Direction of arrival estimation method, direction of arrival estimation device and system

Abstract

The present invention discloses a direction of arrival estimation method, direction of arrival estimation device, and system. The method comprises: using antennas to form a uniform linear array, establishing a received signal model based on array signal input signals, and determining a received signal matrix; performing low-rank matrix approximation on the received signal matrix using a low-rank matrix estimation algorithm to obtain a low-noise, low-dimensional matrix; updating the variable step size of a least mean square algorithm (LMS) using statistical parameters of the low-noise, low-dimensional matrix to update and iteratively calculate weight vector coefficients; and calculating the antenna array pattern and spatial spectrum based on the obtained weight vector coefficients to estimate the direction of arrival of the signal. The present invention uses the low-rank matrix approximation method to obtain a low-noise, low-dimensional matrix from the received signal matrix. Utilizing the instantaneous prediction error of the low-noise, low-dimensional matrix and the variable step size of the noise reduction signal power update algorithm, the method can ensure accurate DOA estimation even under unfavorable conditions such as low signal-to-noise ratio, a small number of antenna array elements, and a small amount of signal sampling data, due to prior noise reduction preprocessing.

Description

Technical Field

[0001] The present invention relates to the technical field of wireless communications and signal processing, and in particular to a direction of arrival estimation method, a direction of arrival estimation device and a system. Background Art

[0002] Direction of Arrival (DOA) estimation uses antenna arrays distributed at different physical locations in space to receive signals from multiple sources in different directions, and uses signal processing methods to calculate the direction of the signal source. It has a wide range of applications in radar, sonar, satellite, and wireless communications.

[0003] To achieve good estimation performance in harsh environments, traditional DOA estimation techniques primarily employ multiple signal classification (MUSIC) methods and related MUSIC variants. These methods typically utilize subspace decomposition based on signal statistical properties, requiring the calculation of the signal space covariance (SCM) and the corresponding eigenvalue decomposition (EVD), resulting in high computational complexity. Meanwhile, DOA estimation methods based on the fixed-step least mean square (FSS-LMS) filter with subspace decomposition iteratively update the weight vector coefficients of the array antenna elements, eliminating the need to calculate the SCM and its EVD. This adaptively creates zero values in the signal direction and estimates the DOA from the spatial spectrum peaks formed by the inverse of the antenna array pattern. Currently available DOA estimation methods, such as VSS-LMS, VSS-BC-LMS, and NA-MMUSIC, significantly degrade in harsh environments, such as low signal-to-noise ratio (SNR), a small number of antenna array elements, a small amount of signal sampling data, and closely spaced signal sources. Furthermore, these estimation methods require tuning multiple parameters to effectively control algorithm convergence and achieve accurate estimates, making them difficult to implement in real-world scenarios.

[0004] Therefore, a DOA estimation method is needed to solve the above problems of high computational complexity and significant performance degradation in harsh environments. Summary of the Invention

[0005] According to a first aspect of the present invention, there is provided a direction of arrival estimation method, comprising:

[0006] Use antennas to form a uniform linear array, establish a receiving signal model based on the array signal input signal, and determine the receiving signal matrix X;

[0007] The low-rank matrix estimation algorithm is used to approximate the received signal matrix X to obtain a low-noise low-dimensional matrix ;

[0008] Through the low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ;

[0009] According to the obtained weight vector coefficient Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal.

