Hybrid source doa estimation method based on householder shrinkage technique

Abstract

The application discloses a mixed source DoA estimation method based on Householder shrinkage technology, and the implementation scheme is as follows: a near-field component is removed from a mixed signal in sequence by using Householder compression technology, and spectrum estimation is realized by using the remaining far-field component, thus avoiding the existence of a near-field source false peak in the spatial spectrum of a far-field source after far-field DoA estimation of an observation signal covariance matrix, and the precision of DoA estimation is improved. By Householder transformation, the orthogonality of a near-field source steering matrix and a transformation matrix is ensured, the extraction of a pure far-field component is realized, and the rank deficiency phenomenon existing in a traditional steering matrix overlapping DoA is overcome. The application only constructs a cumulant matrix, when the number of near-field sources increases, the multiplication operation involved in eigenvalue decomposition is less, the calculation complexity is reduced, and the efficiency of DoA estimation is improved. The application can be applied to high-precision, low-complexity and multi-functional mixed source positioning.

Description

Technical Field

[0001] This invention belongs to the field of array antenna signal processing, and further relates to a hybrid source direction of arrival (DoA) estimation method based on Householder contraction technology in the field of direction of arrival estimation. This invention can be used to estimate the DoA of near-field and far-field signals received by an array. Background Technology

[0002] Direction of arrival (DoA) estimation is widely used in engineering and technical fields such as wireless communication, radar, sonar, and seismic exploration. There are many existing high-resolution far-field DoA estimation algorithms, with rotation-invariant subspace and Multiple Signal Classification (MUSIC) being commonly used. When the target source is located in the Fresnel region and the signal wavefront is a spherical wave, the source localization parameters involve range and angle. For near-field source localization, classic solutions include the propagation factor algorithm (which does not require a two-dimensional search) and the near-field root-finding MUSIC algorithm. However, in practical applications, each loudspeaker may be located anywhere within the range of both far-field and near-field sensors, rendering traditional methods designed specifically for pure far-field or pure near-field source localization inapplicable.

[0003] The University of Electronic Science and Technology of China (UESTC) disclosed a method for locating mixed-field sources based on a reconstructed cumulant matrix in its patent application, "A Multi-Source DoA Estimation Method Based on Digitally Programmable Metasurfaces" (Application No. CN201810480366.1, Publication No. CN 108680894 A). This method proposes to estimate the far-field signal using the covariance matrix of the observed signal, and then separate the near-field and far-field components by reconstructing the far-field cumulant matrix, thereby estimating the near-field source parameters. A drawback of this method is that when using the covariance matrix of the observed signal for far-field DoA estimation, the far-field source DoA, near-field source DoA, and distance parameters satisfy a specific algebraic relationship, resulting in spurious peaks from the near-field source in the spatial spectrum of the far-field source after estimation.

[0004] In their paper "Classification and localization of mixed near-field and far-field sources using mixed-order statistics" (Signal Processing, 2018, 143: 134-139), Zhi Zheng and Jie Sun et al. proposed a method for locating mixed near-field and far-field sources based on mixed-order statistics. This method estimates far-field sources using the traditional MUSIC method based on second-order statistics. Then, using the estimated far-field kurtosis, the far-field source components are removed from the constructed cumulant matrix, and the remaining near-field source components are estimated through a one-dimensional spectral search. A drawback of this method is that when near-field and far-field sources share the same DoA (DoA), the cumulant matrix cannot satisfy full column rank, thus failing to estimate the overlapping DoA.

[0005] In their paper "Passive localization and classification of mixed near-field and far-field sources based on high-order differencing algorithm" (Signal Processing, 2019, 157: 119-130), Amir Masoud Molaei et al. proposed a high-order difference method for mixed source localization. This method utilizes five specially constructed cumulant matrices for matrix cross-difference. The first matrix is ​​modified by changing its rank and using an ESPRIT-like method to form an initial DoA set. The other four matrices are subjected to two differencing operations to eliminate far-field information, resulting in a differencing cumulant matrix, which is then used to estimate the near-field source DoA. The remaining DoA in the set are the far-field sources. If overlapping DoA exists, a kurtosis test mechanism is used for identification. The drawbacks of this method are: the use of multiple cumulant matrices leads to excessive computation; and when the same DoA exists in the near and far fields, it is impossible to determine the type from the initial DoA set, requiring additional steps and increasing the algorithm's complexity. Summary of the Invention

[0006] The purpose of this invention is to address the shortcomings of the prior art by proposing a hybrid source DoA estimation method based on Householder contraction technology. This method solves the problems of being unable to perform DoA estimation when near-field and far-field sources overlap, the presence of spurious peaks in the spatial spectrum of far-field sources, and excessive computational complexity of multiple high-order cumulant matrices.

