Near-field coherent signal source positioning method and system based on overlapped sub-arrays and iterative optimization

Abstract

The invention discloses a near-field coherent signal source positioning method and system based on overlapped sub-arrays and iterative optimization, and belongs to the technical field of signal processing, and the method comprises the steps: dividing the whole array antenna into two arrays, and decomposing a received signal into two receiving sub-arrays; for each receiving sub-array, forming a new covariance matrix by an outer product of back diagonal elements corresponding to the covariance matrix of the receiving sub-array; carrying out eigenvalue decomposition on the new covariance matrix of each array, and constructing an angle polynomial equation based on a spectral function to obtain an angle estimation value corresponding to the center of the array; obtaining respective corresponding target distances by using the angle estimation values of the two array centers, and obtaining an initial angle and a distance estimation value of a signal source relative to the whole array antenna; and optimizing the initial angle and distance estimated values by adopting an alternating oblique projection method to obtain the optimized angle and distance of the signal source. The method has better robustness in a coherent signal environment, and is suitable for high-precision near-field positioning.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a near-field coherent signal source localization method and system based on overlapping sub-arrays and iterative optimization. Background Art

[0002] Signal source localization technology is widely used in multiple fields, including radar, sonar, wireless communication, navigation, and intelligent transportation, etc. In military reconnaissance, environmental monitoring, and various communication and positioning systems, signal source localization technology plays a crucial role. These technologies can not only improve the positioning accuracy but also achieve real-time monitoring and response in a dynamic and complex environment.

[0003] In signal source localization, the difference between the near field and the far field has a crucial impact on the selection and effect of the localization method. In a far-field environment, the signal wavefront is usually a plane wave, and the phase difference of the signal arriving at the array is linear. Therefore, the signal source localization problem is relatively simple, and many traditional methods such as maximum likelihood estimation (MLE), multiple signal classification (MUSIC), etc., can effectively estimate the arrival angle of the signal source. However, when the signal source is in the near-field region, the signal wavefront becomes a spherical wave, and the phase difference of the signal arriving at the array becomes non-linear, which brings higher complexity and requires simultaneous estimation of the arrival angle and distance of the signal source.

[0004] With the introduction of algorithms such as multiple signal classification into the near-field environment, the constraint of the Rayleigh limit is alleviated, and the positioning accuracy is improved. However, these methods have a large computational amount due to the need for two-dimensional or multi-dimensional global search and face challenges in real-time processing. Research shows that the two localization parameters of the near-field signal source, namely distance and arrival angle, can be estimated separately. To avoid using two-dimensional estimation methods, multiple one-dimensional estimators can be used, such as reduced dimension (RD) method, weighted linear prediction method, rank reduced (RARE) method, second order statistics (SOS) method, etc.

[0005] In addition to the computational complexity problem, another challenge in near-field signal source localization lies in the processing of coherent signals. Traditional localization algorithms usually assume that the signal sources are independent. However, in practical applications, especially in the near-field case where multiple signal sources are close to each other and have coherence, the assumptions of traditional methods do not hold. The interference between coherent signal sources causes a significant decrease in the positioning accuracy and makes it impossible to accurately distinguish adjacent signal sources. These problems are particularly prominent in a multi-signal source environment. Therefore, how to improve the positioning accuracy in the case of coherent signal sources, especially in the problem of localizing multiple closely adjacent signal sources, has become a difficult problem that needs to be solved urgently in the current signal source localization technology. Summary of the Invention

[0006] In view of the deficiencies in the prior art, the present invention provides a near-field coherent signal source localization method and system based on overlapping sub-arrays and iterative optimization, which has better robustness in a coherent signal environment and is applicable to high-precision near-field localization problems.

[0007] The present invention provides the following technical solutions:

[0008] In a first aspect, a near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization is provided, including the following steps:

[0009] S1: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two receiving sub-arrays;

[0010] S2: For each receiving sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements;

[0011] S3: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angular polynomial equation based on the spectral function. After solving, obtain the angular estimation value corresponding to the array center;

[0012] S4: Use the angular estimation values of the two array centers to obtain their respective corresponding target distances to obtain the position of the signal source, and based on the position of the signal source, obtain the initial angular and distance estimation values of the signal source relative to the entire array antenna;

[0013] S5: Use the alternating oblique projection method to optimize the initial angular and distance estimation values to obtain the optimized angular and distance of the signal source.

