The distance value is obtained in the same way as when only distant sources exist.

[0057] The small-scale two-dimensional MUSIC in step 4.2 is performed within the range corresponding to the angle cluster obtained in step 2 and the distance cluster obtained in step 3.2. For scenarios where only long-distance signal sources exist or there are outliers in the angle cluster, there is no need to perform the two-dimensional MUSIC step, and the corresponding angle values ​​and distance values ​​can be directly output.

[0058] In one embodiment of the present invention, when a two-dimensional MUSIC joint spectral peak search is performed within an angle and distance range, if the number of spectral peaks obtained by the search is equal to the estimated number of spatial signal sources, all signal sources are located, and the angle and distance values ​​corresponding to the spectral peaks are output. If the number of spectral peaks obtained by the search is not equal to the estimated number of spatial signal sources, the distance range is expanded with a preset step size, and a two-dimensional MUSIC joint spectral peak search is performed within the expanded angle and distance range until the number of spectral peaks obtained by the search is equal to the estimated number of spatial signal sources.

[0059] The step size r is used when the range defined by the angle-distance cluster does not yet include all signal sources to be located. By gradually expanding the distance search range, all signal sources are located. After each expansion of the distance search range, the 2D MUSIC spectrum peak search is performed only within the newly added angle-distance range. This range should not include angle-distance values ​​already searched in previous iterations, thereby ensuring that the complexity of this positioning method is lower than that of the method using direct 2D MUSIC positioning.

[0060] The low-complexity super-resolution positioning method based on near-field FFT-MUSIC is not only applicable to relatively close signal sources, but also to scenarios where signal sources at both near and far distances exist simultaneously. It is also universally applicable to special scenarios where signal sources at different distances in the same direction exist, solving problems such as the high complexity of near-field signal source positioning methods, the difficulty of algorithm design, and the need for angle-distance matching.

[0061] The present invention receives the transmitted signal of a signal source through an antenna array, accumulates multiple snapshots of received signals, constructs a data covariance matrix, estimates the number of spatial signal sources, and determines the noise subspace. Based on the energy leakage problem existing in the positioning method based on the far-field scenario when estimating the near-field signal, a one-dimensional fast Fourier transform is performed in the angle dimension to obtain the directional range of the signal source, and the signal source is divided into two categories: long-range and short-range signal sources according to whether multiple peaks exist in the range. For the short-range signal source, a far-field beamforming spectrum peak search is performed corresponding to the upper and lower bounds of the above-mentioned directional range, respectively, and the distance range is determined by utilizing the characteristics of the beamforming method with low resolution and energy leakage. For the long-range signal source, a high-precision and high-resolution one-dimensional MUSIC spectrum peak search is performed in combination with the noise subspace to obtain the corresponding distance value. A high-precision two-dimensional MUSIC joint spectrum peak search is performed within the direction-distance range to achieve the final positioning of the near-field signal source. The proposed method solves the existing problems of near-field source positioning, such as the difficulty of near-field source positioning, strong coupling of angle-distance parameters, and high algorithm complexity, by locating near-field sources based on FFT-MUSIC. It greatly improves the positioning accuracy and reduces the computational complexity.

[0062] Combine Figure 2 As shown, in a specific embodiment of the present invention, the following steps are included:

[0063] a) Based on the received signal of the antenna array, the covariance matrix R is calculated and the eigenvalue decomposition is performed. The number of sources K in the space is estimated based on the number of larger eigenvalues. The orthogonal characteristics of the signal subspace and the noise subspace are used to form the noise subspace U based on the eigenvectors corresponding to the smaller eigenvalues. n ;

[0064] b) constructing a one-dimensional fast Fourier transform at point P in the angle dimension, combining it with the covariance matrix R obtained in step a) to obtain L angle clusters containing the directions of the source signals, and distinguishing between long and short distance signal sources based on the number of spectral peaks contained in the angle clusters;

[0065] c) FFT positioning has low resolution, and its output exhibits energy diffusion within a large range centered on the true source location. For each angular cluster with more than one spectral peak obtained in process b), two coarse-grained beamforming spectral peak searches in the distance dimension are performed to obtain the corresponding distance cluster. For angle clusters containing only one spectral peak, a one-dimensional MUSIC spectral peak search is performed to obtain the corresponding distance value.