[0010] In some embodiments, the method of forming a uniform linear array using antennas, establishing a received signal model based on array signal input signals, and determining a received signal matrix X includes:

[0011] The signal received by the first antenna is used as the reference signal, and the signals received by the remaining antennas are used as auxiliary signals. The expression of the reference signal of the received signal at any sampling time k is:

[0012] ;(1)

[0013] in, represents the mth signal source at time k; represents the noise signal in the signal received by the first antenna at time k;

[0014] The expression of the auxiliary signal of the received signal at any sampling time k is:

[0015] ;(2)

[0016] in, Indicates the steering factor corresponding to the mth signal source on the nth antenna receiving signal; represents the noise signal in the signal received by the nth antenna at time k;

[0017] The expression of the total received signal vector for any received signal at time k is:

[0018] ;(3)

[0019] in, represents the actual signal received by each antenna in the array at time k;

[0020] Indicates the array has the mth signal source The steering vector of

[0021] represents the noise signal received by each antenna in the array at time k;

[0022] The received signal matrix X corresponding to K sampling times is:

[0023] (4)

[0024] In some embodiments, the low-rank matrix approximation is performed on the received signal matrix X by a low-rank matrix estimation algorithm to obtain a low-noise low-dimensional matrix ,include:

[0025] Introducing variables G and H, construct the following optimization problem:

[0026] ;(5)

[0027] in, ;

[0028] Solve the optimization problem, fix The value of , iteratively updated , thereby updating We can get:

[0029] ;(6)

[0030] ;(7)

[0031] ;(8)

[0032] Where H represents conjugate transpose, and + represents matrix pseudo-inverse operation;

[0033] When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, that is:

[0034] ;(9)

[0035] in, is a positive constant, The value range can be 10 -4 to 10 -6 .

[0036] In some embodiments, the low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ,include:

[0037] ;(10)

[0038] ;(11)

[0039] Where e(k) is the signal estimation error, Represents the k-th column of the low-noise low-dimensional matrix Remove the first element Post-noise reduction signal;

[0040] Update iterative calculation of weight vector coefficients The expression:

[0041] ;(12)

[0042] Low-noise low-dimensional matrix The statistical parameters include the instantaneous prediction error and noise reduction signal power ;

[0043] Update variable step size The expression:

[0044] ;(13)

[0045] in, , is a constant (0,1), the accumulation of instantaneous prediction errors , noise reduction signal power .

[0046] In some embodiments, when the weight vector coefficient Stop the iteration when the update iteration reaches the optimal solution; or, preset the maximum number of iterations K, when the weight vector coefficient When the number of iterations k>K, stop the iteration.

[0047] In some embodiments, the weight vector coefficients obtained according to Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal, including:

[0048] ;(14)

[0049] ;(15)

[0050] in, Represents the weight vector coefficients containing the reference signal and the auxiliary signal; represents the array steering vector, is the angle grid parameter.

[0051] According to a second aspect of the present invention, there is provided a direction of arrival estimation device, comprising:

[0052] a matrix determination unit, configured to establish a received signal model based on the array signal input signal and determine a received signal matrix X;

[0053] The preprocessing unit is used to perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise low-dimensional matrix ;

[0054] Update unit, used to pass low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ;

[0055] Calculation unit, used to obtain the weight vector coefficient Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal.

[0056] According to a third aspect of the present invention, there is provided a direction of arrival estimation system, comprising an antenna array, which uses any of the above-mentioned direction of arrival estimation methods.

[0057] According to a fourth aspect of the present invention, a computer-readable storage medium is provided, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed, the direction of arrival estimation method as described in any one of the above items is used.

[0058] The beneficial effects of the present invention are as follows: the method of the present invention establishes a received signal matrix based on the proposed model for the received input signal, converts the received signal matrix into a low-noise, low-dimensional matrix through a low-rank matrix approximation method, and then utilizes the instantaneous prediction error of the low-noise, low-dimensional matrix and the variable step size of the noise reduction signal power update algorithm. Due to the prior noise reduction preprocessing, accurate DOA estimation can still be guaranteed under unfavorable conditions such as low signal-to-noise ratio, a small number of antenna array elements, and a small amount of signal sampling data. Secondly, the method of the present invention does not require the covariance matrix and its eigenvalue decomposition (EVD) used in traditional methods, thereby reducing computational complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 This is a flow chart of a method for estimating a direction of arrival according to a first embodiment of the present invention;