[0014] Optionally, the array antenna is arranged as a uniform linear array of 2M + 1 sensors. When K completely correlated narrowband signals are incident on the array antenna, with the array center of the array antenna as the phase reference point, the signal y m (t) received by the m-th sensor is:

[0015]

[0016] where s k (t) is the signal of the k-th signal source received by the phase reference point, and n m (t) is the complex Gaussian white noise independent of the signal, and τ mk is the phase delay of the signal propagating from the reference point to the m-th sensor; where λ is the signal wavelength, d is the sensor spacing, r k and θ k are the distance and angle of the k-th signal source, respectively;

[0017] The received signal vector y(t) of the overall array antenna is y(t)=[y -M (t),...,y M (t)] T is transformed into:

[0018] y(t)=As(t)+n(t);

[0019] where s(t)=[s1(t),…,s K (t)] T is a K×1 dimensional signal vector, n(t)=[n -M (t),…,n M (t)] T is a (2M + 1)×1 dimensional noise vector, and A is a (2M + 1)×K dimensional array steering matrix; A=[a(r1,θ1),…,a(r K ,θ K )]; a(r k ,θ k ) is the steering vector,

[0020] Optionally, step S1 is specifically:

[0021] The two arrays respectively include the first 2M sensors and the last 2M sensors, and the received signals of the two receiving sub-arrays are specifically:

[0022]

[0023] Optionally, step S2 is specifically:

[0024] S21: Obtain the covariance matrices R1 and R2 of the two receiving sub-arrays respectively;

[0025]

[0026] where y1(t) and y2(t) are the received signals of the two receiving sub-arrays respectively; T is the number of snapshots, and the superscript H is the transpose conjugate operator;

[0027] S22: Extract the anti-diagonal elements r i of the covariance matrices R1 and R2 respectively;

[0028]

[0029] where the element r m,2M+2-m in the m-th row and the (2M + 2 - m)-th column is expressed as: and represent the power of the k-th source and the noise power respectively.

[0030] S23: Based on the anti-diagonal element r i Construct two new covariance matrices R y1 and R y2 ;

[0031]

[0032] wherein, R y1 and R y2 are both 2M×2M-dimensional matrices, and the superscript T is the transpose operator.

[0033] Optionally, step S3 is specifically:

[0034] S31: Perform sub-band processing on the new covariance matrices R y1 and R y2 , specifically: According to the SSP method, use the method of window sliding with a set window size S to extract multiple S×S-dimensional sub-matrices from R y1 , R y2 and average all the extracted sub-matrices to obtain a smoothed S×S-dimensional matrix R ; smoothi ;

[0035]

[0036] wherein, q represents the qth sliding window, and P = 2M - S + 1 is the number of sub-matrices;

[0037] S32: Perform eigenvalue decomposition on the matrix R smoothi to obtain the noise subspace U ni ;

[0038]

[0039] wherein, Λ si and Λ ni are respectively the K×K-dimensional and (S - K)×(S - K)-dimensional diagonal matrices corresponding to the ith matrix R smoothi , and U si and U ni are respectively the S×K-dimensional and S×(S - K)-dimensional signal subspace and noise subspace corresponding to the ith matrix R smoothi ;

[0040] S33: Decompose the steering vector a(r k , θ k ) into parameters Γ(ω) that are only related to the angle and parameters b(φ) that are related to both the angle and the distance;

[0041]

[0042] S34: Transform the MUSIC spectrum function into a polynomial - form equation related to θ k :

[0043]

[0044] where,

[0045] S35: Transform the problem of solving the polynomial - form equation into: solving the roots z of the following formula k , and obtain the angle estimation values corresponding to the two array centers according to the relationship between the roots and the angle θ and

[0046]

[0047] Optionally, step S4 is specifically:

[0048] S41: Based on the angle estimation values and of the two array centers, obtain the target distances and

[0049] corresponding to each array center through geometric relationshipsS42: Use the angle estimation values and and as well as the target distances

[0050]

[0051] S43: According to the position of the signal source k, calculate the initial angle of the signal source k relative to the overall array antenna and the distance estimation value

[0052]

[0053] Optionally, step S5 is specifically:

[0054] S51: Use all the initial angles of the signal sources relative to the overall array antenna and the distance estimation values as the initial values of the iteration;

