A method for ultra-short baseline direction estimation based on arbitrary formation

Abstract

The present invention discloses a method for estimating the direction of an ultra-short baseline based on an arbitrary array. The present invention describes the distribution of array elements of an arbitrary array through three-dimensional coordinates and establishes a receiving model of the array; uses different baseline vectors, based on the weighted incoherent signal subspace method, divides the signal frequency band and weights the spatial spectra of different subbands according to the signal-to-noise ratio, and estimates the signal incident angle according to the peak position of the spatial spectrum; performs parameter regression on all baseline azimuth estimation results to estimate the direction of the transmitter. The present invention improves the direction estimation method of the ultra-short baseline for ultra-short baseline positioning scenarios, wherein the ISSM method can suppress the influence of phase ambiguity, so that the array element spacing can exceed half the wavelength of the signal; the parameter regression method extends the direction estimation to arbitrary arrays, further improving the accuracy and stability of the direction estimation with a limited increase in complexity.

Description

Technical Field

[0001] The present invention belongs to the field of underwater positioning and relates to an ultra-short baseline direction estimation method based on an arbitrary formation. Specifically, the ultra-short baseline direction estimation method is optimized to make the direction estimation method applicable to an ultra-short baseline array of an arbitrary formation and to improve the direction estimation performance. Background Art

[0002] The ocean provides humanity with a vast array of resources, but due to the limitations of the underwater environment, various types of underwater unmanned mobile nodes have gradually become a vital force in underwater operations. Accurate positioning of mobile nodes is crucial for ensuring their successful completion of various tasks and safe return, and is also an important prerequisite for ensuring accurate data collection. Because electromagnetic wave signals are severely attenuated underwater, acoustic signals are currently the most suitable method for achieving long-distance underwater communication. Underwater acoustic positioning is a commonly used positioning method, including long-baseline positioning, short-baseline positioning, and ultra-short-baseline positioning. Although the ultra-short-baseline positioning method is less accurate than long-baseline positioning, it has also been widely used due to its ease of installation and use.

[0003] In ultra-short baseline positioning, the receiver uses a multi-hydrophone array to receive positioning signals. Distance is estimated by calculating the signal's propagation time, and direction is estimated by calculating the time delay or phase difference between the received signals between different array elements. This method is used to locate the sound source at the transmitter. Distance estimation is relatively simple and mature, requiring only measuring the signal's propagation time and multiplying it by the equivalent speed of sound. However, direction estimation is more challenging due to the baseline length, which typically does not exceed 1 meter.

[0004] Traditional ultra-short baseline positioning is usually based on a cross-orthogonal planar four-element array. The unit vector pointing to the transmitter is denoted as p s Under the plane wave approximation, p is calculated by estimating the time delay or phase difference of the received signals of the two array elements in the x direction. s The cosine of the angle with the positive direction of the x-axis is cosθ x , and then calculate p by estimating the time delay or phase difference of the received signals of the two array elements in the y direction s The cosine of the angle with the positive direction of the y-axis is cosθ y When using a plane array, the default setting is that the transmitter is located on one side of the plane array. Here, the default setting is that the coordinate in the z direction is positive, so

[0005] To improve the direction estimation performance of ultra-short baseline arrays, in addition to increasing the sampling rate, broadening the positioning signal bandwidth, and increasing the signal duration, the number of array elements can also be increased. As the number of elements increases and the array becomes more complex, traditional methods are no longer sufficient to simply estimate the transmitter's direction. More rational direction estimation methods are needed. Furthermore, further improving the accuracy and stability of direction estimation using ultra-short baselines is also a critical consideration.

[0006] The Chinese invention patent with application number 201910574431.1 proposes a method for estimating the bearing of an ultra-short baseline of an arbitrary array and describes the related systems, equipment and storage media. Its limitation lies in the relatively complex calculation process. The Chinese invention patent with application number CN202110138315.2 proposes a method for locating underwater sound sources with an ultra-short baseline based on broadband compressed sensing. Since it needs to traverse the two-dimensional space, the amount of calculation is large. The Chinese invention patent with application number 202110111140.6 proposes a method for locating underwater sound sources with an ultra-short baseline based on a two-dimensional arbitrary array space. Since the patent uses a two-dimensional high-resolution spectrum estimation method, on the one hand, it is necessary to traverse the two-dimensional space, resulting in a large amount of calculation for the method; on the other hand, it is necessary to meet the requirement that the array element spacing is less than half the wavelength of the acoustic signal, resulting in limited estimation accuracy.

