An underwater multi-target direction estimation method based on improved adaptive matching pursuit

Abstract

The application discloses an underwater multi-target direction estimation method based on improved adaptive matching pursuit, and belongs to the technical field of array signal processing and underwater target direction estimation. The method steps are as follows: target signals are obtained through array acquisition, and complex processing is performed on the obtained target signal data; a spatial dictionary set used for improved adaptive matching pursuit is constructed based on target signal wave direction; adaptive search is performed on the constructed spatial dictionary set, and atom screening is completed according to the change of residual energy; the number of waves and sparse signals are estimated according to the complete wave direction angle set used when the spatial dictionary set is constructed and in combination with the index set determined by completing the atom screening, and the estimated spatial sparse signals are converted into target directions. The application solves the problem that the number of target waves and target wave directions cannot be adaptively and accurately estimated in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of array signal processing and underwater target direction estimation, and particularly relates to an underwater multi-target direction estimation method based on an improved adaptive matching pursuit. BACKGROUND

[0002] Underwater multi-target direction estimation is one of the core technologies in the fields of ocean exploration and underwater robot navigation. Accurate acquisition of the number and direction information of underwater targets can not only improve the performance of underwater communication, navigation and detection systems, but also has important significance for practical applications. However, the existing target direction estimation algorithms have the following limitations: traditional beamforming algorithms: it is difficult to simultaneously consider high resolution and high robustness; subspace-based algorithms: they rely on the pre-known number of targets and cannot effectively handle coherent signals; neural network-based algorithms: they have poor adaptability in different scenarios.

[0003] In recent years, with the development of compressed sensing theory, sparse recovery methods have gradually become an important means for high-precision target direction estimation. As a representative of sparse recovery algorithms, greedy algorithms have attracted widespread attention due to their low computational complexity and high reconstruction accuracy. However, traditional sparse recovery algorithms require pre-estimation of sparsity, which limits their application range. Although the adaptive matching pursuit algorithm (SAMP) eliminates the dependence on sparse degree estimation, it still has the following challenges in the problem of target direction estimation:

[0004] 1. Difficulty in selecting iteration step size: improper step size setting may introduce additional atoms and cause algorithm failure;

[0005] 2. Support set cardinality affects estimation effect: too large support set cardinality reduces the accuracy of least squares estimation and affects the sparse recovery effect;

[0006] 3. Termination condition is difficult to estimate: the prior dependence of the algorithm on noise energy limits its practicality.

[0007] To solve the above problems, the application proposes an underwater multi-target direction estimation method based on an improved adaptive matching pursuit algorithm, which optimizes the incoming wave signal processing to achieve high-precision and multi-target underwater direction estimation. This method aims to overcome the shortcomings of traditional algorithms and provide more reliable technical support for underwater target positioning. SUMMARY

[0008] The technical problem to be solved is:

[0009] In order to avoid the shortcomings of the prior art, the application provides an underwater multi-target direction estimation method based on improved adaptive matching pursuit, which realizes adaptive and accurate estimation of the number of incoming waves and the direction of incoming waves by screening atoms through a least square similarity criterion and referring to the energy change degree of adjacent residuals to determine the iteration termination.

[0010] The technical scheme of the application is as follows: an underwater multi-target direction estimation method based on improved adaptive matching pursuit, and the specific steps are as follows:

[0011] The target signal is acquired through an array, and the target signal data is complex processed;

[0012] An improved adaptive matching pursuit space dictionary set is constructed based on the direction of incoming waves of the target signal;

[0013] The constructed space dictionary set is adaptively searched, and atom screening is completed according to the change of residual energy;

[0014] The number of incoming waves and the sparse signal are estimated according to the complete incoming wave direction angle set used when the space dictionary set is constructed and the index set determined when the atom screening is completed, and the estimated space sparse signal is converted into the target direction.

[0015] The further technical scheme of the application is that the method for complex processing of the target signal data is that the real signal received by each array element of the array is expressed as x(t), and the Hilbert transform of the real signal x(t) is expressed as follows:

[0016]

[0017] In the formula, is a complex signal, which is the Hilbert transform result of x(t); τ represents an integral variable;

[0018] The result of the Hilbert transform of the real signal received by each array element of the array under the same snap is expressed by a vector y.

[0019] The further technical scheme of the application is that the construction method of the space dictionary set is as follows:

[0020] K real signals from K incoming wave directions are received by M array elements;

[0021] A complete incoming wave direction angle set is established based on the incoming wave direction of the real signal;

[0022] On the basis of the complete set of the wave direction angle, the first array element of the array is taken as a reference point, and a spatial dictionary set A is designed according to the array structure characteristics as follows:

[0023]

[0024] In the formula, j is an imaginary unit, f is a carrier frequency of the incoming wave signal, tau m (Theta n ) is a time delay of the signal from the angle theta n to the mth array element relative to the reference point, m=2,...,M, n=1,...,N.