[0007] The technical approach to achieving the objective of this invention is as follows: This invention utilizes Householder compression technology to sequentially remove near-field components from the mixed signal, and then uses the remaining far-field components to achieve spectral estimation. This avoids the problem in existing technologies where far-field DoA estimation using the covariance matrix of the observed signal results in spurious near-field source peaks in the spatial spectrum of the far-field sources. This invention uses a transformation matrix constructed by the Householder transform, ensuring it is orthogonal to the near-field components of the steering matrix, thereby guaranteeing the full rank of the covariance matrix and avoiding the rank deficiency problem of the steering matrix caused by overlapping DoA. This invention constructs only a cumulant matrix, and the pure far-field signal obtained by multiplying the Householder transform matrix with the mixed signal has a lower dimensionality compared to the mixed signal. Furthermore, as the number of near-field sources increases, the dimensionality of the far-field covariance matrix becomes even lower, further reducing the multiplication operations involved in eigenvalue decomposition.

[0008] The specific steps to achieve the objective of this invention include the following:

[0009] Step 1: Generate a higher-order cumulant matrix. Utilize the over-symmetric structure property of the far-field steering vector and use spatial self-difference techniques to remove the far-field components from the higher-order cumulant matrix.

[0010] Step 2: Calculate the DoA estimate of the near-field component using a spatial spectrum estimation algorithm;

[0011] Step 3: Through one-dimensional spectral search, utilize the sampling covariance matrix Estimate the distance to the near-field source;

[0012] Step 4: Construct the transformation matrix H through Householder transformation, and use Householder compression technique to remove the near-field components from the mixed signal in sequence;

[0013] Step 5: Use spectral peak search to obtain the DoA estimate of the far-field source.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] First, because the present invention uses Householder compression technology to sequentially remove near-field components from the mixed signal and then uses the remaining far-field components to achieve spectral estimation, it avoids the problem of near-field source spurious peaks in the spatial spectrum of the far-field source obtained after estimation caused by using the covariance matrix of the observed signal for far-field DoA estimation in the prior art. This makes the present invention improve the accuracy of near-field source and far-field source DoA estimation.

[0016] Second, this invention ensures the orthogonality of the near-field source steering matrix and the transformation matrix through Householder transformation, thereby enabling the extraction of pure far-field components. This overcomes the rank deficiency phenomenon of traditional steering matrices due to overlapping DoA, allowing this invention to estimate the overlapping DoA of near-field and far-field sources.

[0017] Third, this invention constructs only a cumulant matrix, and due to the reduction in the dimension of the far-field covariance matrix, the number of multiplication operations involved in eigenvalue decomposition decreases when the number of near-field sources increases, thereby reducing the computational complexity of this invention and improving the efficiency of DoA estimation for near-field and far-field sources. Attached Figure Description

[0018] Figure 1 This is a flowchart of the present invention;

[0019] Figure 2 This is a diagram of the symmetrical uniform array structure based on hybrid near and far fields of the present invention;

[0020] Figure 3 This is a schematic diagram of the far-field spatial spectrum of the present invention and the 0PMUSIC method;

[0021] Figure 4 This is a schematic diagram showing the relationship between the root mean square error of non-overlapping near and far field DoA and near field source distance in the simulation experiment of this invention and the SNR and snapshot number.

[0022] Figure 5 This is a schematic diagram showing the relationship between the root mean square error of the overlapping near and far field DoA and the near field source distance in the simulation experiment of this invention and the SNR and the number of snapshots. Detailed Implementation

[0023] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] Reference Figure 1 The specific implementation steps of the embodiments of the present invention will be further described below.

[0025] Step 1: Construct a DOA estimation model for mixed far-field and near-field sources.