[0007] In summary, existing ultra-short baseline array direction estimation methods still have some shortcomings. On the one hand, the direction estimation method needs to be effectively extended to scenarios with multiple elements and complex arrays, so that it can adapt to the direction estimation of any array. On the other hand, the real-time performance of the positioning system must be considered. In other words, while improving the accuracy and stability of direction estimation, the algorithm complexity should not be too high. Summary of the Invention

[0008] The purpose of the present invention is to address the shortcomings of traditional ultra-short baseline array direction estimation methods and provide an ultra-short baseline direction estimation method based on arbitrary formations, expand the direction estimation method to arbitrary formations, and improve the accuracy and stability of direction estimation.

[0009] The system of the present invention includes a transmitting end and a receiving end. The transmitting end is an underwater acoustic communication device or other sound source equipment, which can send a known broadband positioning signal. The receiving end includes an ultra-short baseline array and a signal processing module. The ultra-short baseline array is composed of N arbitrarily distributed array elements. The receiving end establishes an array space model based on the array element distribution: first, select any point in the ultra-short baseline array space as the array center, and establish a coordinate system with the array center as the origin; if the ultra-short baseline array is a three-dimensional array, select a point in the three-dimensional space as the array center and establish a coordinate system; if the ultra-short baseline array is a planar array, select a point in the plane where the planar array is located as the array center, and establish a coordinate system with the plane where the array is located as xOy; express the coordinate position of each array element to obtain the baseline vector pi,j =p j -p i , p i,j is the baseline vector between the i-th array element and the j-th array element, p i =[x i ,y i ,z i ] T is the position of the i-th array element, p j =[x j ,y j ,z j ] T is the position of the jth array element, i,j∈[1,N] and i<j, and the superscript T represents transposition. The specific steps of the method of the present invention are:

[0010] Step (1) The transmitter generates a known broadband positioning signal and sends it to the outside world.

[0011] Step (2) The receiving end receives the signal x of all elements of the ultra-short baseline array. i (k) Perform matched filtering, i = 1, ..., N, k represents the kth sampling point;

[0012] Step (3) If the average value of the peak value after matched filtering exceeds the threshold, the filtered signal is passed to the subsequent module for direction estimation and step (4) is executed, otherwise return to step (2);

[0013] Step (4) The receiving end uses the weighted incoherent signal-subspace method (ISSM) to estimate the cosine value of the angle between different baseline vectors and the signal incident direction to obtain the azimuth estimation result. To reduce the amount of calculation, some baseline vectors can be selected for estimation; the details are as follows:

[0014] (4-1) constitutes the baseline vector p i,j The received signal x after matched filtering of the i-th array element and the j-th array element m,i (k) and x m,j (k) Perform fast Fourier transform respectively and take the in-band sequence X of the unilateral spectrum m,i (k) and X m,j (k); Divide the frequency band into P sub-bands uniformly and construct the frequency domain model X for each sub-band m,i,j,p =[X m,i,p ,X m,j,p ] H , X m,i,p (k) and X m,j,p (k) are X m,i (k) and X m,jThe p-th subband sequence of (k), p = 1,…,P, the superscript H indicates the conjugate transpose;

[0015] (4-2) Calculate the covariance matrix of each subband sequence Among them, K p Indicates the number of sampling points in the p-th subband.

[0016] Perform eigenvalue decomposition on the covariance matrix: Among them, Σ s,p Represents the larger of the two eigenvalues, and its corresponding eigenvector U s,p Constitute the signal subspace; Σ n,p Represents the smaller of the two eigenvalues, and its corresponding eigenvector U n,p Construct the noise subspace.