[0060] Figure 2 A structural block diagram of the low-rank matrix approximation based on the received signal matrix of the present invention;

[0061] Figure 3 It is a structural block diagram of the least mean square filter adaptive algorithm based on low-noise low-dimensional matrix of the present invention;

[0062] Figure 4 It is a structural block diagram of the present invention;

[0063] Figure 5 This is an experimental comparison diagram of the spatial spectrum between the present invention and the existing direction of arrival estimation method;

[0064] Figure 6 This is an experimental comparison chart of the root mean square error (RMSE) between the present invention and the existing direction of arrival estimation method;

[0065] Figure 7 This is an experimental comparison diagram of the success resolution probability between the present invention and the existing direction of arrival estimation method;

[0066] Figure 8 This is an experimental comparison chart of the computational complexity between the present invention and the existing direction of arrival estimation method;

[0067] Figure 9 This is a flowchart of a method for estimating a direction of arrival according to a second embodiment of the present invention;

[0068] Figure 10 This is a structural block diagram of a direction of arrival estimation device according to a third embodiment of the present invention. DETAILED DESCRIPTION

[0069] For better understanding and implementation, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0070] The terms "including" and "having" and any variations thereof in the embodiments of the present invention are intended to cover non-exclusive inclusions. For example, a process, method, system, product or apparatus that includes a series of steps or modules is not necessarily limited to those steps or modules explicitly listed, but may include other steps or modules not explicitly listed or inherent to these processes, methods, products or apparatus.

[0071] Example 1

[0072] like Figures 1 to 4 As shown, an embodiment of the present invention discloses a direction of arrival estimation method. The method can be applied to radar, sonar, satellite, and wireless communication systems. However, the embodiment of the present invention is not limited to the application system. A direction of arrival estimation method of this embodiment may include the following operations:

[0073] S10: Using antennas to form a uniform linear array, establishing a receiving signal model based on the array signal input signal, and determining a receiving signal matrix X.

[0074] Specifically, N omnidirectional antennas can be used to form a uniform linear array to estimate the direction of arrival of M narrowband signal sources in space.

[0075] The signal received by the first antenna is used as the reference signal. The first antenna is the reference antenna unit, and the signals received by the remaining antennas are used as auxiliary signals. The expression of the reference signal of the received signal at any sampling time k is:

[0076] ;(1)

[0077] in, represents the reference signal, represents the mth signal source at time k, represents the noise-free signal received by the reference antenna unit (the first antenna), Represents the noise signal in the signal received by the reference antenna unit (the first antenna) at time k.

[0078] The expression of the auxiliary signal of the received signal at any sampling time k is:

[0079] ;(2)

[0080] in, Indicates the auxiliary signal, It represents the steering factor of the mth signal source on the nth antenna receiving signal. represents the noise-free auxiliary array signal vector, represents the noise signal of the auxiliary array, that is, the noise signal in the signal received by the n-th antenna at time k.

[0081] The expression of the total received signal vector for any received signal at time k is:

[0082] ;(3)

[0083] in, represents the actual signal received by each antenna in the array at time k;

[0084] represents the noise-free signal received by each antenna in the array at time k;

[0085] Indicates the array has the mth signal source The steering vector of represents the mth source signal, ;

[0086] represents the noise signal received by each antenna in the array at time k;

[0087] The received signal matrix X corresponding to K sampling times is:

[0088]

[0089] (4)

[0090] X is the received signal matrix, which includes the noise-free signal and the noise signal, U represents the noise-free signal matrix, and V represents the noise signal matrix.

[0091] Representing the received signal as the array above naturally allows the original signal and the noise signal to be superimposed on the same received signal matrix for processing. However, in reality, it is impossible to completely separate the original signal from the noise signal. Therefore, if the received signal is preprocessed to obtain a matrix that approximates the original signal, the original signal's direction of arrival and other related information can be easily analyzed based on this approximate matrix. This process is called low-rank matrix approximation. In addition, by expanding the received signal by sampling time, the DOA estimation algorithm can be improved by analyzing the instantaneous error corresponding to different sampling times. This avoids the complexity of traditional methods of calculating the covariance matrix.