[0026] In an embodiment of the present invention, a hybrid near-field and far-field signal source is incident on a symmetrical sensor array consisting of 11 array elements with an element spacing of 0.075 meters. There are four hybrid near-field and far-field signal sources in the space: two near-field sources and two far-field sources. Multi-shot sampling is performed on the sensor array, such as... Figure 2 As stated above.

[0027] In the embodiments of the present invention, the incident signal X(t) is:

[0028] X(t)=A N SN (t)+A F S F (t)+N(t)

[0029] Among them, A N A F Let S represent the near-field array manifold and the far-field array manifold, respectively. N S F Let N(t) represent the near-field signal matrix and the far-field signal matrix, respectively, and let t represent the noise matrix.

[0030] Step 2: Generate a higher-order cumulant matrix using the received signal, and use the over-symmetric structure property of the far-field steering vector to remove the far-field components in the higher-order cumulant matrix using spatial self-difference technique.

[0031] Calculate the value of each element in the higher-order cumulant matrix C according to the following formula:

[0032]

[0033] Where u, p∈[-M, M] represent the u-th row and p-th column of the higher-order cumulant matrix C, respectively, and M takes the value equal to Figure 2 The total number of array elements on one side of the array element diagram, cum represents the fourth-order cumulative operation, x u (t) represents the received signal of the u-th array element at time t, (·) * This indicates the conjugate operation. s represents the kurtosis of the k-th signal source. k (t) represents the signal of the k-th source at time t, and j represents the imaginary unit symbol. λ represents the wavelength of the incident signal, sin represents the sine function, cos represents the cosine function, and θ k Let r represent the DoA of the k-th source. k This represents the distance from the k-th source to the center of the array.

[0034] The higher-order cumulant matrix can be written as the following equivalent matrix:

[0035]

[0036] Among them, C 4N，s C 4F，s Let B represent the near-field kurtosis matrix and the far-field kurtosis matrix, respectively. N B F Let represent the near-field virtual array manifold and the far-field virtual array manifold, respectively. H This indicates the conjugate transpose operation.

[0037] The oversymmetric structure property of the far-field steering vector satisfies the following equation:

[0038]

[0039]

[0040] Where J represents a commutation matrix with elements 1 on the anti-diagonal and elements 0 in all other positions, (·) * This indicates a conjugate operation.

[0041] The spatial self-difference is achieved by the following equation:

[0042] C D =JCJ-C *

[0043] Among them, C D This represents the self-difference matrix of the observed signal.

[0044] Step 3, construct the near-field covariance matrix C N Then, eigenvalue decomposition is performed on it, and the DoA estimate of the near-field component is calculated using the following spatial spectrum estimation algorithm.

[0045] The near-field covariance matrix C N Constructed from the following formula:

[0046]

[0047] The spatial spectrum estimation algorithm is implemented by the following formula:

[0048]

[0049] Among them, P N • Represents the near-field spectral peak search function. Let b represent the estimated DoA of the k-th near-field source, and b· represent the near-field virtual steering matrix B. N In the column vector, θ represents the angle traversed during the spectral peak search process, and Q... n T represents the noise subspace composed of the eigenvectors corresponding to the T smallest eigenvalues ​​among the O eigenvalues ​​obtained by eigenvalue decomposition of the near-field covariance matrix CN, where T = OE, O is equal to the number of array elements, and E is equal to the number of near-field sources.

[0050] Step 4, construct the sampling covariance matrix Estimating the distance to the near-field source using a one-dimensional spectral search:

[0051] The sampling covariance matrix Constructed from the following formula:

[0052]

[0053] Where L represents the number of snapshots, E nDenotes the noise subspace, E n Represents the sampled signal subspace, ∑ s This represents a diagonal matrix consisting of P large eigenvalues, where P equals the number of near-field sources, ∑ n Let G represent a diagonal matrix consisting of G small eigenvalues, where G = DP and D takes the value equal to the number of matrix elements.

[0054] The one-dimensional spectral search is achieved by the following formula:

[0055]

[0056] in, The value of a represents the estimated distance from the near-field source to the center element of the array, r represents the distance traversed during the spectral peak search, and a represents the distance traversed during the spectral peak search. N • Represents the near-field steering matrix A N The column vectors in.

[0057] Step 4: Construct the transformation matrix H through Householder transformation, and use Householder compression technique to remove the near-field components from the mixed signal in sequence.

