A pre-processing method for coherent signal DOA estimation of a logarithmic spiral array
By using a logarithmic spiral array model and virtual array transformation technology, the rank of the signal covariance matrix is restored. Combined with the improved MUSIC algorithm, the problem of DOA estimation of coherent signal sources in logarithmic spiral arrays is solved, and high-precision coherent signal source localization is achieved.
Patent Information
- Application Number
- CN202111163357.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-09-30
- Publication Date
- 2025-10-24
- Estimated Expiration
- 2041-09-30
AI Technical Summary
Traditional DOA estimation algorithms cannot effectively handle coherent signals in logarithmic spiral arrays, resulting in rank loss. Existing methods are mainly for equidistant uniform linear arrays and uniform circular arrays, and there is a lack of effective methods for DOA estimation of coherent signal sources in logarithmic spiral arrays.
By establishing a logarithmic spiral array model and using virtual array transformation technology, the logarithmic spiral array is converted into a uniform linear array to restore the rank of the signal covariance matrix. An improved MUSIC algorithm is then used for DOA estimation, including eigenvalue decomposition and spectral peak search in the signal and noise subspaces.
Accurate DOA estimation of coherent signal sources in logarithmic spiral arrays is achieved with sharp spectral peaks, small estimation errors, and good estimation performance. It can handle coherent signal sources with very small intervals.
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Figure CN113848555B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of noise detection, and particularly relates to a pretreatment method for DOA estimation of a logarithmic spiral array coherent signal in the field of noise detection. BACKGROUND
[0002] At present, in the field of noise detection, DOA estimation is usually used to estimate the approximate direction of noise, but due to target echoes, multipath effects, and co-frequency interference, coherent signals are generated, at which time the rank of the signal covariance matrix is defective, resulting in the failure of traditional DOA estimation algorithms.
[0003] In recent years, the research on the DOA estimation method of coherent signals has attracted great attention, and most of the current DOA estimation methods of coherent signal sources are for equidistant uniform linear arrays and uniform circular arrays. However, in the field of noise detection, especially in the noise detection of automobile sirens, the research on the DOA estimation of coherent signal sources of logarithmic spiral arrays is less. Under this background, the present application provides a pretreatment method for the DOA estimation of coherent signals of a logarithmic spiral array. SUMMARY
[0004] The present application aims to provide a pretreatment method for the DOA estimation of coherent signals of a logarithmic spiral array, so as to solve the problem that the traditional DOA estimation algorithm of coherent signals cannot be used for a logarithmic spiral array.
[0005] To achieve the above-mentioned purpose, the present application provides the following technical scheme: a pretreatment method for the DOA estimation of coherent signals of a logarithmic spiral array, comprising the following steps
[0006] 1) First, the logarithmic spiral array is used to receive coherent signals to obtain a real signal covariance matrix matrix
[0007] 2) According to the position of the signal, the observation area is divided into Θ1~Θ k , and the array flow matrix of the virtual array is determined according to the observation area
[0008] 3) The transformation relationship between the real array and the virtual array is obtained as follows:
[0009] 4) Thus, the data covariance matrix of the virtual array is obtained:
[0010] 5) In order to restore the rank of the signal covariance matrix, the virtual array data covariance matrix is processed:
[0011] 6) The eigenvalue decomposition of R X is performed to obtain the signal subspace Us and noise subspace U N ;
[0012] 7) Calculate its MUSIC spatial spectrum, through the spectrum peak search, the angle corresponding to the maximum value of the peak value is the angle of the coherent signal source positioning.
[0013] Compared with the prior art, the present application has the beneficial effects that:
[0014] By establishing a logarithmic spiral array model, a preprocessing method for coherent signal DOA estimation of a logarithmic spiral array applied in the noise detection field is creatively invented, the technology can estimate two coherent signal sources with very small interval, the spectral peak is sharp, the estimation error is very small, and the estimation effect is good. BRIEF DESCRIPTION OF DRAWINGS
[0015] Figure 1 The logarithmic 32-element spiral array structure of the present application.
[0016] Figure 2 The geometric relationship diagram of any two elements in space of the present application.