[0092] S20: Perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise low-dimensional matrix .

[0093] This step is the process of preprocessing the received signal: Figure 2 As shown, after down-converting, demodulating, and analog-to-digital conversion of the received signal, a low-noise, low-dimensional matrix approximating the received signal matrix X is obtained using the low-rank matrix approximation method. There are many methods for low-rank matrix approximation. This embodiment provides an implementation method of a low-rank matrix approximation algorithm (LRMA):

[0094] Introducing variables G and H, construct the following optimization problem:

[0095] ;(5)

[0096] in, ;

[0097] Solve the optimization problem, fix The value of , iteratively updated , thereby updating We can get:

[0098] ;(6)

[0099] ;(7)

[0100] ;(8)

[0101] Where H represents conjugate transpose, and + represents matrix pseudo-inverse operation;

[0102] When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, that is:

[0103] ;(9)

[0104] in, is a small positive constant, The value range is 10 -4 to 10 -6 .

[0105] The above-mentioned low-rank matrix estimation algorithm (LRMA) is used to calculate the denoised observation values of the entire antenna array to obtain a low-noise low-dimensional matrix .

[0106] S30: Through low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient .like Figure 3 As shown, this step specifically includes:

[0107] S31: Using low-noise low-dimensional matrices Improved variable step size least mean square algorithm (VSS-LMS).

[0108] ;(10)

[0109] ;(11)

[0110] in, represents the signal estimation error, Represents the k-th column of the low-noise low-dimensional matrix Remove the first element Post-denoising signal, weight vector coefficient To update the iteration to approach the optimal solution . Figure 3 and Figure 4 in , which can also be expressed as .

[0111] S32: Update the iterative calculation weight vector coefficients through the following expression .

[0112] ;(12)

[0113] Weight vector coefficient According to the optimal solution after each step of the algorithm The error will be lower than the previous one, thus updating the iteration to the optimal solution or within an acceptable error range Stop iteration after reaching a certain value.

[0114] S33: Update variable step size value.

[0115] According to the low-noise low-dimensional matrix The instantaneous prediction error of the statistical parameters and noise reduction signal power Calculate the variable step size The value of

[0116] Update variable step size The expression:

[0117] ;(13)

[0118] in, , is a constant (0,1), the accumulation of instantaneous prediction errors , noise reduction signal power .

[0119] According to the low-noise low-dimensional matrix The variable step size of the transient statistical parameter update LMS algorithm is a great improvement on the performance of the original LMS algorithm. It ensures that the step size is within the most appropriate range so that the algorithm can converge at the fastest speed and obtain the weight vector coefficients. The optimal solution of .

[0120] S40: According to the obtained weight vector coefficient Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal.

[0121] ;(14)

[0122] ;(15)

[0123] in, Represents the weight vector coefficients containing the reference signal and the auxiliary signal; represents the array steering vector, is the angle grid parameter.

[0124] Simulation experiment and analysis of this embodiment

[0125] The performance of the proposed method in terms of spatial spectrum, root mean square error (RMSE), resolution probability and computational complexity is analyzed through numerical simulations and compared with the MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS and NA-MMUSIC methods.A uniform linear array (ULA) consisting of 12 omnidirectional antenna elements with half-wavelength element spacing is considered.

[0126] (1) Experimental analysis of spatial spectrum: Using signals from three different directions (0°, 5°, and 30°), the spatial spectrum was calculated based on 12 antennas and 300 iterations. The simulation results are shown in the figure below. Figure 5 As shown. Figure 5 (a), (b), (c), and (d) represent the results at different signal-to-noise ratios (SNRs) of -10dB, -5dB, 0dB, and 5dB. Simulation results show that, due to the noise reduction preprocessing of the received signal, the method of this embodiment can more accurately estimate the direction of the signal source. However, at low SNRs, the MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS, and NA-MMUSIC methods are unable to resolve the signal directions of closely spaced sources at 0° and 5°.