[0055]

[0056] S52: Use the angle and distance of the (l - 1) - th iteration to calculate the oblique projection matrix along the direction of the k - th signal source for the current l (l = 1, 2,..., L) - th iteration

[0057]

[0058] Among them, is the steering vector a(θ k ,r k ), Let Γ k (θ k ,r k ) is the orthogonal projection matrix projected onto the null space of the kth signal source, M s ×M s dimensional identity matrix, and M s =2M+1;

[0059] S53: Based on the oblique projection matrix Define K virtual signal vectors and will The covariance matrix of It is expressed as: Yes k (t) signal power;

[0060] S54: Based on the covariance matrix DOA estimator for the kth signal source for:

[0061]

[0062] in,

[0063] S55: Update the oblique projection matrix And the covariance matrix And based on the updated covariance matrix and the angle estimate of the DOA estimator Calculating distance

[0064]

[0065] S56: Continuously iterate until the predicted number of iterations is reached or the following stop conditions are met, and then output the optimal angle and distance;

[0066]

[0067] Among them, μ is the set threshold.

[0068] Second aspect, there is provided a near-field coherent signal source localization system based on overlapping sub-arrays and iterative optimization, including:

[0069] Data receiving module: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two received sub-arrays;

[0070] Covariance calculation module: For each received sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements;

[0071] Eigenvalue decomposition module: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angular polynomial equation based on the spectral function. After solving, obtain the angular estimation value corresponding to the array center;

[0072] Coarse estimation module: Use the angular estimation values of the two array centers to obtain their respective corresponding target distances to obtain the position of the signal source, and based on the position of the signal source, obtain the initial angular and distance estimation values of the signal source relative to the entire array antenna;

[0073] Iterative optimization module: Use the alternating oblique projection method to optimize the initial angular and distance estimation values to obtain the optimized angular and distance of the signal source.

[0074] Third aspect, there is provided a computer device, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, the steps of the near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization described in any item of the first aspect are implemented.

[0075] Fourth aspect, a computer-readable storage medium is used to store a computer program; when the computer program is executed by a processor, the steps of the near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization described in any item of the first aspect are implemented.

[0076] Compared with the prior art, the beneficial effects of the present invention are:

[0077] Through sub-array decomposition, the Root method, and geometric calculation, the present invention improves the accuracy of angle and distance estimation while reducing the computational complexity. First, the array is divided into two sub-arrays to improve the signal resolution ability and reduce the influence of coherent signals. Then, the Root method is used to directly solve the DOA angle estimation, avoiding the high-complexity spectral peak search of the traditional MUSIC method and significantly reducing the computational amount. Next, the distance is calculated using geometric relationships without additional searching, thereby further improving the computational efficiency and accuracy. Compared with the traditional method, this method has better robustness in a coherent signal environment and is applicable to high-precision near-field localization problems. Description of the Drawings

[0078] Figure 1 is a schematic flowchart of the method for localizing near-field coherent signal sources based on overlapping subarrays and iterative optimization according to the present invention;

[0079] Figure 2 is a schematic diagram of the decomposition of the array antenna with a uniform linear array structure according to the present invention;

[0080] Figure 3 is a scatter plot of the estimation results under 100 test times provided in Embodiment 2 of the present invention;

[0081] Figure 4 are the estimation results of the angles of two signal sources in multiple iteration steps by using the method of the present invention in Embodiment 2;

[0082] Figure 5 are the estimation results of the distances of two signal sources in multiple iteration steps by using the method of the present invention in Embodiment 2;

[0083] Figure 6 is an RMSE curve graph of angle estimation by the method provided in Embodiment 2 of the present invention under different SNRs;

[0084] Figure 7 is an RMSE curve graph of distance estimation by the method provided in Embodiment 2 of the present invention under different SNRs;

[0085] Figure 8 is a structural block diagram of the system for localizing near-field coherent signal sources based on overlapping subarrays and iterative optimization according to the present invention. Detailed implementation manners

[0086] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention, and cannot be used to limit the protection scope of the present invention.

[0087] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above accompanying drawings are used to distinguish similar objects, and do not have to be used to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described here can be implemented in an order different from those illustrated or described here. In addition, the term "comprising" and any deformation thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0088] Embodiment 1

[0089] AsFigure 1 As shown in the figure, a near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization is provided, including the following steps:

[0090] S1: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two receiving sub-arrays.