[0017] Figure 3 The VA-MMUSIC algorithm transformation error curve diagram of the first embodiment of the present application
[0018] Figure 4 The estimation effect comparison diagram of the MMUSIC algorithm and the VA-MMUSIC algorithm of the first embodiment of the present application.
[0019] Figure 5 The VA-MMUSIC algorithm transformation error curve diagram of the second embodiment of the present application.
[0020] Figure 6 The estimation effect comparison diagram of the MMUSIC algorithm and the VA-MMUSIC algorithm of the second embodiment of the present application.
[0021] Figure 7 The VA-MMUSIC algorithm root mean square error comparison diagram of different fast shots and different signal-to-noise ratios of the third embodiment of the present application
[0022] Figure 8 The estimation effect comparison diagram of the MMUSIC algorithm and the VA-MMUSIC algorithm of the fourth embodiment of the present application.
[0023] Figure 9 The estimation effect comparison diagram of the MMUSIC algorithm and the VA-MMUSIC algorithm of the fourth embodiment of the present application. DETAILED DESCRIPTION
[0024] Clearly, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all the other embodiments obtained by a person of ordinary skill in the art without creative work are within the protection scope of the present application.
[0025] Please refer to Figures 1-2 The present application provides a technical solution: a pretreatment method for coherent signal DOA estimation of a logarithmic spiral array, comprising the following steps
[0026] 1) First, the logarithmic spiral array receives coherent signals to obtain a real signal covariance matrix matrix
[0027] 2) According to the position of the signal, the observation area is divided Θ1~Θ k The array flow matrix of the virtual array is determined for the observation area
[0028] 3) The transformation relationship between the real array and the virtual array is obtained as follows:
[0029] 4) Thus, the data covariance matrix of the virtual array is obtained:
[0030] 5) In order to restore the rank of the signal covariance matrix, the virtual array data covariance matrix is processed:
[0031] 6) The eigenvalue decomposition of R X can obtain the signal subspace U s and the noise subspace U N ;
[0032] 7) Calculate the MUSIC spatial spectrum, and through spectral peak search, the angle corresponding to the maximum value of the peak value is the angle of the coherent signal source positioning.
[0033] Establish a coherent signal receiving model of a logarithmic spiral array
[0034] Modeling is performed through MATLAB to construct a mathematical model of the logarithmic spiral array, determine the position coordinates of each element of the logarithmic spiral array, and obtain the steering vector array of the logarithmic spiral array through calculation. Assuming that the logarithmic spiral array receiving array is composed of M elements, N far-field narrowband signals are incident on each element of the array in the form of plane waves, and the noise is Gaussian white noise and is not related to the signal. Then, the coherent signal output expression of the logarithmic spiral array can be expressed as:
[0035] X(t) = A(t)S(t) + N(t) (1)
[0036] Virtual array transformation of logarithmic spiral array
[0037] After receiving the coherent signals by using the logarithmic spiral array, the virtual array transformation of the logarithmic spiral array is needed. The virtual array transformation is to divide the space into several regions, to subdivide a certain region of the space, to respectively calculate the steering vector of the real array in the region and the steering vector of the virtual array after the virtual transformation, to derive a relationship between the real logarithmic spiral array and the virtual array after the transformation according to the principle of minimum norm of the transformation error, to obtain the data covariance matrix of the virtual array, and then to use the improved MUSIC algorithm to perform the DOA estimation.
[0038] The specific content of the model is as follows
[0039] (1) Coherent signal model
[0040] For two stationary signals s i (t) and s k (t), the correlation coefficient can be defined as:
[0041]
[0042] According to Schwartz inequality, |p ik |≤1, therefore, the correlation between the two signals can be defined as:
[0043] I. When p ik =0, s i (t) and s k (t) are independent;
[0044] II. When 0<|p ik |<1, s i (t) and s k (t) are correlated.
[0045] III. When |p ik |=1, s i (t) and s k (t) are coherent.
[0046] From the above definition, when the two signals are coherent signals, they satisfy the following formula:
[0047] s i (t) = w i s k (t) (3)
[0048] In the formula, w i is a complex constant.