[0127] (2) Experimental analysis of the root mean square error (RMSE). The root mean square error (RMSE) of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS, NA-MMUSIC and the method proposed in this embodiment was calculated. The results are shown in the figure below. Figure 6 shown. Figure 6 (a), 6(b), 6(c) and 6(d) respectively represent the analysis results corresponding to different signal-to-noise ratios, different numbers of antennas, different numbers of iterations and different interval source angles between the two signal sources. Figure 6 It can be seen that under the condition of low signal-to-noise ratio, the RMSE of the method proposed in this embodiment is the smallest. Under the conditions of different numbers of antennas, different numbers of iterations, and different interval source angles between the two signal sources, the RMSE of the method proposed in this embodiment is the smallest compared with other algorithms. This shows that the method of this embodiment has good robustness under various conditions and has a great performance advantage.

[0128] (3) Experimental analysis of the probability of successfully distinguishing the signal source. The probabilities of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS, NA-MMUSIC and the method proposed in this embodiment were calculated. The results are as follows: Figure 7 express. Figure 7(a), 7(b), and 7(c) respectively represent the probabilities of successfully distinguishing the signal source direction as 0° and 5° under different signal-to-noise ratios, different numbers of antennas, and different numbers of iterations. As can be seen from the figure, the method proposed in this embodiment has the highest probability of successfully distinguishing the signal source among all algorithms under harsh conditions such as low signal-to-noise ratio, small number of antenna array elements, and small number of iterations (small amount of signal sampling data). Under conditions of high and low noise ratios, large number of antenna array elements, and large number of iterations, the probability of successfully distinguishing the signal source is comparable to that of other algorithms. Figure 7 (d) shows the analysis results corresponding to different separation angles between the two signal sources (separation angles of 3°-6°). As can be seen from the figure, when the separation angle between the two signal sources is less than 5°, the probability of successfully distinguishing the signal sources by the method proposed in this embodiment is the highest. When the separation angle is greater than 5°, the probability of successfully distinguishing the signal sources is comparable to that of the MUSIC algorithm.

[0129] (4) Experimental analysis of computational complexity: The computational complexity of MUSIC, FSS-LMS, VSS-LMS, VSS-BC-LMS, NA-MMUSIC and the proposed method were calculated. The results are shown in Figure 4. Figure 8 express. Figure 8 (a) and (b) represent the analysis results corresponding to different numbers of antennas and different numbers of iterations, respectively. The method proposed in this embodiment does not require the covariance matrix and its eigenvalue decomposition (EVD) method used in traditional methods, so it has lower computational complexity.

[0130] The direction of arrival estimation method of the present invention is based on the received signal modeling, combined with the low-rank matrix approximation and variable step-size least mean square adaptive filter method, and gradually analyzed and improved to obtain a new DOA estimation algorithm, achieving the following three major technical effects. First, under harsh conditions such as low signal-to-noise ratio, small number of antenna array elements, and small amount of signal sampling data, high-precision estimation can still be guaranteed. Secondly, since the proposed method does not require the covariance matrix and its eigenvalue decomposition (EVD) method in the traditional method, it has lower computational complexity. Moreover, in terms of parameter adjustment, there are few adjustment parameters and only one , compared with other DOA estimation algorithms, it has better operability.

[0131] Example 2

[0132] like Figure 9 As shown, an embodiment of the present invention discloses a direction of arrival estimation method. The method can be applied to radar, sonar, satellite, and wireless communication systems. However, the embodiment of the present invention is not limited to the application system. A direction of arrival estimation method of this embodiment may include the following operations:

[0133] The implementation of steps S10 to S40 is basically the same as that of the first embodiment, and only the differences are described. In this embodiment, the weight vector coefficient is updated and iteratively calculated by the following expression: .