[0066] d) performing two-dimensional super-resolution MUSIC algorithm positioning within the range defined by the angle-distance cluster to obtain K' spectral peaks;

[0067] e) If the number of signal sources K' found in step d) equals the number of signal sources K estimated based on the eigenvalues ​​in step a), all signal sources are considered successfully located, and the angle and distance values ​​corresponding to the spectrum peaks are output. Otherwise, the range cluster defined in step c) is considered to not include all signal sources. The range cluster is expanded by a step size r, and steps d) - e) are repeated.

[0068] Figure 3 This diagram shows an application scenario for a low-complexity super-resolution positioning method based on near-field FFT-MUSIC. A large-scale antenna array is used to receive signals in space, and there are also multiple signal sources that are close or far away from the base station.

[0069] Figure 4 This figure shows the effect of a low-complexity super-resolution localization method based on near-field FFT-MUSIC. Four signal sources can be seen in the figure, one of which is far away. Figure 4 (a) shows the direct positioning of the distant source. Figure 4 (b) shows the localization of close-range signal sources achieved by defining the two-dimensional MUSIC search range (as shown in the red box).

[0070] M = 2N + 1 represents the number of antenna elements, d represents the spacing between antenna elements, y represents the array receiving signal, λ represents the wavelength of the signal, J represents the number of snapshots, R represents the covariance matrix calculated based on the received signal, K represents the number of signal sources in space, and the position of the signal source is represented by (r k ,θ k ) indicates; U n represents the noise subspace. Γ is the threshold, is the angle cluster obtained by one-dimensional FFT, where and α i Respectively represent the upper and lower boundaries of the i-th angle cluster, β j ,j=1,…,P f Indicates the angle value of the distant signal source, n g With n l are the number of points searched for angle and distance, Δ g With Δ l is the corresponding search step; similarly, use γ i With l j Respectively represent the corresponding i and β j The distance cluster or distance value, v(r,θ) is the near-field direction vector, and s represents the step size of the range of updating the distance cluster.

[0071] Based on the above definitions, the specific implementation steps of the method in the embodiment of the present invention can be summarized as follows:

[0072] (1) Initial data collection phase. By collecting J snapshots of the antenna array’s received signal Y, according to R=YY H / J obtains the covariance matrix. By performing eigenvalue decomposition on R, we get K larger eigenvalues ​​and MK smaller eigenvalues. According to the orthogonal relationship between the noise subspace and the signal subspace, we get the noise subspace U consisting of the eigenvectors corresponding to the smaller eigenvalues. n .

[0073] (2) Angle search stage. The one-dimensional fast Fourier transform matrix of point P is constructed as follows:

[0074]

[0075] By performing one-dimensional FFT on the covariance matrix R by column and one-dimensional IFFT on the row, we get R′, and the output result is p FFT =diag{R'}.

[0076] (3) The stage of judging the source of the distance. Due to the existence of energy diffusion, there will be more than K peaks. The continuous parts greater than the threshold Γ are selected to form multiple angle clusters. If there are multiple peaks in an angle cluster, it is recorded as If there is only one peak in a certain angle cluster, the signal source at this angle is far away, so only a single angle value is output, which is recorded as β j For each angle cluster with multiple peaks, check whether there are outliers: if there are no outliers, it is considered that there is no long-distance signal source within the angle range; otherwise, it is considered that the signal source corresponding to the outlier also belongs to the long-distance range, and the corresponding angle value is also recorded as β j .

[0077] (4) Long-distance signal source search stage. In the case where only long-distance signal sources exist, since there is no energy leakage problem, high-precision distance parameter estimation can be performed directly. Based on the β obtained in (3), j , construct a one-dimensional MUSIC spectrum peak search function: By searching the spectrum peak, the corresponding distance value l is obtained j .