[0091] As Figure 2 shown in the uniform linear array, consider a near-field scenario where K completely correlated narrowband signals are incident on a uniform linear array containing 2M + 1 sensors. Assume that the center of the array is the phase reference point. Then the signal y m (t) received by the m-th sensor is:

[0092]

[0093] where s k (t) is the signal of the k-th signal source received by the phase reference point, n m (t) is the complex Gaussian white noise independent of the signal, and τ mk is the phase delay of the signal propagating from the reference point to the m-th sensor;

[0094]

[0095] where λ is the signal wavelength, d is the sensor spacing, r k and θ k are the distance and angle of the k-th signal source respectively.

[0096] The received signal vector y(t) = [y -M (t),..., y M (t)] T is transformed into:

[0097] y(t) = As(t) + n(t);

[0098] where s(t) = [s1(t),..., s K (t)] T is a K×1 dimensional signal vector, n(t) = [n -M (t),..., n M (t)] T is a (2M + 1)×1 dimensional noise vector, and A is a (2M + 1)×K dimensional array steering matrix;

[0099] A = [a(r1,θ1),..., a(r K ,θ K )];

[0100] where \(a(r\) k ,\(\theta\) k ) is the steering vector, and the steering vector \(a(r\) k ,\(\theta\) k ) is expressed as:

[0101]

[0102] By performing a second-order Taylor expansion on \(\tau\) mk , we have:

[0103]

[0104] where represents the high-order terms. After ignoring the high-order terms and substituting the phase delay \(\tau\) mk into the signal model, it can be written as:

[0105]

[0106] Therefore, the steering vector \(a(r\) k ,\(\theta\) k ) can be expressed as:

[0107]

[0108] If \(\tau\) mk \(\approx m\omega\) k + m 2 \(\varphi\) k , then where and the steering vector \(a(r\) k ,\(\theta\) k ) can be expressed as:

[0109]

[0110] The uniform linear array is divided into two parts. The two arrays respectively include the first 2M sensors and the last 2M sensors, and the centers of the arrays are -1 / 2 and 1 / 2 respectively.

[0111] Each sub-array has an independent reference point, thereby retaining more array aperture information and reducing array performance loss. The received signals of the two receiving sub-arrays are specifically:

[0112]

[0113] S2: For each receiving sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements.

[0114] The covariance matrix of the received signal can be expressed as:

[0115]

[0116] Among them, T is the number of snapshots.

[0117] S21: Obtain the covariance matrices R1 and R2 of the two receiving sub-arrays respectively;

[0118] Since the overall array antenna is divided into array 1 and array 2, the covariance matrices R1 and R2 of the two receiving sub-arrays;

[0119]

[0120] Among them, y1(t) and y2(t) are the received signals of the two receiving sub-arrays respectively; T is the number of snapshots, and the superscript H is the transpose conjugate operator;

[0121] S22: Extract the anti-diagonal elements r i of the covariance matrices R1 and R2; the anti-diagonal elements of the covariance matrix R. It is found that these elements are only related to the DOA. The elements in the m-th row and the (2M + 2 - m)-th column of the covariance matrix are expressed as:

[0122]

[0123] Among them, and represent the power of the k-th source and the noise power respectively.

[0124] By extracting the anti-diagonal elements of R1 and R2, two virtual far-field models related only to the DOA can be obtained:

[0125]

[0126] S23: Based on the anti-diagonal elements r i construct two new covariance matrices R y1 and R y2 ;

[0127]

[0128] Among them, R y1 and R y2 are both 2M×2M-dimensional matrices, representing the covariance matrices formed by the outer products of the anti-diagonal elements, and the superscript T is the transpose operator.

[0129] S3: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angle polynomial equation based on the spectral function, and obtain the angle estimation value corresponding to the array center after solving.

[0130] Step S3 specifically includes:

[0131] S31: For the new covariance matrix Ry1 and R y2 Perform sub-band processing.

[0132] Specifically: According to the SSP method, with the set window size S, use the window sliding method to extract multiple S×S-dimensional sub-matrices from R y1 ,R y2 ;

[0133]

[0134] Average all the extracted sub-matrices to obtain a smoothed S×S-dimensional matrix R smoothi ;

[0135]

[0136] where q represents the q-th sliding window, and P = 2M - S + 1 is the number of sub-matrices.