[0134] ;(12)

[0135] In this step, the weight vector coefficients The conditions for stopping iteration are different. Initially, k=1, the maximum number of iterations K is pre-set, and then the iteration weight vector coefficients are updated. When k>K, stop the iteration and output the weight vector coefficient after iteration value.

[0136] Example 3

[0137] like Figure 10 As shown, an embodiment of the present invention discloses a direction of arrival estimation device 5 , which receives a source signal through an antenna array. The device 5 includes: a matrix determination unit 51 , a preprocessing unit 52 , an updating unit 53 and a calculation unit 54 .

[0138] The matrix determination unit 51 is used to establish a received signal model according to the array signal input signal and determine the received signal matrix X. Specifically, the matrix determination unit 51 performs the following steps to establish the received signal model and determine the received signal matrix X:

[0139] The signal received by the first antenna is used as the reference signal. The first antenna is the reference antenna unit, and the signals received by the remaining antennas are used as auxiliary signals. The expression of the reference signal of the received signal at any sampling time k is:

[0140] ;(1)

[0141] in, represents the reference signal, represents the mth signal source at time k, represents the noise-free signal received by the reference antenna unit (the first antenna), Represents the noise signal in the signal received by the reference antenna unit (the first antenna) at time k.

[0142] The expression of the auxiliary signal of the received signal at any sampling time k is:

[0143] ;(2)

[0144] in, Indicates the auxiliary signal, It represents the steering factor of the mth signal source on the nth antenna receiving signal. represents the noise-free auxiliary array signal vector, represents the noise signal of the auxiliary array, that is, the noise signal in the signal received by the n-th antenna at time k.

[0145] The expression of the total received signal vector for any received signal at time k is:

[0146] ;(3)

[0147] in, represents the actual signal received by each antenna in the array at time k;

[0148] represents the noise-free signal received by each antenna in the array at time k;

[0149] Indicates the array has the mth signal source The steering vector of represents the mth source signal, ;

[0150] represents the noise signal received by each antenna in the array at time k;

[0151] The received signal matrix X corresponding to K sampling times is:

[0152]

[0153] (4)

[0154] X is the received signal matrix, which includes the noise-free signal and the noise signal, U represents the noise-free signal matrix, and V represents the noise signal matrix.

[0155] Representing the received signal as the array above naturally allows the original signal and the noise signal to be superimposed on the same received signal matrix for processing. However, in reality, it is impossible to completely separate the original signal from the noise signal. Therefore, if the received signal is preprocessed to obtain a matrix that approximates the original signal, the original signal's direction of arrival and other related information can be easily analyzed based on this approximate matrix. This process is called low-rank matrix approximation. In addition, by expanding the received signal by sampling time, the DOA estimation algorithm can be improved by analyzing the instantaneous error corresponding to different sampling times. This avoids the complexity of traditional methods of calculating the covariance matrix.

[0156] The preprocessing unit 52 is used to perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise low-dimensional matrix Specifically, the pre-processing unit 52 performs the following LRMA algorithm to perform low-rank matrix approximation on the received signal matrix X to obtain a low-noise low-dimensional matrix :

[0157] Introducing variables G and H, construct the following optimization problem:

[0158] ;(5)

[0159] in, ;

[0160] Solve the optimization problem, fix The value of , iteratively updated , thereby updating We can get:

[0161] ;(6)

[0162] ;(7)

[0163] ;(8)

[0164] Where H represents conjugate transpose, and + represents matrix pseudo-inverse operation;

[0165] When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, that is:

[0166] ;(9)

[0167] in, is a small positive constant, The value range is 10 -4 to 10 -6 .