[0017] According to the signal power P s,p =Σ s,p -Σ n,p and noise power P n,p =Σ n,p Get the subband signal-to-noise ratio SNR p =10·lg(P s,p / P n,p ), and then obtain the subband weight Among them, w and b are adjustable parameters.

[0018] (4-3) Based on the ISSM method in broadband signal super-resolution spectrum theory, the spatial spectrum of the weighted ISSM method is defined in, θ represents the signal incident angle, d represents the length of the baseline vector, c represents the speed of sound, and f p Represents the center frequency of the pth subband, j represents an imaginary number. θ is traversed in the range of 0 to π to find the peak position of the spatial spectrum, and the signal incident angle corresponding to the peak is is the azimuth estimation result, that is, the signal incident direction and the baseline vector p i,j The angle between the baseline vector and the signal incident direction is obtained by

[0019] Steps (4-1) to (4-3) represent the computational process of the weighted ISSM method. To reduce the computational complexity, the spatial spectrum can be first traversed at larger intervals within the range 0 to π, followed by a smaller interval within the interval consisting of points before and after the peak position. Furthermore, the spatial spectrum definition method of the weighted ISSM method in step (4-3) can suppress the effects of phase ambiguity, allowing the baseline vector length to be greater than half a wavelength.

[0020] Step (5) The ultra-short baseline array at the receiving end estimates the unit vector p pointing from the receiving end to the transmitting end by means of parameter regression based on all the selected baseline vectors and their azimuth estimation results. s . Signal incident direction -p s and the baseline vector p i,j The cosine of the angle is expressed as Among them, cosθ s,i,j Indicates -p s and p i,j The cosine of the angle, d i,j Indicates the baseline length; p s and cosθ s,i,j For a linear relationship, the position estimates of multiple baselines are used to calculate p based on the parametric regression method. s , the optimal estimate is the unit vector estimate st Among them, Θ and S are d i,j cosθ s,i,j and p i,j The constructed matrix, ρ(·) represents the loss function, and ||·||2 represents the two-norm.

[0021] If the ultra-short baseline array is a stereo array, the specific process of the parameter regression method is as follows:

[0022] (5-a) Initialize the weight matrix W as the identity matrix and transform the problem into weighted least squares according to the iterative reweighted least squares method, that is,

[0023] (5-b) Initialize the Lagrangian factor λ = 0;

[0024] (5-c) is converted into The constraint solution is converted to an unconstrained solution, that is, the Lagrangian function The numerical solution of λ is solved iteratively by the gradient descent method; according to renew I is the identity matrix; according to Update λ, where μ λ is the adjustable step size, t is the number of iterations;

[0025] (5-d) If The difference between the square of the modulus and 1 is less than the threshold, or the number of iterations reaches the upper limit, Normalize, execute (5-e), otherwise return to step (5-c);

[0026] (5-e) Update the weight of each baseline vector Where ρ′(·) represents the effect of ρ(·) on p s The derivative ofi,j Construct the weight matrix W in sequence. The weight matrix W is a diagonal matrix. Determine whether the number of iterations has reached the upper limit. If it has reached the upper limit, the estimation is completed and the unit vector estimation is obtained. Otherwise, execute (5-b).

[0027] Steps (5-a) to (5-e) are applicable to any 3D array. When ρ(·) takes the L2 error function, the problem becomes a least-squares estimation problem. In this case, the weights are always the identity matrix, so there is no need to iteratively update the weight matrix. When ρ(·) takes the L1 error function or the Huber loss function, the problem becomes a robust estimation problem, which can reduce the impact of outliers on the direction estimate. To reduce the computational effort, the number of iterations can be reduced.

[0028] When the array is a planar array, due to the matrix SS T The rank deficiency of , therefore, is different from the calculation process of the stereo array. If the ultra-short baseline array is a planar array, the specific process of the parameter regression method is as follows:

[0029] (5-A) Initialize the weight matrix W as the identity matrix and transform the problem into weighted least squares according to the iterative reweighted least squares method, that is,

[0030] (5-B) Initialize the adjustment factor 0<δ<<1;

[0031] (5-C) According to the weighted least squares formula, update

[0032] (5-D) Update the weight of each baseline Use w i,j Construct the weight matrix W in sequence. The weight matrix W is a diagonal matrix. Determine whether the number of iterations has reached the upper limit. If so, execute (5-E). Otherwise, continue to execute (5-C).