[0058] The transformation matrix H constructed through the Householder transformation is achieved by the following formula:

[0059] Y = [(a i / ||a i ||), H]

[0060] Where Y represents the Householder reflection matrix, a i Let ||·|| represent the i-th column of the guidance matrix, and ||·|| represent the magnitude of the guidance vector.

[0061] The removal of near-field components from the mixed signal using the Householder shrinkage technique is achieved by the following formula:

[0062] x′(t)=H H x(t)

[0063] Where x′(t) represents the far-field signal remaining after removing the near-field component from the mixed signal using the Householder shrinkage technique.

[0064] Step 5, construct the far-field covariance matrix R F Then, eigenvalue decomposition is performed, and the estimated value of the far-field source DoA is obtained using the following spectral peak search:

[0065]

[0066] Among them, P F · represents the far-field spectral peak search function, aF · represents the far-field steering matrix A F and the column vectors in it, represents the estimated value of the far-field source DoA, U n represents the noise subspace composed of the eigenvectors corresponding to W of the T eigenvalues obtained by performing eigenvalue decomposition on the far-field covariance matrix R F Among them, W = J - Z - V, and the value of V is equal to the number of far-field sources.

[0067] The effects of the present invention can be further demonstrated by the following simulations.

[0068] 1. Simulation experiment conditions.

[0069] The software platform for the simulation experiment of the present invention is: Windows 10 operating system and Matlab R2021b.

[0070] 2. Simulation content and result analysis.

[0071] There are three simulation experiments in the present invention.

[0072] Simulation experiment 1 is a simulation of the false peaks of near-field sources existing in the far-field source spatial spectrum using the method of the present invention and the existing technology OPMUSIC method. When two far-field sources are located at (-5°, ∞) and (25°, ∞), and the near-field source is located at (-30°, 3λ), the far-field spatial spectrum function values are obtained respectively, and then the relationship between the obtained function values and the angles is plotted as Figure 3 the two curves shown.

[0073] In simulation experiment 1, the existing technology OPMUSIC method used refers to:

[0074] The method proposed by Jin He et al. in their published paper "Efficient Application of MUSIC Algorithm Under the Coexistence of Far-Field and Near-Field Sources" (IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2012, 60(4): 2066 - 2070).

[0075] The spatial spectrum used in simulation experiment 1 of the present invention is a symmetric uniform array, the number of array elements is set to 11, the element spacing d = λ / 4, the incident sources are all non-Gaussian signals with equal-power statistics, the wavelength is λ, the Fresnel region of the near-field signal is 2.45λ < r < 12.5λ, the background noise is an additive uniform white complex Gaussian random process, the signal-to-noise ratio is 15, and the number of snapshots is 200.

[0076] The following is combined with Figure 3 The simulation diagram further describes the effect of this experiment.

[0077] Figure 3 The horizontal axis represents the range of angle changes during the spectrum search process, in degrees, and the vertical axis represents the far-field spatial spectral function value, in dB. Figure 3 In the figure, the curves marked with solid lines represent the relationship between the far-field spatial spectrum function values ​​and the angle obtained by simulation using the method proposed in this invention, while the curves marked with dashed lines represent the relationship between the far-field spatial spectrum function values ​​and the angle obtained using the existing OPMUSIC method.

[0078] from Figure 3 As can be seen, both the far-field spatial spectral function values ​​obtained by the method of this invention and the OPMUSIC method reach their maxima at angles of -5° and 25°. However, the OPMUSIC method exhibits a spurious peak at the same angle as the near-field source DoA.

[0079] Simulation Experiment 2 uses the method of this invention and four existing techniques (OPMUSIC method, TSMDA method, HODA method, and CRB method) to simulate the relationship between the root mean square error (RMSE) of non-overlapping far-field and near-field source distances and the signal-to-noise ratio (SNR) and the number of snapshots. When the two far-field sources are located at (-5°, ∞) and (25°, ∞), and the two near-field sources are located at (-27°, 2.1λ) and (10°, 4.3λ), the RMSE of the near-field source, far-field source, and near-field source distance are obtained. The relationship between the obtained RMSE and the SNR is then plotted as shown in the figure. Figure 4 (a) Figure 4 (b) Figure 4 The relationship between the 10 curves shown in (c) and the number of snapshots is plotted as follows: Figure 4 (d) Figure 4 (e) Figure 4 The 10 curves shown in (f)

[0080] The prior art 1 is the OPMUSIC method in simulation experiment 1.