[0049] In the simulation process, the signal can be expressed in the following form:
[0050]
[0051] In the above formula, u i (t) is the amplitude of the received signal, and ω0 is the angular frequency of the signal, wherein
[0052] ω0=2πf=2πc / λ (5)
[0053] is the initial phase of the signal.
[0054] (2) Array model
[0055] The present application studies an eight-arm logarithmic spiral array, which is composed of eight logarithmic spiral arms. The curve of each logarithmic spiral arm is expressed as:
[0056] r(θ)=r1exp[cot(v)θ] (6)
[0057] r1 is the minimum circle radius composed of the starting points of the eight spiral lines, the spiral angle is v, and θ is the polar angle. In the formula, exp represents the exponential function of e, and cot represents the cotangent function. The coordinates corresponding to each array element are shown in Table 1, and the array structure model is shown in Figure 1
[0058]
[0059]
[0060] Table 1 Eight-arm 32-element logarithmic spiral array coordinates
[0061] Consider that N far-field narrow-band coherent signals are incident on a logarithmic spiral array composed of M array elements, wherein the directions of arrival of each signal source are respectively: The wavelength is λ, θ represents the azimuth angle, represents the elevation angle.
[0062] Assume that the noise signal source is a narrow-band signal, and the signal can be expressed in the following complex envelope form:
[0063]
[0064] In the above formula, u i (t) is the amplitude of the received signal, and ω0 is the angular frequency of the signal, wherein
[0065] ω0=2πf=2πc / λ (8)
[0066] is the initial phase of the signal.
[0067] Under the assumption of narrowband far-field signal source, we have:
[0068]
[0069] Then we have:
[0070]
[0071] Then the signal received by the kth element can be obtained as:
[0072]
[0073] In the above equation: g ki is the gain of the kth element to the ith signal, n l (t) represents the noise of the kth element at time t, τ ki represents the time delay of the ith signal relative to the reference element when it reaches the kth element.
[0074] The signals received by the M elements at a certain time are arranged into a column vector, and then we have:
[0075]
[0076] Under ideal conditions, assuming that each element in the array is isotropic and there is no influence of channel inconsistency, mutual coupling and other factors, the gain in the above equation can be ignored. Under this assumption, the above equation can be simplified as:
[0077]
[0078] Writing the above equation in vector form, we have:
[0079] X(t) = A(t)S(t) + N(t) (14)
[0080] where X(t) is the Mxl snapshot data vector of the array, N(t) is the Mxl noise data vector of the array, S(t) is the Nxldata vector of the spatial signal, A(t) is the MxN array manifold matrix of the spatial array, and:
[0081] A = [a1(ω0) a2(ω0) … a N (ω0)] (15)
[0082] The steering vector can be expressed as:
[0083]
[0084] In the above equation, ω0 = 2πf, where f is the frequency of the signal.
[0085] From the above formula, we can know that after knowing the logarithmic spiral array model, we need to derive the delay expression τ between each array element to obtain the coherent signal array receiving model, as follows: Figure 2 shown.
[0086] Depend on Figure 2 It can be seen that, assuming that one of them is the reference element (located at the origin), the coordinates of the other element are (x k ,y k )(k=1,2,…,M), and assume that the signal incident parameters are where θ i represents the azimuth, represents the pitch angle, and the delay expression τ between array elements can be expressed as:
[0087]
[0088] Substituting the above formula back into Formula 16, we get the steering vector of the logarithmic spiral array, and then we get the signal vector X(t) received by the logarithmic spiral array. The data covariance matrix of the logarithmic spiral array is:
[0089]
[0090] Since the actual received data matrix is of finite length, the estimated value of the covariance matrix can be obtained:
[0091]
[0092] The specific processing methods are as follows
[0093] After the logarithmic spiral array receives the coherent signal and obtains the covariance matrix of the output signal, a virtual array transformation is performed on the received covariance matrix. The core of the virtual array transformation is to divide the spatial area, subdivide a specific area, and find the steering vectors within the area, including the steering vectors of the original array and the steering vectors of the virtual array after the transformation, and then find the transformation relationship between the two steering vectors. The present invention applies virtual array transformation technology to the logarithmic spiral array, realizing the virtual transformation of the logarithmic spiral array to a uniform linear array. This makes it possible to localize the sound source of the coherent signal.