[0078] (5) Close-range search stage. For the case of close-range signal sources, whether or not there are outliers, it is necessary to construct the number of points n based on the angle range obtained in (3). l , the search step is Δ l The distance-dimensional beamforming spectrum peak search function: P bf =v(r,θ) H Rv(r,θ), where v(r,θ) is the direction vector corresponding to the near field, According to the spectrum of the beamforming method, there are real angle distance values ​​(r k ,θ k ) as the center, the energy diffusion characteristics in the angle-distance direction can be seen. α i as well as At the true value θ k On both sides of the spectrum, the corresponding peak search function will have a local minimum, so it is possible to obtain a value greater than P bf The distance range of the minimum threshold Γ is denoted as γ i .

[0079] (6) High-precision positioning stage: Within the angle and distance ranges obtained in steps (3) and (5), a two-dimensional MUSIC algorithm is used to achieve joint estimation and automatic pairing of angles and distances within the range.

[0080] (7) Long-distance signal source positioning stage: Output the long-distance signal source angle and corresponding distance value obtained in steps (3) and (4) to achieve long-distance signal source positioning.

[0081] (8) Signal source number determination stage. Based on the number of spectrum peaks searched in step (6) and the number of distant signal sources obtained in step (7), check whether they are equal to the number of signal sources K obtained in step (1). If they are equal, output the angular distance value corresponding to the spectrum peak and the angular distance value of the distant signal source.

[0082] (9) Distance cluster range update phase. If step (8) is not satisfied, it is considered that the distance cluster range determined in step (5) is insufficient to include all signal sources. This may be because the setting of the threshold Γ depends on experience, or the distances of the signal sources within the angle cluster vary greatly, causing the spectrum peak search functions to affect each other. In this case, it is necessary to expand the range of the distance cluster by a step size s.

[0083] (10) Positioning update phase. Within the expanded range cluster, a two-dimensional MUSIC algorithm is used to search for spectrum peaks. This range should not include the range of the distance cluster determined in step (4) to ensure that the total number of searches does not exceed that of a direct global search. Thereafter, steps (8) and (9) are repeated until all signal sources are located.

[0084] The above method uses data collection and offline calculation (step (1)) to determine the angle range and distinguish between long-distance and short-distance signal sources through low-complexity one-dimensional FFT (steps (2)-(3)). Furthermore, a coarse-grained distance range is determined through a one-dimensional distance search (steps (4)-(5)). Finally, high-precision near-field signal source positioning is achieved (steps (6)-(7)). The method also includes improvement measures for cases where the signal source distribution is relatively extreme, thereby improving the robustness and universality of the method (steps (8)-(10)).

[0085] The low-complexity super-resolution positioning method based on near-field FFT-MUSIC in an embodiment of the present invention, based on the low computational complexity of the fast Fourier transform, converts the traditional angle-distance two-dimensional joint search into a one-dimensional search in the angle and distance dimensions. The one-dimensional FFT is used to directly estimate the signal incident angle, and the sources at longer distances and closer distances are distinguished based on whether a single spectral peak exists, and are located separately, further reducing the computational complexity. For close-range sources, a two-dimensional small-scale super-resolution MUSIC spectral peak search is performed to achieve high-precision estimation and automatic matching of angle-distance parameters. The present invention solves the current problems of difficult near-field source positioning, high computational complexity, and the need to pair angle-distance parameters through methods such as combining coarse and fine granularity searches and combining far- and near-field positioning algorithms, thereby greatly improving positioning accuracy and efficiency. In addition, the present method does not rely on the calculation of spatial correlation, thus breaking the limitation of existing methods that require array element spacing to be less than a quarter wavelength, and is compatible with more general antenna architectures.

[0086] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials 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 expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or N embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples without contradiction.

[0087] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of technical features indicated. Thus, a feature specified as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "N" means at least two, such as two, three, etc., unless otherwise specifically defined.

[0088] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, segment or portion of code comprising one or N executable instructions for implementing a custom logical function or step of a process, and the scope of the preferred embodiments of the present invention includes alternative implementations in which functions may be performed out of the order shown or discussed, including performing functions in a substantially simultaneous manner or in the reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present invention pertain.