[0137] S32: Perform eigenvalue decomposition on matrix R smoothi to obtain the noise subspace U ni ;

[0138]

[0139] where Λ si and Λ ni are the K×K-dimensional and (S - K)×(S - K)-dimensional diagonal matrices corresponding to the i-th matrix R smoothi respectively, and U si and U ni are the signal subspace and noise subspace of the S×K-dimensional and S×(S - K)-dimensional corresponding to the i-th matrix R smoothi respectively.

[0140] S33: Decompose the steering vector a(r k ,θ k ) into parameters Γ(ω) related only to the angle and parameters b(φ) related to both the angle and the distance;

[0141]

[0142] S34: Under the approximate model, transform the MUSIC spectral function into a polynomial form equation related to θ k :

[0143]

[0144] where U ni is the noise subspace obtained by decomposing R smoothi .

[0145] S35: Transform the problem of solving a polynomial - form equation into: finding the roots \(z\) of the following formula k , and obtain the estimated angle corresponding to the two array centers according to the relationship between the root and the angle \(\theta\) and

[0146] Assume \(\Gamma(\omega)\) can be written in the following form:

[0147]

[0148] Transform the problem into the form of a polynomial:

[0149]

[0150] Solve the roots \(z\) of the polynomial, and select the root \(z\) on the unit circle closest to \(K\) k , and obtain the estimated angles corresponding to different array centers

[0151] S4: Use the estimated angles of the two array centers to obtain their respective corresponding target distances to obtain the position of the signal source, and according to the position of the signal source, obtain the initial angle and distance estimates of the signal source relative to the overall array antenna.

[0152] S41: Based on the estimated angles of the two array centers and Obtain the target distance corresponding to each array center through geometric relationships and

[0153] Specifically, given the angle the distance from the \(k\) - th signal source to different center points can be obtained through geometric relationships

[0154]

[0155] Use the geometric relationship of DOA to establish the following equation:

[0156]

[0157] Solve the linear equation system to calculate the distance between the two phase points:

[0158]

[0159] Through it can be obtained and

[0160] In some other embodiments, by using what has been obtained From geometric relationships, it can be obtained that:

[0161]

[0162] S42: Use the angle estimation value and and the target distance and to calculate the position of the signal source k;

[0163] Specifically, use DOA and distance to calculate the Cartesian coordinates of the signal source:

[0164]

[0165] Therefore, the position of the k-th signal source can be obtained through the following formula:

[0166]

[0167] S43: According to the position of the signal source k, use the following formula to calculate the initial angle of the signal source k relative to the overall array antenna

[0168]

[0169] By using geometric methods to inversely deduce the Cartesian coordinates, finally, the rough estimated angle and distance of the signal source relative to the center point of the array and

[0170] S5: Use the alternating oblique projection method to optimize the initial angle and distance estimation values to obtain the optimized angle and distance of the signal source.

[0171] Specifically, S51: Take the initial angles of all signal sources relative to the overall array antenna and the distance estimation values

[0172]

[0173] as the initial values of the iteration; and the distance Calculate the oblique projection matrix

[0174] along the direction of the k-th signal source for the current l (l = 1, 2,..., L) iteration. Let be the steering vector a(θ k ,r k) array steering matrix, that is:

[0175]

[0176] Let Γ k (θ k ,r k ) is the orthogonal projection matrix projected onto the null space of the kth signal source, that is:

[0177]

[0178] in, M s ×M s dimensional identity matrix, and M s =2M+1.

[0179] In the lth iteration (l = 1, 2, ..., L), the oblique projection matrix P along the direction of the kth signal source can be calculated by using the DOA and distance estimates of the (l-1)th step k :

[0180]

[0181] S53: Based on the oblique projection matrix Define K virtual signal vectors and will The covariance matrix of It is expressed as: Yes k (t) signal power.

[0182] Specifically, the oblique projection matrix has the following properties:

[0183]

[0184] Through the oblique projection matrix To eliminate the influence of other signal sources (except the kth signal source), K virtual signal vectors are defined

[0185]

[0186] in, It is an oblique projection matrix that eliminates the components of other signal sources by projecting the signal onto a subspace that only retains the kth signal source.