[0168] Update unit 53, used to update the low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient Specifically, the updating unit 53 uses a low-noise low-dimensional matrix Improved variable step size least mean square algorithm (VSS-LMS);

[0169] ;(10)

[0170] ;(11)

[0171] in, represents the signal estimation error, Represents the k-th column of the low-noise low-dimensional matrix Remove the first element Post-denoising signal, weight vector coefficient To update the iteration to approach the optimal solution . Figure 3 and Figure 4 in , which can also be expressed as .

[0172] The updating unit 53 updates the iteratively calculated weight vector coefficients by the following expression: .

[0173] ;(12)

[0174] Weight vector coefficient Update and iterate to the optimal solution Then stop the iteration.

[0175] Update unit 53 updates the variable step size value.

[0176] According to the low-noise low-dimensional matrix The instantaneous prediction error of the statistical parameters and noise reduction signal power Calculate the variable step size The value of

[0177] Update unit 53 updates the variable step size The expression:

[0178] ;(13)

[0179] in, , is a constant (0,1), the accumulation of instantaneous prediction errors , noise reduction signal power .

[0180] According to the low-noise low-dimensional matrix The variable step size of the transient statistical parameter update LMS algorithm is a great improvement on the performance of the original LMS algorithm. It ensures that the step size is within the most appropriate range so that the algorithm can converge at the fastest speed and obtain the weight vector coefficients. The optimal solution of .

[0181] The calculation unit 54 is used to calculate the weight vector coefficient according to the obtained Calculating antenna array patterns and spatial spectrum Specifically, the calculation unit 54 executes the following expression to estimate the direction of arrival of the signal.

[0182] ;(14)

[0183] ;(15)

[0184] in, Represents the weight vector coefficients containing the reference signal and the auxiliary signal; represents the array steering vector, is the angle grid parameter.

[0185] Example 4

[0186] An embodiment of the present invention provides a direction of arrival estimation system, including an antenna array, which is constructed as a uniform linear array. The system may also include a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the system implements the steps of the direction of arrival estimation method in the first or second embodiment.

[0187] Example 5

[0188] An embodiment of the present invention discloses a computer-readable storage medium storing a computer program for electronic data exchange, wherein the computer program enables a computer to execute the direction of arrival estimation method described in the first or second embodiment.

[0189] Example 6

[0190] An embodiment of the present invention discloses a computer program product, which includes a non-transitory computer-readable storage medium storing a computer program, and the computer program is operable to enable a computer to execute the direction of arrival estimation algorithm described in the first or second embodiment.

[0191] The embodiments described above are merely illustrative, wherein the modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical modules, i.e., they may be located in one place or distributed across multiple network modules. Some or all of the modules may be selected based on actual needs to achieve the objectives of the embodiments. Persons of ordinary skill in the art will be able to understand and implement the embodiments without inventive effort.

[0192] Through the detailed description of the above embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by means of hardware. Based on this understanding, the above technical solution, in essence, or the portion that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a read-only memory (ROM), a random access memory (RAM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), a one-time programmable read-only memory (OTPROM), an electronically erasable programmable read-only memory (EEPROM), a compact disc read-only memory (CD-ROM), or other optical disk storage, magnetic disk storage, magnetic tape storage, or any other computer-readable medium capable of carrying or storing data.

[0193] Finally, it should be noted that the method for estimating the direction of arrival disclosed in the embodiment of the present invention is only a preferred embodiment of the present invention and is only used to illustrate the technical solution of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A method for estimating a direction of arrival, characterized in that: include: Use antennas to form a uniform linear array, establish a receiving signal model based on the array signal input signal, and determine the receiving signal matrix X; The low-rank matrix estimation algorithm is used to approximate the received signal matrix X to obtain a low-noise low-dimensional matrix ; Through the low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ; According to the obtained weight vector coefficient Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal; The low-rank matrix estimation algorithm is used to perform low-rank matrix approximation on the received signal matrix X to obtain a low-noise low-dimensional matrix ,include: Introducing variables G and H, construct the following optimization problem: ；(5) in, ; Solve the optimization problem, fix The value of , iteratively updated , thereby updating We can get: ；(6) ；(7) ；(8) Where H represents conjugate transpose, and + represents matrix pseudo-inverse operation; When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, that is: ；(9) in, is a positive constant, The value range is 10 -4 to 10 -6 .