[0081] The TSMDA method in prior art 2 refers to:

[0082] The method proposed by G. Liu et al. in their paper “Two-Stage Matrix Differencing Algorithm for Mixed Far-Field and Near-Field Sources Classification and Localization” (IEEE SENSORS JOURNAL, 2014, 14(6): 1957-1965).

[0083] The HODA method in prior art 3 refers to:

[0084] The method proposed by Amir Masoud Molaei et al. in their paper “Passive localization and classification of mixed near-field and far-field sources based on high-order differentiation algorithm” (Signal Processing, 2019, 157: 119-130).

[0085] The CRB method in prior art 4 refers to:

[0086] Amir Masoud Molaei et al. proposed a method for determining the lower bound of the variance of unbiased estimators in their paper “The Stochastic CRB for Array Processing: A Textbook Derivation” (IEEE SIGNAL PROCESSING LETTERS, 2001, 8(5): 148-150).

[0087] In simulation experiment 2 of this invention, when the signal-to-noise ratio (SNR) changes from -5 to 35 with a step size of 5, the number of snapshots is set to 200; when the number of snapshots changes from 100 to 1000 with a step size of 100, the SNR is set to 15; other parameters are the same as in simulation experiment 1.

[0088] The following is combined with Figure 4 The simulation diagram further describes the effect of this experiment.

[0089] Figure 4 (a) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the DoA estimation of the near field source. Figure 4In (a), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by the method proposed in this invention, respectively.

[0090] from Figure 4 (a) It can be seen that the mean square error of the near-field source DoA estimation obtained by the method of the present invention continuously decreases with the increase of the signal-to-noise ratio. Under the same signal-to-noise ratio, the mean square error of the near-field source DoA estimation obtained by the method of the present invention is always smaller than the mean square error obtained by the simulation of the first three prior art techniques, and has higher estimation accuracy, which is closest to the curve of prior art 4.

[0091] Figure 4 (b) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the DoA estimation of the far field source. Figure 4 In (b), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by simulation using prior art 1, the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 2, the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 3, the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 4, and the curves marked with red dashed lines and circles represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by the method proposed in this invention.

[0092] from Figure 4 (b) It can be seen that the mean square error of the far-field source DoA estimation obtained by the method of the present invention is not much different from that of the existing method 1, but the mean square error obtained by the method of the present invention is much smaller than the mean square error obtained by simulation of the two existing technologies 2 and 3.

[0093] Figure 4(c) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the distance estimation of the near field sources. Figure 4 In (c), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by simulation using prior art 1, the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 2, the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 3, the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 4, and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by the method proposed in this invention.

[0094] from Figure 4 (c) It can be seen that the simulation results are consistent with the above. Figure 4 The description in (a) is consistent with the results.

[0095] Figure 4 (d) The horizontal axis represents the number of snapshots of the mixed near and far field sources, and the vertical axis represents the mean square error of the DoA estimation of the near field source. Figure 4 In (d), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0096] from Figure 4 (d) It can be seen that the simulation results are consistent with the above. Figure 4 The description in (a) is consistent with the results.

[0097] Figure 4 (e) represents the number of snapshots of the mixed near and far field sources on the horizontal axis, and the mean square error of the DoA estimation of the far field source on the vertical axis. Figure 4In (e), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0098] from Figure 4 (e) It can be seen that the simulation results are consistent with the above findings. Figure 4 The description in (b) is consistent with the result.

[0099] Figure 4 (f) The horizontal axis represents the number of snapshots of the mixed near and far field sources, and the vertical axis represents the mean square error of the distance estimation of the near field sources. Figure 4 In (f), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0100] from Figure 4 (f) It can be seen that the simulation results are consistent with the above findings. Figure 4 The description in (c) is consistent with the result.

[0101] Simulation Experiment 3 uses the method of this invention and four existing techniques (OPMUSIC method, TSMDA method, HODA method, and CRB method) to simulate the relationship between the root mean square error (RMSE) of overlapping far-field and near-field sources and the near-field distance as a function of signal-to-noise ratio (SNR) and snapshot number. When the two far-field sources are located at (-20°, ∞) and (10°, ∞), and the two near-field sources are located at (25°, 3.1λ) and (10°, 5.8λ), the RMSE of the near-field source, far-field source, and near-field distance are obtained. The obtained RMSE is then plotted against the SNR as shown in the figure. Figure 5 (a) Figure 5 (b) Figure 5 The relationship between the 10 curves shown in (c) and the number of snapshots is plotted as follows: Figure 5 (d) Figure 5 (e) Figure 5 The 10 curves shown in (f)

[0102] In simulation experiment 3, the four existing technologies used are the same as those in simulation experiment 2.