[0187] In this way, The main component of is the signal of the kth signal source, and the influence of other signal sources is significantly weakened or eliminated. And, The covariance matrix of Expressed as:

[0188]

[0189] According to the above formula, it can be rewritten as:

[0190]

[0191] Where is the signal power of s k (t).

[0192] S54: Based on the covariance matrix The DOA estimator for the k-th signal source is:

[0193] Wherein,

[0194] Specifically, according to the principle of vector dot product, the following relationship is satisfied:

[0195]

[0196] It can be easily seen from this that when θ = θ k the left side of the formula reaches the maximum value Therefore, in the l-th iteration, the DOA estimator for the k-th signal source can be expressed as:

[0197]

[0198] S55: Update the oblique projection matrix and the covariance matrix and based on the updated covariance matrix and the angle estimation value of the DOA estimator calculate the distance

[0199] By performing a peak search on it, the k-th DOA estimate at the l-th step can be obtained, that is Then based on the DOA estimate update the oblique projection matrix in the l-th iteration as follows:

[0200]

[0201] Where

[0202] By using to replace it can be rewritten as

[0203]

[0204] Among them, is the noise-free covariance matrix.

[0205] Correspondingly, the distance estimator based on the ML technique is expressed as:

[0206]

[0207] S56: Continuously iterate until the predicted number of iterations is reached or the following stop condition is satisfied, and then output the optimal angle and distance;

[0208] Specifically, by performing a peak search on the above formula, the k-th distance estimate at the l-th step can be obtained This process will continue to iterate until the stop condition is met, that is, the preset number of iterations L is reached or the difference between two iterations is less than a threshold:

[0209]

[0210] where μ is the set threshold.

[0211] Embodiment 2

[0212] Provide a specific simulation example. In this simulation example, consider a uniform linear array composed of 11 isotropic sensors. The distance d between two adjacent sensors in the linear array is set to d = λ / 4, where λ is the signal wavelength. Therefore, the Fresnel region in this simulation example is [2.45λ, 12.5λ]. Assume that two signal sources are incident from [4λ, 10°] and [5.2λ, 35°] respectively.

[0213] Simulation 1: Set the number of snapshots L to 1000, the signal-to-noise ratio SNR to 10 dB, and two signal sources are incident from [4λ, 10°] and [5.2λ, 35°] respectively. Figure 3 Shows the estimated scatter plot of the incident signal under the above conditions by the method proposed in this embodiment. In the figure, represents the true signal source position, · represents the estimated signal source position. By observing the result graph, the conclusion is drawn that the estimated values all fall within a small range near the true values and can be effectively estimated.

[0214] Simulation 2: Set the number of snapshots L to 1000, the signal-to-noise ratio SNR to 15 dB, two signal sources are incident from [4λ, 10°] and [5.2λ, 35°] respectively, and set the number of iterations to 50 times. Figure 4 And Figure 5Shows the estimation results of the angles and distances of two signal sources in multiple iteration steps of the method proposed in this embodiment. In the figure, the red horizontal line represents the true signal source position, and the blue curve represents the variation of the angle value and distance value estimated by the method of the present invention with the number of iterations. It can be seen from the result graph that as the number of iterations increases, the method proposed by the present invention can accurately estimate the angles and distances of the two signal sources.

[0215] Simulation 3: Set the number of snapshots L to 1000, and two signal sources are incident from [4λ, 10°] and [5.2λ, 35°] respectively. Figure 6 and Figure 7 Shows the image of the RMSE of the angle value and distance value estimated by the method proposed in this embodiment changing with SNR. In this simulation, the number of Monte Carlo trials is set to 200. It can be clearly seen from the figure that the root mean square errors of the angle and distance estimations of the method proposed in this embodiment decrease with the increase of the signal-to-noise ratio, and this method has excellent performance.

[0216] In the simulation, the performance estimation standard is the root mean square error (RMSE), which is defined as:

[0217]

[0218] where N is the number of Monte Carlo trials, is the simulation data value, which is the estimated value of the distance or angle in this simulation, and a i is the true data value.

[0219] In summary, from the analysis of the simulation effect diagram and running time, it can be known that the method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization proposed by the present invention meets the requirements of resolution and real-time performance for near-field coherent signal source parameter estimation, and has excellent performance.