[0094] First, we divide an observation area. We can assume that the signal is located in the area Θ and divide the area Θ into the following equal parts:
[0095] Θ=[θ1 θ1+Δθ θ2+2Δθ … θ r -Δθθ r ] (20)
[0096] In the above formula, θ1, θ rFor left and right boundaries, Δθ is the step, then the array manifold of the real log spiral array is:
[0097] A = [a(θ1) a(θ1+Δθ) a(θ1+2Δθ)... a(θ r )] (21)
[0098] In the same region Θ, we assume the array manifold matrix of the virtual array is:
[0099]
[0100] Obviously, there is a fixed transformation relationship B between the array manifold matrix A of the log spiral array and the array manifold matrix of the virtual array. k , and satisfies:
[0101]
[0102] From the above formula, the following transformation relationship can be obtained:
[0103]
[0104] Assume the data covariance matrix of the log spiral array in this paper is The environmental noise is white noise with power σ 2 I, then the real array data covariance matrix is:
[0105]
[0106] In the formula, is the autocovariance matrix of the signal vector. The data covariance matrix of the virtual array is:
[0107]
[0108]
[0109]
[0110] The improved MUSIC algorithm is to process the data covariance matrix output by the virtual array, so that the rank of the signal covariance matrix is restored, and the signal direction can be effectively estimated.
[0111] After the log spiral array is virtually converted into a uniform linear array, the output vector N times the sampling data X = [x(1),..., x(N)] is obtained, and the estimation value of the covariance matrix is In general cases is only a Hermite matrix, not a Toeplitz matrix. Using the Toeplitz property, the The matrix is modified to obtain the estimate of Toeplitz covariance matrix The Toeplitz matrix is reconstructed, and the rank of the matrix is only related to the DOA of the signal, and is not affected by the correlation of the signal, thus achieving the purpose of decorrelation. On this basis, R X Eigenvalue decomposition is performed to obtain the noise subspace, and the eigenvectors of the noise subspace are substituted into
[0112] It can be seen from formula (3.7) that the signal covariance matrix obtained by the virtual array is:
[0113]
[0114] Let I v be an M x M inverse unit matrix, that is:
[0115]
[0116] Let
[0117] In the above formula, R is the conjugate matrix of R .
[0118] Eigenvalue decomposition is performed on R X :
[0119] R X = U∑U H (30)
[0120] Eigenvalue decomposition of R X can obtain the signal subspace U s and the noise subspace U N , that is:
[0121] R X = U s ∑ s U s H +U N ∑ N U N H (31)
[0122] Under ideal conditions, the two spaces are orthogonal, and the following is obtained:
[0123]
[0124] The MUSIC spatial spectrum is calculated, that is
[0125]
[0126] The maximum peak value is found by searching the spectrum algorithm in MATLAB simulation The angle corresponding to the maximum value is the angle positioned by the algorithm.
[0127] The application of the algorithm is as follows
[0128] In order to verify the effectiveness of the VA-MMUSIC algorithm for DOA estimation, the mathematical model adopts an eight-arm logarithmic spiral array, and the simulation experiment adopts an eight-arm logarithmic spiral array structure with 32 array elements to receive signals, and the VA-MMUSIC is used to virtually expand the array element number to a uniform linear array structure with 36 array elements.
[0129] It is assumed that the signals incident to the eight-arm logarithmic spiral array are far-field narrow-band coherent signals, and the added noise is Gaussian white noise.
[0130] Embodiment one
[0131] In this embodiment, two coherent signals are set to be incident to the eight-arm 32-element logarithmic spiral array at an azimuth angle of 20° and 60° and a pitch angle of 0°, the linear array element number after virtualization is 36, the element spacing is λ / 2, the number of fast shots is 1024, the noise between each element is independent, the transformation region is assumed to be between 18° and 60°, the transformation region is subdivided, the search step is set to 0.01°, and the MMUSIC algorithm and the VA-MMUSIC algorithm are simulated under the condition of a signal-to-noise ratio of 20 dB. The transformation error of the VA-MMUSIC algorithm is as shown in Figure 3 The effect comparison between the MMSUIC algorithm and the VA-MMUSIC algorithm is as shown in Figure 4 .