[0033] (5-E) output by (5-D) Plane coordinates of Re-update when when

[0034] Step (6) outputs the unit vector estimate This is the final direction estimate.

[0035] This paper improves the direction estimation performance of ultra-short baseline arrays by establishing a spatial coordinate system for them, using the weighted ISSM method to estimate the signal incidence angle for different baseline vectors, and employing a parametric regression method to estimate the transmitter direction. Compared to traditional methods, this paper generalizes the direction estimation method to any array, achieving higher accuracy and stability in direction estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 Flowchart of the present invention;

[0037] Figure 2 Schematic diagram of the inverse ultra-short baseline system model;

[0038] Figure 3 Schematic diagram of the formation structure of a three-dimensional four-element array;

[0039] Figure 4 This is a flowchart of the weighted ISSM direction estimation method;

[0040] Figure 5 Schematic diagram of the process of stereo array direction estimation method based on parameter regression;

[0041] Figure 6 Schematic diagram of the process of the planar array direction estimation method based on parameter regression;

[0042] Figure 7 This is a comparison chart of the estimation error curves of the direction estimation method based on weighted ISSM and parameter regression and the traditional direction estimation method based on time delay. DETAILED DESCRIPTION

[0043] A method for estimating direction of ultra-short baseline based on arbitrary formation, the flow chart of which is as follows Figure 1 In order to more clearly illustrate the method flow of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and examples. Figure 2 The schematic diagram of the reverse ultra-short baseline system model of this embodiment is shown in FIG. The ultra-short baseline array is installed on an underwater mobile node. The beacon node is the transmitting end, including a sonicator or other sound source device. The beacon node periodically sends a known broadband positioning signal. The underwater mobile node is the receiving end, including an ultra-short baseline array of any formation and a corresponding signal processing module. The underwater mobile node estimates the beacon direction based on the received signal of the array. The receiving end establishes a receiving model of the array. In this embodiment, the ultra-short baseline array is based on the Figure 3Taking the three-dimensional four-element array shown in the figure as an example, the position coordinates of elements 1, 2, 3, and 4 are (0.075m, 0, 0), (-0.075m, 0, 0), (0, 0.075m, 0.075m), and (0, -0.075m, 0.075m), respectively. The number of elements is N = 4. The elements are combined in pairs to construct the baseline vectors, and the baseline vectors are p respectively. 1,2 =[-0.15,0,0] T 、p 1,3 =[-0.075,0.075,0.075] T 、p 1,4 =[-0.075,-0.075,0.075] T 、p 2,3 =[0.075,0.075,0.075] T 、p 2,4 =[0.075,-0.075,0.075] T and p 2,4 =[0,-0.15,0] T , a total of six. Shaped like p 2,1 The baseline vector is only equal to p 1,2 The directions are opposite, so only the latter is considered. Let the unit vector in the direction of the source be p s =[x s ,y s ,z s ] T , direction estimation requires solving p s .

[0044] The specific process of direction estimation is achieved through the following steps:

[0045] Step (1) The transmitter generates a known broadband positioning signal and sends it to the outside world. This embodiment uses a chirp signal of 8 to 12 kHz with a signal duration of 40 ms.

[0046] Step (2) The receiving end receives the signal x of all elements of the ultra-short baseline array. i (k) performs matched filtering, i = 1, ..., N, k represents the kth sampling point, and the signals after matched filtering of x1(k) and x2(k) are recorded as x m,1 (k) and x m,2 (k).