[0220] Embodiment 3

[0221] As Figure 8 shown, a near-field coherent signal source localization system based on overlapping sub-arrays and iterative optimization includes:

[0222] Data receiving module: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two receiving sub-arrays;

[0223] Covariance calculation module: For each receiving sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements;

[0224] Eigenvalue decomposition module: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angular polynomial equation based on the spectral function. After solving, obtain the angular estimation value corresponding to the array center;

[0225] Rough estimation module: Use the angular estimation values of the two array centers to obtain the corresponding target distances respectively, so as to obtain the position of the signal source. And according to the position of the signal source, obtain the initial angular and distance estimation values of the signal source relative to the overall array antenna;

[0226] Iterative optimization module: Adopt the alternating oblique projection method to optimize the initial angular and distance estimation values, and obtain the optimized angular and distance of the signal source.

[0227] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0228] Embodiment 4

[0229] The present invention provides a computer device, including a processor and a memory; wherein, when the processor executes the computer program stored in the memory, the steps of the above near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization are implemented.

[0230] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0231] Embodiment 5

[0232] The present invention provides a computer-readable storage medium for storing a computer program; when the computer program is executed by a processor, the steps of the above near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization are implemented.

[0233] For a more specific process of the above method, reference can be made to the corresponding content disclosed in the foregoing embodiments, and details will not be elaborated here.

[0234] In this specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the systems, devices, and storage media disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and reference can be made to the description in the method part for the relevant parts.

[0235] Those skilled in the art can clearly understand that the technologies in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solutions in the embodiments of the present invention, in essence, or the parts that contribute to the prior art can be embodied in the form of a software product. This computer software product can be stored in a storage medium, such as ROM / RAM, magnetic disk, optical disc, etc., and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments or some parts of the embodiments of the present invention.

[0236] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization, characterized in that, It includes the following steps: S1: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two received sub-arrays; S2: For each received sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements; S3: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angular polynomial equation based on the spectral function. After solving, obtain the angular estimation value corresponding to the array center; S4: Use the angular estimation values of the two array centers to obtain their respective corresponding target distances to obtain the position of the signal source, and based on the position of the signal source, obtain the initial angle and distance estimation values of the signal source relative to the entire array antenna; S5: Use the alternating oblique projection method to optimize the initial angle and distance estimation values to obtain the optimized angle and distance of the signal source.

2. The near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization according to claim 1, wherein The array antenna is arranged in a uniform linear array of 2M + 1 sensors. When K completely correlated narrowband signals are incident on the array antenna, taking the center of the array of the array antenna as the phase reference point, the signal y m (t) received by the m-th sensor is as follows: where s k (t) is the signal of the k-th signal source received at the phase reference point, and n m (t) is complex Gaussian white noise independent of the signal, and τ mk is the phase delay of the signal propagating from the reference point to the m-th sensor; where λ is the signal wavelength, d is the spacing between sensors, r k and θ k are the distance and angle of the k-th signal source, respectively; The received signal vector y(t) of the entire array antenna is y -M (t),..., y M (t)] T is transformed into: y(t) = As(t) + n(t); where s(t) = [s1(t),..., s K (t)] T is a K×1 dimensional signal vector, n(t) = [n -M (t),..., n M (t)] T is a (2M+1)×1 dimensional noise vector, A is a (2M+1)×K dimensional array steering matrix; A = [a(r1,θ1),..., a(r K ,θ K )]; a(r k ,θ k ) is the steering vector, 3. The near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization according to claim 2, characterized in that Step S1 is specifically as follows: The two arrays respectively include the first 2M sensors and the last 2M sensors, and the received signals of the two received sub-arrays are specifically:

4. The near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization according to claim 1, characterized in that Step S2 is specifically as follows: S21: Respectively obtain the covariance matrices R1 and R2 of the two received sub-arrays; where y1(t) and y2(t) are the received signals of the two received sub-arrays respectively; T is the number of snapshots, and the superscript H is the transpose conjugate operator; S22: Extract the anti-diagonal elements r of the covariance matrices R1 and R2 respectively i ; Among them, the element r in the m-th row and the (2M + 2 - m)-th column m,2M+2-m is expressed as: and represent the power of the k-th source and the noise power respectively. S23: Based on the anti-diagonal element r i Construct two new covariance matrices R y1 and R y2 ; where R y1 and R y2 are both 2M×2M matrices, and the superscript T is the transpose operator.