[0103] Except for the positions of the near and far field signal sources, the parameters of simulation experiment 3 are the same as those of simulation experiment 2.

[0104] The following is combined with Figure 5 The simulation diagram further describes the effect of this experiment.

[0105] Figure 5 (a) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the DoA estimation of the near field source. Figure 5 In (a), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source DoA estimation and the signal-to-noise ratio obtained by the method proposed in this invention, respectively.

[0106] from Figure 5(a) It can be seen that the mean square error of the near-field source DoA estimation obtained by the method of the present invention continuously decreases with the increase of the signal-to-noise ratio. Under the same signal-to-noise ratio, the mean square error of the near-field source DoA estimation obtained by the method of the present invention is always smaller than the mean square error obtained by the simulation of the first three prior art techniques, and has higher estimation accuracy, which is closest to the curve of prior art 4.

[0107] Figure 5 (b) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the DoA estimation of the far field source. Figure 5 In (b), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by simulation using prior art 1, the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 2, the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 3, the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by prior art 4, and the curves marked with red dashed lines and circles represent the relationship between the mean square error of far-field source DoA estimation and the signal-to-noise ratio obtained by the method proposed in this invention.

[0108] from Figure 5 (b) It can be seen that the mean square error of the far-field source DoA estimation obtained by the method of the present invention is not much different from that of the existing method 1, but the mean square error obtained by the method of the present invention is much smaller than the mean square error obtained by simulation of the two existing technologies 2 and 3.

[0109] Figure 5 (c) The horizontal axis represents the signal-to-noise ratio of the mixed near and far field sources, in dB, and the vertical axis represents the mean square error of the distance estimation of the near field sources. Figure 5 In (c), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by simulation using prior art 1, the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 2, the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 3, the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by prior art 4, and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source distance estimation and the signal-to-noise ratio obtained by the method proposed in this invention.

[0110] from Figure 5 (c) It can be seen that the simulation results are consistent with the above. Figure 5 The description in (a) is consistent with the results.

[0111] Figure 5 (d) The horizontal axis represents the number of snapshots of the mixed near and far field sources, and the vertical axis represents the mean square error of the DoA estimation of the near field source. Figure 5 In (d), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source DoA estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0112] from Figure 5 (d) It can be seen that the simulation results are consistent with the above. Figure 5 The description in (a) is consistent with the results.

[0113] Figure 5 (e) represents the number of snapshots of the mixed near and far field sources on the horizontal axis, and the mean square error of the DoA estimation of the far field source on the vertical axis. Figure 5 In (e), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of far-field source DoA estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0114] from Figure 5 (e) It can be seen that the simulation results are consistent with the above findings. Figure 5 The description in (b) is consistent with the result.

[0115] Figure 5 (f) The horizontal axis represents the number of snapshots of the mixed near and far field sources, and the vertical axis represents the mean square error of the distance estimation of the near field sources. Figure 5 In (f), the curves marked with green dashed lines and triangles represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by simulation using prior art 1, respectively; the curves marked with cyan dashed lines and squares represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 2, respectively; the curves marked with pink dashed lines and plus signs represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 3, respectively; the curves marked with blue dashed lines and solid lines represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by prior art 4, respectively; and the curves marked with red dashed lines and circles represent the relationship between the mean square error of near-field source distance estimation and the number of snapshots obtained by the method proposed in this invention, respectively.

[0116] from Figure 5 (f) It can be seen that the simulation results are consistent with the above findings. Figure 5 The description in (c) is consistent with the result.

[0117] The simulation experiments above show that the method of the present invention uses Householder compression technology to avoid the problem of near-field source pseudo-peaks in the spatial spectrum of far-field sources in the prior art, thereby improving the accuracy of DoA estimation. It also uses Householder transformation to overcome the rank deficiency phenomenon of traditional turning matrix due to overlapping DoA, and realizes reasonable classification of signal source types and estimation of overlapping DoA. It is a very practical method for locating parameters of far-field and near-field mixed sources.