[0132] Figure 3 The transformation error is defined as follows:
[0133]
[0134] In the above formula, A(θ) is the array flow pattern of the logarithmic spiral array, and A virt (θ) is the array flow pattern of the virtual array.
[0135] From the transformation error curve of Figure 3 it can be clearly seen that the transformation error of the VA-MMUSIC algorithm is relatively large outside the transformation region, but the error is almost 0 within the transformation region of 18° to 60°.
[0136] From the transformation error curve of Figure 4It can be seen that, compared with the MMUSIC algorithm, the VA-MMUSIC algorithm has a lower starting position, and starts to vibrate at -30 or below, while the MMUSIC algorithm starts to vibrate at -3 or above, which indicates that the VA-MMUSIC algorithm has better resolution. It can also be clearly seen from the figure that the VA-MMUSIC algorithm has a sharper spectral peak, and the VA-MMUSIC algorithm is smoother than the MMUSIC algorithm, without the emergence of redundant false peaks, and the imaging effect is obviously better.
[0137] Example Two
[0138] This example sets two coherent signals to be incident to an 8-arm 32-element logarithmic spiral array at an azimuth angle of 20° and 25° and a pitch angle of 0°. The number of virtual linear array elements is 36, the element spacing is λ / 2, the number of snapshots is 1024, the transformation region is assumed to be between 18° and 25°, the search step is set to 0.01°, and the MMUSIC algorithm and the VA-MMUSIC algorithm are simulated under the condition of 1024 snapshots and a signal-to-noise ratio of 20 dB. The transformation error of the VA-MMUSIC algorithm is shown in Figure 5 , and the effect comparison between the MMUSIC algorithm and the VA-MMUSIC algorithm is shown in Figure 6 .
[0139] From the transformation error curve in Figure 5 , it can be clearly seen that although the transformation error of the VA-MMUSIC algorithm is relatively large outside the transformation region, the error is almost 0 within the transformation region of 18° to 25°.
[0140] From the transformation error curve in Figure 6 , it can be seen that when the azimuth angle interval of the two coherent signal sources incident to the logarithmic spiral array is small, the estimation accuracy is slightly lower than when the interval is large, but the spectral peak is still sharp, and when the two coherent signal sources are close to each other, the DOA estimation of the two coherent signal sources can still be realized. It is verified that the VA-MMUSIC algorithm can still achieve accurate estimation for coherent signal sources with close angle intervals, while the original MMUSIC algorithm cannot estimate the azimuth angles of two close coherent signal sources, and has lost its estimation effect for close signal sources. However, the improved VA-MMUSIC algorithm still has good estimation effect.
[0141] Example Three
[0142] In this embodiment, two coherent signals are incident on a logarithmic spiral array at azimuth angles of 20° and 24°, and at an elevation angle of 0°. Assuming the transformation space is between 18° and 24°, this transformation region is subdivided, and the search step is set to 0.01°. The signal-to-noise ratio is increased from 0 dB to 20 dB in increments of two signal-to-noise ratios. The number of snapshots is set to 256, 512, and 1024, respectively. 20 Monte-Carlo experiments are performed at each signal-to-noise ratio node to verify the estimation performance of this VA-MMUSIC algorithm.
[0143] In this experiment, we need to estimate the azimuth angle of two signals. The error of each experiment is the sum of the errors of the two signal estimates. The calculation formula of the root mean square error (RMSE) can be defined as follows:
[0144]
[0145] Where k, k1 are the number of experiments performed at 2 dB intervals, θ1, θ2 are the azimuths of the two coherent signal sources, which are 20° and 24° respectively in this experiment. It represents the estimated value of the kth experiment. After a total of 660 Monte-Carlo experiments, the root mean square error is obtained as Figure 7 shown.
[0146] from Figure 7 It can be seen that with the increase of the signal-to-noise ratio, the root mean square error of this algorithm becomes smaller and smaller, indicating that this algorithm has a relatively good ability to estimate the azimuth angle of the signal source. When the number of snapshots increases, its root mean square error also decreases accordingly, indicating that the estimation performance of this algorithm increases with the increase of the number of snapshots.