Claims

1. A low-complexity super-resolution positioning method based on near-field FFT-MUSIC, characterized in that: The following steps are involved: Step 1: Receive signals transmitted by signal sources at different locations through an antenna array, obtain the covariance matrix of the received signal and perform eigenvalue decomposition, estimate the number of spatial signal sources and determine the noise subspace based on the decomposed eigenvalues; Step 2: performing a one-dimensional fast Fourier transform in the angle domain to obtain an angle range containing true source direction information, and classifying the signal source into a long-distance source and a short-distance source based on whether the angle range contains multiple peaks; Step 3.1: For distant signal sources, a one-dimensional MUSIC algorithm is used in combination with the noise subspace to search the super-resolution distance dimension, and the distance value of the distant signal source is determined based on the spectrum peak. Step 3.2: For close-range signal sources, perform far-field beamforming spectrum peak search based on the upper and lower bounds of the angular range, and determine the distance range of the close-range signal source based on a preset threshold. Step 4.1, locate the distant signal source according to the angle and distance value of the distant signal source; Step 4.2: Perform a two-dimensional MUSIC combined spectrum peak search within the angle and distance range to locate the close-range signal source; Step 5: Check whether the number of estimated signal sources is equal to the actual number of signal sources. If there are signal sources that are not successfully estimated, expand the search range and repeat the spectrum peak search step in step 4.

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2. The method according to claim 1, characterized in that In step 1, the covariance matrix of the received signal is obtained and eigenvalue decomposition is performed. The number of spatial information sources is estimated based on the decomposed eigenvalues ​​and the noise subspace is determined, including: By performing eigendecomposition on the covariance matrix, we obtain K larger eigenvalues ​​and MK smaller eigenvalues. The number of signal sources in the space is estimated based on the K larger eigenvalues. Based on the orthogonal relationship between the noise subspace and the signal subspace, we obtain the noise subspace composed of the eigenvectors corresponding to the MK smaller eigenvalues.

3. The method according to claim 1, characterized in that Step 2 specifically includes: A one-dimensional fast Fourier transform is performed in the angular domain, and combined with the covariance matrix, multiple angular clusters containing the signal directions of the source are obtained. The distant and close sources are distinguished according to the number of spectral peaks contained in the angular cluster. When only distant sources exist in the angular cluster, the number of spectral peaks in the angular cluster is 1; when only close sources exist in the angular cluster, the heights of the irregular spectral peaks in the angular cluster are approximately equal; when both close and distant sources exist in the angular cluster, the spectral peaks in the angular cluster show one or more outliers that are significantly higher than other spectral peaks.

4. The method according to claim 1, wherein Step 5 specifically includes: When performing a two-dimensional MUSIC joint spectrum peak search within the angle and distance range, if the number of spectrum peaks obtained by the search is equal to the estimated number of spatial signal sources, all signal sources are located, and the angle and distance values ​​corresponding to the spectrum peaks are output. If the number of spectrum peaks obtained by the search is not equal to the estimated number of spatial signal sources, the distance range is expanded with a preset step size, and a two-dimensional MUSIC joint spectrum peak search is performed within the expanded angle and distance range until the number of spectrum peaks obtained by the search is equal to the estimated number of spatial signal sources.

5. The method according to claim 1, wherein For distant signal sources, construct a one-dimensional MUSIC spectrum peak search function: Among them, v(r,β j ) is the near field direction vector, β j is the estimated angle value, U n is the noise subspace.

6. The method according to claim 1, characterized in that For a close-range signal source, the distance-dimensional beamforming spectrum peak search function constructed when searching for the far-field beamforming spectrum peak based on the upper and lower bounds of the angle range is: P bf =v(r,θ) H Rv(r,θ) Where v(r,θ) is the near-field direction vector, are the upper and lower bounds of the angle range, and R is the covariance matrix; Determine the distance range of the close-range signal source based on the preset threshold, including: According to the spectrum of the beamforming method, there are real angle distance values ​​(r k ,θk) as the center, the energy diffusion characteristics in the angle-distance direction, the search angle range α i as well as Located on both sides of the true angle value θk, the corresponding spectrum peak search function will have a local minimum, and according to the preset threshold, a value greater than the spectrum peak search function P is obtained. bf The distance range of the minimum threshold Γ is obtained to obtain the distance range of the close-range signal source.

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