[0047] Step (3) If the average value of the peak value after matched filtering exceeds the threshold, the filtered signal is passed to the subsequent module for direction estimation and step (4) is executed, otherwise return to step (2);

[0048] Step (4) The receiving array selects some or all baselines and uses the weighted ISSM method to estimate the cosine value of the angle between different baseline vectors and the signal incident direction. In this embodiment, all baseline vectors are selected, that is, p is selected. 1,2 、p 1,3 、p 1,4 、p 2,3 、p 2,4 and p 3,4 Used for bearing estimation. Part of the baseline can also be selected. Figure 4 As shown, the baseline vector p constructed by array element 1 and array element 2 1,2 For example, the weighted ISSM method is as follows:

[0049] (4-1) For signal x m,1 (k) and x m,2 (k) Perform fast Fourier transform respectively and take the in-band sequence of the unilateral spectrum, which are recorded as X m,1 (k) and X m,2 (k), the frequency band is evenly divided into P sub-bands (P=5 in this embodiment), where the center frequency of the p-th sub-band is denoted as f p .X m,1 (k) and X m,2 The p-th subband sequence of (k) is denoted as X m,1,p (k) and X m,2,p (k), construct the frequency domain model of the p-th subband: X m,1,2,p =[X m,1,p ,X m,2,p ] H .

[0050] (4-2) Calculate the covariance matrix of the subband sequence: Among them, K p Indicates the number of samples in the pth subband. Perform eigenvalue decomposition on the covariance matrix:

[0051] Among them, Σ s,p Represents the larger of the two eigenvalues, and its corresponding eigenvector U s,p Constitute the signal subspace; Σ n,p Represents the smaller of the two eigenvalues, and its corresponding eigenvector U n,p Construct the noise subspace.

[0052] According to the signal power P s,p =Σ s,p -Σ n,p and noise power P n,p =Σ n,p Get the subband signal-to-noise ratio SNR p =10·lg(P s,p / Pn,p ), and then obtain the subband weight Adjustable parameters w=3, b=4.

[0053] (4-3) Calculate the spatial spectrum of the weighted ISSM method: in, d represents the baseline vector p 1,2 The length (in this embodiment, d = |p 1,2 |=0.15m), c represents the speed of sound (in this embodiment, c=1500m / s). The peak position of the spatial spectrum is found by traversing θ in the range of 0~π, and the corresponding is the azimuth estimation result, that is, the signal incident direction and the baseline vector p i,j Then calculate the cosine value of the angle between the baseline vector and the signal incident direction To reduce the amount of traversal calculation, in this embodiment, the spatial spectrum is first traversed within 0-π with a step size of 1°, and then the interval consisting of a point before and after the peak position is selected for traversal with a step size of 0.01°.

[0054] In this embodiment, the center frequency of the positioning signal is 10 kHz, corresponding to a half-wavelength of 0.075 m. The baseline length is greater than the half-wavelength, but the ISSM method can suppress phase ambiguity.

[0055] Step (5) The receiving array estimates the unit vector p of the transmitting end direction by parameter regression based on all selected baselines and their orientation estimates. s The current formation is a three-dimensional array, and the method flow is as follows Figure 5 As shown, p is solved by parameter regression s ,Right now: st Among them, Θ and S are d i,j cosθ s,i,j and p i,j The matrices constructed in sequence are:

[0056] S=[p 1,2 ,p 1,3 ,p 1,4 ,p 2,3 ,p 2,4 ,p 3,4 ];

[0057] Θ=[d 1,2 cosθ s,1,2 ,d 1,3 cosθ s,1,3 ,d 1,4 cosθ s,1,4 ,d 2,3 cosθ s,2,3 ,d 2,4cosθ s,2,4 ,d 3,4 cosθ s,3,4 ] T .

[0058] In this embodiment, the L1 norm is taken as the loss function, and then:

[0059] The direction estimation method based on parameter regression is as follows:

[0060] (5-1) Initialize the weight matrix W as the identity matrix. In this embodiment,

[0061] Then, according to the iterative reweighted least squares method, the problem is transformed into weighted least squares, that is, st

[0062] (5-2) Initialize the Lagrangian factor λ = 0.

[0063] (5-3) According to the weighted least squares formula renew Then according to Update λ; where μ λ For adjustable step length, take 10 -4 .like The difference between the square of the modulus and 1 is less than the threshold value of 10 -4 , or the number of iterations reaches the upper limit, Normalize and go to the next step; otherwise, continue to execute (5-3). In this embodiment, the number of iterations is 100.