[0147] Example 4
[0148] In order to verify the performance of the VA-MMUSIC algorithm for coherent signals with relatively close signal spacing, this embodiment conducts two simulation experiments. The first assumes that the azimuth angles of the two coherent signals are 20° and 22° respectively. The second assumes that the azimuth angles of the two coherent signals are 20° and 23°. They are incident on an 8-arm, 32-element logarithmic spiral array. The number of elements in the virtual linear array is 36, the element spacing is λ / 2, the number of snapshots is 1024, and the noise between each element is independent of each other. Assuming that the transformation area is between 20° and 23°, this transformation area is subdivided, the search step is set to 0.01°, and the signal-to-noise ratio is 20dB, simulation experiments are performed on the MMUSIC algorithm and the VA-MMUSIC algorithm respectively:
[0149] from Figure 8 and Figure 9It can be seen that when the interval of two coherent signals is within 2°, the MMUSIC algorithm cannot achieve accurate DOA estimation of two coherent signals at a signal-to-noise ratio of 20 dB and a number of snapshots of 1024, while the VA-MMUSIC algorithm can still achieve accurate estimation of coherent signals when the interval is 3°, although the spectral peak is not as sharp as when the interval is larger, and the estimation error is kept within the range of 0.5°. However, when the interval of two coherent signals is 2°, the spectral peak of one of the two signals is almost invisible, and the estimation performance decreases.
[0150] The simulation results show that the VA-MMUSIC algorithm overcomes the defect of the traditional MUSIC algorithm that cannot accurately estimate coherent sources of the logarithmic spiral array by using the virtual array method for pretreatment, and can effectively estimate the DOA of coherent signal sources with high estimation accuracy. When the azimuth angle interval of two signals is small, the corresponding transformation space is reduced, and the DOA estimation of two signals with small interval can be achieved.
Claims
1. A pre-processing method for coherent signal DOA estimation of a logarithmic spiral array, characterized in that: Comprising the following steps: 1) First, the log-spiral array is used to receive the coherent signal, and the real signal covariance matrix is obtained as ; 2) dividing the observation region Θ according to the position of the signal , determining the array flow matrix of the virtual array for the delimited observation region ; 3) the transformation relationship between the real array and the virtual array is obtained as: ; A is an array flow pattern matrix, 4) the data covariance matrix of the virtual array is obtained: ; 5) To restore the rank of the signal covariance matrix, the virtual array data covariance matrix is processed: ; is the inverse identity matrix; 6) to Eigenvalue decomposition gives the signal subspace and the noise subspace ; 7) Calculate its MUSIC spatial spectrum, through the spectral peak search, the angle corresponding to the peak value of the maximum is the angle of the coherent signal source positioning; Virtual array transformation of logarithmic spiral array: After receiving the coherent signal by using the logarithmic spiral array, the virtual array transformation of the logarithmic spiral array is needed. The virtual array transformation is to divide the space into several regions, to subdivide a certain region of the space, to respectively calculate the steering vector of the real array in the region and the steering vector of the virtual array after the virtual transformation, to derive a relationship between the real logarithmic spiral array and the virtual array steering vector according to the principle of minimum norm of transformation error, to obtain the data covariance matrix of the virtual array, and then to use the improved MUSIC algorithm to perform DOA estimation. In the transformation region of 18° to 60°, the error is almost 0.
2. The pre-processing method for coherent signal DOA estimation of a logarithmic spiral array according to claim 1, characterized in that: Also comprising Establishing a coherent signal receiving model of logarithmic spiral array Modeling through MATLAB, constructing a mathematical model of the logarithmic spiral array, determining the position coordinates of each element of the logarithmic spiral array, and calculating the steering vector array of the logarithmic spiral array; assuming that the receiving array of the logarithmic spiral array is composed of M elements, N far-field narrowband signals are incident on each element of the array in the form of plane waves, the noise is assumed to be Gaussian white noise and unrelated to the signal, and then the coherent signal output expression of the logarithmic spiral array can be expressed as: （1）； where N(t) is the M×1-dimensional noise data vector of the array, S(t) is the N×1-dimensional data vector of the spatial signal, and A(t) is the M×N-dimensional array flow matrix of the spatial array.