5. The method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization according to claim 2, wherein Step S3 is specifically as follows: S31: Perform sub-band processing on the new covariance matrices R y1 and R y2 specifically as follows: According to the SSP method, use the method of window sliding with a set window size S to extract multiple S×S-dimensional sub-matrices from R y1 ,R y2 and average all the extracted sub-matrices to obtain a smoothed S×S-dimensional matrix R ; smoothi ; where q represents the qth sliding window, and P = 2M - S + 1 is the number of sub-matrices; S32: Eigenvalue decompose matrix R smoothi to obtain the noise subspace U ni ; where, Λ si and Λ ni are the diagonal matrices of dimension K×K and (S-K)×(S-K) corresponding to the i-th matrix R smoothi respectively, and U si and U ni are the signal subspace and noise subspace of dimension S×K and S×(S-K) corresponding to the i-th matrix R smoothi respectively; S33: Decompose the steering vector a(r k , θ k ) into a parameter Γ(ω) related only to the angle and a parameter b(φ) related to both the angle and the distance; S34: Convert the MUSIC spectral function into a polynomial-form equation related to θ k : Among them, S35: Transform the problem of solving the polynomial-form equation into: finding the roots z of the following formula k , and obtain the angle estimation values corresponding to the two array centers based on the relationship between the roots and the angle θ and 6. The method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization according to claim 1, wherein Step S4 is specifically as follows: S41: Angle estimation value based on the centers of two arrays and Obtain the target distance corresponding to the center of each array through geometric relationships and S42: Use the angle estimation value and as well as the target distance and to calculate the position of signal source k; S43: According to the position of the signal source k, calculate the initial angle of the signal source k relative to the entire array antenna using the following formula and the distance estimation value 7. The method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization according to claim 2, wherein Step S5 is specifically as follows: S51: Take the initial angles of all signal sources relative to the overall array antenna and the distance estimation values as the initial values for iteration; S52: Use the angle of the (l - 1)th time and distance Calculate the oblique projection matrix in the direction of the kth signal source for the current l (l = 1, 2,..., L) iterations Among them, let be the array steering matrix of the steering vector a(θ k , r k ) that does not include the k-th signal source, Let Γ k (θ k , r k ) be the orthogonal projection matrix projected onto the null space of the k-th signal source, be the M s × M s dimensional identity matrix, and M s = 2M + 1; S53: Based on the oblique projection matrix Define K virtual signal vectors And take The covariance matrix of Expressed as: Is the signal power of s k (t); S54: Based on the covariance matrix DOA estimator of the k-th signal source is as follows: Among them, S55: Update the skew projection matrix and the covariance matrix and based on the updated covariance matrix and the angle estimation value of the DOA estimator calculate the distance S56: Continuously iterate until the predicted number of iterations is reached or the following stop condition is satisfied, and then output the optimal angle and distance; where μ is a set threshold.

8. A near-field coherent signal source localization system based on overlapping sub-arrays and iterative optimization, characterized in that It includes: Data reception module: Use an array antenna with a uniform linear array structure to receive signals, and divide the entire array antenna into two arrays to decompose the received signals into two received sub-arrays; Covariance calculation module: For each received sub-array, extract the anti-diagonal elements of its covariance matrix, and form a new covariance matrix from the outer product of the corresponding anti-diagonal elements; Eigenvalue decomposition module: For the new covariance matrix of each array, perform eigenvalue decomposition on it, extract the noise subspace, and construct an angular polynomial equation based on the spectral function. After solving, obtain the angular estimation value corresponding to the array center; Rough estimation module: Use the angular estimation values of the two array centers to obtain their respective corresponding target distances to obtain the position of the signal source, and based on the position of the signal source, obtain the initial angle and distance estimation values of the signal source relative to the entire array antenna; Iterative optimization module: Use the alternating oblique projection method to optimize the initial angle and distance estimation values to obtain the optimized angle and distance of the signal source.

9. A computer device, characterized in that, It includes a processor and a memory; wherein, when the processor executes the computer program stored in the memory, it implements the steps of the near-field coherent signal source localization method based on overlapping sub-arrays and iterative optimization described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, For storing a computer program; when the computer program is executed by a processor, it implements the steps of the method for localizing near-field coherent signal sources based on overlapping sub-arrays and iterative optimization according to any one of claims 1-7.

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