[0064] (5-4) According to the formula Update the weight of each baseline. In this embodiment, according to the definition of L1 loss function, w i,j The specific updates are: Where σ is a small number to prevent the denominator from being 0. In this embodiment, σ=10 -8 Then use w i,j Build W in order:

[0065]

[0066] Determine whether the number of iterations has reached the upper limit. If so, the calculation process is completed and the direction estimate is obtained. Otherwise, continue to execute (5-2). In this embodiment, the number of iterations is 4.

[0067] If the array is a planar array, the method based on parameter regression is as follows Figure 6 The specific process is as follows:

[0068] (A) Initialize the weight matrix W as the identity matrix and transform the problem into weighted least squares according to the iterative reweighted least squares method, that is, st

[0069] (B) Initialization adjustment factor 0<δ<<1;

[0070] (C) Update according to the weighted least squares formula

[0071] (D) Update the weight of each baseline Use w i,j Construct the weight matrix W in sequence. The weight matrix W is a diagonal matrix. Determine whether the number of iterations has reached the upper limit. If so, execute (E). Otherwise, continue to execute (C).

[0072] (E) Output from step (D) Plane coordinates of Re-update when when

[0073] Step (6) outputs the unit vector estimate This is the final direction estimate.

[0074] Figure 7 The figure shows a comparison of the estimation error curves of the direction estimation method based on weighted ISSM and parameter regression and the traditional direction estimation method based on time delay. The direction estimation error is the average of the root mean square error of the direction angle estimation for 218 different directions. It can be seen that compared with the traditional direction estimation method based on time delay, the direction estimation method based on weighted ISSM and parameter regression can effectively reduce the direction estimation error and improve the stability of direction estimation.

[0075] The above description of the embodiments is merely an enumeration of the implementation forms of the present invention. The scope of protection of the present invention should not be limited to the specific forms described in the embodiments. Improvements and modifications made to the present invention by those skilled in the art based on the disclosure of the present invention should be within the scope of protection of the present invention.

Claims

1. A method for estimating the direction of an ultra-short baseline based on an arbitrary array, the system comprising a transmitting end and a receiving end; the transmitting end is an underwater acoustic communication device or other sound source equipment, capable of sending a known broadband positioning signal; the receiving end comprises an ultra-short baseline array and a signal processing module, the ultra-short baseline array being composed of N arbitrarily distributed array elements; the receiving end establishes an array space model according to the array element distribution: first, an arbitrary point in the ultra-short baseline array space is selected as the array center, and a coordinate system is established with the array center as the origin; if the ultra-short baseline array is a three-dimensional array, a point is selected in three-dimensional space as the array center and a coordinate system is established; if the ultra-short baseline array is a planar array, a point in the plane where the planar array is located is selected as the array center, and a coordinate system is established with the plane where the array is located as xOy; the characteristic is that Here’s how: Step (1) The transmitting end generates a known broadband positioning signal and sends it to the outside world; Step (2) The receiving end receives the signal x of all elements of the ultra-short baseline array. i (k) Perform matched filtering, i = 1, ..., N, k represents the kth sampling point; Step (3) If the average value of the peak value after matched filtering exceeds the threshold, the filtered signal is passed to the subsequent module for direction estimation and step (4) is executed, otherwise return to step (2); Step (4) The receiving end uses the weighted incoherent signal subspace method ISSM to estimate the cosine value of the angle between different baseline vectors and the signal incident direction to obtain the azimuth estimation result; Specifically: (4-1) constitutes the baseline vector p i,j The received signal x after matched filtering of the i-th array element and the j-th array element m,i (k) and x m,j (k) Perform fast Fourier transform respectively and take the in-band sequence X of the unilateral spectrum m,i (k) and X m,j (k); Divide the frequency band into P sub-bands uniformly and construct the frequency domain model X for each sub-band m,i,j,p =[X m,i,p ,X m,j,p ] H , X m,i,p (k) and X m,j,p (k) are X m,i (k) and X m,j The p-th subband sequence of (k), p = 1,…,P, the superscript H indicates the conjugate transpose; (4-2) Calculate the covariance matrix of each subband sequence Among them, K p Indicates the number of sampling points in the p-th subband; Perform eigenvalue decomposition on the covariance matrix: Among them, Σ s,p Represents the larger of the two eigenvalues, and its corresponding eigenvector U s,p Constitute the signal subspace; Σ n,p Represents the smaller of the two eigenvalues, and its corresponding eigenvector U n,p Construct the noise subspace; According to the signal power P s,p =Σ s,p -Σ n,p and noise power P n,p =Σ n,p Get the subband signal-to-noise ratio SNR p =10·lg(P s,p / P n,p ), and then obtain the subband weight Among them, w and b are adjustable parameters; (4-3) Based on the incoherent signal subspace method ISSM in the broadband signal super-resolution spectrum theory, the spatial spectrum of the weighted ISSM method is defined in, θ represents the signal incident angle, d represents the length of the baseline vector, c represents the speed of sound, and f p Represents the center frequency of the pth subband, j represents an imaginary number; θ is traversed in the range of 0 to π to find the peak position of the spatial spectrum, and the signal incident angle corresponding to the peak is the azimuth estimation result, that is, the signal incident direction and the baseline vector p i,j The angle between the baseline vector and the signal incident direction is obtained by Step (5) The ultra-short baseline array at the receiving end estimates the unit vector p pointing from the receiving end to the transmitting end by means of parameter regression based on all the selected baseline vectors and their azimuth estimation results. s ; Step (6) outputs the unit vector estimate This is the final direction estimate.