2. A method for estimating direction of arrival according to claim 1, characterized in that: The method of forming a uniform linear array using antennas, establishing a received signal model based on the array signal input signal, and determining a received signal matrix X includes: The signal received by the first antenna is used as the reference signal, and the signals received by the remaining antennas are used as auxiliary signals. The expression of the reference signal of the received signal at any sampling time k is: ；(1) in, represents the mth signal source at time k; represents the noise signal in the signal received by the first antenna at time k; The expression of the auxiliary signal of the received signal at any sampling time k is: ；(2) in, Indicates the steering factor corresponding to the mth signal source on the nth antenna receiving signal; represents the noise signal in the signal received by the nth antenna at time k; The expression of the total received signal vector for any received signal at time k is: ；(3) in, represents the actual signal received by each antenna in the array at time k; Indicates the array has the mth signal source The steering vector of represents the noise signal received by each antenna in the array at time k; The received signal matrix X corresponding to K sampling times is: (4)。 3. A method for estimating direction of arrival according to claim 2, characterized in that: The low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ,include: ；(10) ；(11) Where e(k) is the signal estimation error, Represents the k-th column of the low-noise low-dimensional matrix Remove the first element Post-noise reduction signal; Update iterative calculation of weight vector coefficients The expression: ；(12) Low-noise low-dimensional matrix The statistical parameters include the instantaneous prediction error and noise reduction signal power ; Update variable step size The expression: ；(13) in, , is a constant (0,1), the accumulation of instantaneous prediction errors , noise reduction signal power .

4. A method for estimating direction of arrival according to claim 3, characterized in that: When the weight vector coefficient Stop the iteration when the update iteration reaches the optimal solution; or, The maximum number of iterations K is preset, when the weight vector coefficient When the number of iterations k>K, stop the iteration.

5. A method for estimating direction of arrival according to claim 4, characterized in that: The weight vector coefficient obtained according to Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal, including: ；(14) ；(15) in, Represents the weight vector coefficients containing the reference signal and the auxiliary signal; represents the array steering vector, is the angle grid parameter.

6. A direction of arrival estimation device according to the direction of arrival estimation method according to any one of claims 1 to 5, characterized in that: include: a matrix determination unit, configured to establish a received signal model based on the array signal input signal and determine a received signal matrix X; The preprocessing unit is used to perform low-rank matrix approximation on the received signal matrix X through a low-rank matrix estimation algorithm to obtain a low-noise low-dimensional matrix ; Update unit, used to pass low-noise low-dimensional matrix Variable step size of the least mean square algorithm LMS for statistical parameter update , update the iterative calculation weight vector coefficient ; Calculation unit, used to obtain the weight vector coefficient Calculating antenna array patterns and spatial spectrum , estimate the direction of arrival of the signal; The low-rank matrix estimation algorithm is used to perform low-rank matrix approximation on the received signal matrix X to obtain a low-noise low-dimensional matrix ,include: Introducing variables G and H, construct the following optimization problem: ；(5) in, ; Solve the optimization problem, fix The value of , iteratively updated , thereby updating We can get: ；(6) ；(7) ；(8) Where H represents conjugate transpose, and + represents matrix pseudo-inverse operation; When the low-rank matrix estimation algorithm reaches the termination condition, it exits the iteration early, that is: ；(9) in, is a positive constant, The value range is 10 -4 to 10 -6 .

7. A direction of arrival estimation system, comprising an antenna array, characterized in that: It also includes the direction of arrival estimation device according to claim 6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed, the direction of arrival estimation method according to any one of claims 1 to 5 is used.

Images