Claims

1. A hybrid source DoA estimation method based on Householder contraction technique, characterized in that, Near-field DoA estimation is performed using the cumulant matrix via spatial self-difference technique. A Householder transform is used to construct a transformation matrix orthogonal to the near-field steering components. Householder compression is then used to sequentially remove the near-field components from the mixed signal. The steps of this DoA estimation method are as follows: Step 1: Generate a higher-order cumulant matrix. Utilize the over-symmetric structure property of the far-field steering vector and use spatial self-difference techniques to remove the far-field components from the higher-order cumulant matrix. The higher-order cumulant matrix is ​​as follows: ； in, Represents a higher-order cumulant matrix. , These represent the near-field array manifold and the far-field array manifold, respectively. , Let these represent the near-field kurtosis matrix and the far-field kurtosis matrix, respectively. , Let these represent the near-field virtual array manifold and the far-field virtual array manifold, respectively. This represents the conjugate transpose operation; Step 2: Calculate the DoA estimate of the near-field component using the following spatial spectrum estimation algorithm: ； in, This represents the near-field spectral peak search function. Indicates the first Estimates of DoA for each near-field source. Represents the near-field virtual steering matrix The column vectors in This represents the angles traversed during the spectral peak search process. This indicates that by analyzing the near-field covariance matrix... After performing eigenvalue decomposition, the following was obtained Among the eigenvalues, by The noise subspace is composed of the eigenvectors corresponding to the smallest eigenvalues. , The value of is equal to the number of array elements. The value of is equal to the number of near-field sources; Step 3: Through one-dimensional spectral search, utilize the sampling covariance matrix Estimate the distance to the near-field source; Step 4: Construct the transformation matrix using the Householder transformation. Householder compression technology is used to remove near-field components from the mixed signal sequentially; Step 5: Use spectral peak search to obtain the DoA estimate of the far-field source.

2. The hybrid source DoA estimation method based on Householder contraction technique according to claim 1, characterized in that, The oversymmetric structure property of the far-field steering vector described in step 1 satisfies the following equation: ； ； in, This represents a swap matrix where the elements on the anti-diagonal are 1s and the elements in other positions are 0s. This indicates a conjugate operation.

3. The hybrid source DoA estimation method based on Householder contraction technique according to claim 2, characterized in that, The spatial self-difference described in step 1 is achieved by the following equation: ； in, This represents the self-difference matrix of the observed signal.

4. The hybrid source DoA estimation method based on Householder contraction technique according to claim 3, characterized in that, The one-dimensional spectral search described in step 3 is achieved by the following formula: ； in, This represents an estimated distance from the near-field source to the center element of the array. This represents the distance value traversed during the spectral peak search process. Represents the near-field steering matrix The column vectors in This indicates that the covariance matrix of the observed signal is used to... After performing eigenvalue decomposition, the following was obtained Among the eigenvalues, by The noise subspace is composed of the eigenvectors corresponding to the smallest eigenvalues. , The value of is equal to the number of near-field sources. The value of is equal to the number of array elements.

5. The hybrid source DoA estimation method based on Householder contraction technique according to claim 4, characterized in that, The transformation matrix constructed using the Householder transformation described in step 4 It is achieved by the following formula: ； in, Represents the Householder reflection matrix. The first element of the guidance matrix List, This represents the magnitude of the steering vector.

6. The hybrid source DoA estimation method based on Householder contraction technique according to claim 5, characterized in that, The removal of near-field components from the mixed signal using the Householder shrinkage technique described in step 4 is achieved by the following formula: ； in, This represents the far-field signal remaining after removing the near-field component from the mixed signal using the Householder shrinkage technique.

7. The hybrid source DoA estimation method based on Householder contraction technique according to claim 6, characterized in that, The peak search described in step 5 is achieved by the following formula: ； in, This represents the far-field spectral peak search function. Represents the far-field steering matrix The column vectors in This represents the estimated DoA value of the far-field source. This indicates that by adjusting the far-field covariance matrix... Eigenvalue decomposition Among the eigenvalues, by The noise subspace composed of the eigenvectors corresponding to the smallest eigenvalues, , The value of is equal to the number of far-field sources.

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