2. The method for estimating direction of an ultra-short baseline based on an arbitrary formation according to claim 1, wherein: In step (4), all or part of the baseline vectors are selected for estimation.

3. The method for estimating direction of an ultra-short baseline based on an arbitrary formation according to claim 1, wherein: In step (5), the signal incident direction -p s and the baseline vector p i,j The cosine of the angle is expressed as Among them, cosθ s,i,j Indicates -p s and p i,j The cosine of the angle, d i,j Indicates the baseline length; p s and cosθ s,i,j For a linear relationship, the position estimates of multiple baselines are used to calculate p based on the parametric regression method. s , the optimal estimate is the unit vector estimate Among them, Θ and S are d i,j cosθ s,i,j and p i,j The constructed matrix, ρ(·) represents the loss function, and ||·||2 represents the two-norm.

4. The method for estimating direction of an ultra-short baseline based on an arbitrary formation according to claim 3, wherein: In step (5), if the ultra-short baseline array is a stereo array, the specific process of the parameter regression method is as follows: (5-a) Initialize the weight matrix W as the identity matrix and transform the problem into weighted least squares according to the iterative reweighted least squares method, that is, (5-b) Initialize the Lagrangian factor λ = 0; (5-c) is converted into The constraint solution is converted to an unconstrained solution, that is, the Lagrangian function The numerical solution of λ is solved iteratively by the gradient descent method; according to renew I is the identity matrix; according to Update λ, where μ λ is the adjustable step size, t is the number of iterations; (5-d) If The difference between the square of the modulus and 1 is less than the threshold, or the number of iterations reaches the upper limit, Normalize, execute (5-e), otherwise return to step (5-c); (5-e) Update the weight of each baseline vector Where ρ′(·) represents the effect of ρ(·) on p s The derivative of i,j Construct the weight matrix W in sequence, which is a diagonal matrix; determine whether the number of iterations has reached the upper limit. If so, the estimation is completed and the unit vector estimate is obtained. Otherwise, execute (5-b).

5. The method for estimating direction of an ultra-short baseline based on an arbitrary formation according to claim 3, wherein: In step (5), if the ultra-short baseline array is a planar array, the specific process of the parameter regression method is as follows: (5-A) Initialize the weight matrix W as the identity matrix and transform the problem into weighted least squares according to the iterative reweighted least squares method, that is, (5-B) Initialize the adjustment factor 0<δ<<1; (5-C) According to the weighted least squares formula, update (5-D) Update the weight of each baseline Use w i,j Construct the weight matrix W in sequence. The weight matrix W is a diagonal matrix. Determine whether the number of iterations has reached the upper limit. If so, execute (5-E). Otherwise, continue to execute (5-C). (5-E) output by (5-D) Plane coordinates of Re-update when when

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