[0025] A further technical scheme of the present application is that the coherent parameter needs to be initialized before the atomic screening, that is, the residual signal r0=y, the iteration number t=1, the stage number stage=1, and the index set The step length s=1, and the number of atomic screening L=1.

[0026] A further technical scheme of the present application is that the specific process of the atomic screening is as follows:

[0027] The inner product U of the spatial dictionary set A and the residual r t-1 is calculated.

[0028] The maximum value in U is selected, and the A sequence number j corresponding to the value is recorded as the potential index set J.

[0029] The index set and the candidate support set are updated.

[0030] The least square solution of the updated candidate support set to express the array received signal y is solved.

[0031] The first L maximum elements in the vector element value of the least square solution are selected, and the indexes corresponding to the elements are recorded as F.

[0032] The residual is updated.

[0033] According to the change of the residual energy, when the iteration number and the residual energy change meet the requirements, the atomic screening is completed, and the iteration is stopped.

[0034] A further technical scheme of the present application is that the calculation process of the atomic screening is as follows:

[0035] The inner product U of the spatial dictionary set A and the residual r t-1 is expressed as: u=abs(A T r t-1 ).

[0036] The index set is updated as Lambda t =Lambda t-1 U J.

[0037] The candidate support set is updated as A t = A t-1 ∪{a j},j∈J;

[0038] The least square solution expression is:

[0039] The residual error is updated as

[0040] Further technical solutions of the application are as follows:

[0041] If ||r new ||2≥||r t-1 ||2, stage is updated as stage+1, L is updated as stage*s, and the next iteration is returned;

[0042] If ||r new ||2<||r t-1 ||2, the index set Λ t is updated as F, and the residual error value change I t is recorded. t-1 ||2-||r new ||2; meanwhile, the multi-target direction estimation iteration termination discrimination is made: if the iteration number t is greater than or equal to 3, I t <0.7*I t-2 and I t-1 <0.7*I t-2 are satisfied simultaneously, the atomic screening is completed, and the iteration is stopped; otherwise, r t is updated as r new , t is updated as t+1, and the iteration is continued.

[0043] Further technical solutions of the application are as follows: the number of incoming waves K is estimated as the dimension of the column vector .

[0044] Further technical solutions of the application are as follows: the direction of the incoming wave of the target signal is estimated as the angle obtained by indexing the pre-constructed complete incoming wave direction angle set Θ=[θ1,θ2,…,θ N ] according to the element values in the index set Λ t-2 .

[0045] An underwater multi-target direction estimation system based on an improved adaptive matching pursuit includes an array sensor, a signal complex processing module, an atomic screening module and an estimation module.

[0046] The real signal of the target signal is acquired through the array sensor.

[0047] convert the real signal into a complex signal through a signal complex processing module;

[0048] complete atom screening through an atom screening module, and complete atom screening according to the change of residual energy;

[0049] complete estimation of the number of incoming waves and sparse signals through an estimation module, and convert the estimated spatial sparse signal into a target direction.

[0050] Beneficial effects

[0051] The present application has the following beneficial effects: the algorithm proposed in the present application converts the target direction estimation problem into a sparse signal reconstruction problem by establishing a spatial sparse wave direction estimation model, breaks through the limitation of array aperture, and realizes higher resolution direction estimation. The specific advantages are as follows:

[0052] Improved iteration step selection: by analyzing the specific characteristics of the wave direction estimation problem, a safer iteration step selection scheme is proposed, which effectively solves the problem of step selection difficulty in the classic adaptive matching pursuit algorithm, and improves the robustness and applicability of the algorithm.

[0053] Optimize the base of the potential index set: by reasonably reducing the base of the potential index set, the problem of too many outliers caused by too large support set affecting the least square estimation effect is solved, thereby improving the accuracy and robustness of wave direction estimation.

[0054] Improved iteration termination condition: based on the observation of the ratio of the residual change of the adjacent two iterations, an iteration termination condition based on the change of residual energy is proposed, which overcomes the dependence of the classic algorithm on noise energy estimation, and enhances the applicability of the algorithm in complex noise environment.

[0055] In addition, the improved algorithm proposed in the present application breaks through the limitation of the number of snapshots, and can adaptively realize high-precision estimation of the number and direction of targets even in the case of limited snapshots or single snapshot. This advantage makes the algorithm have wider applicability and higher reliability in practical application. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 is a flowchart of the present application;

[0057] Figure 2 is a simulation test result graph of the present application example when the signal-to-noise ratio is 20dB;

[0058] Figure 3 is a simulation test result graph of the present application example when the signal-to-noise ratio is 10dB;

[0059] Figure 4A simulation test result graph of the present application example at a signal-to-noise ratio of 0 dB. DETAILED DESCRIPTION

[0060] The embodiments described below with reference to the drawings are exemplary and are intended to explain the present application, and cannot be understood as a limitation of the present application.

[0061] The existing greedy algorithm is a mature algorithm in the theory of compressed sensing, and the basic idea is to use the sparse representation of a signal in a redundant dictionary, to gradually select the atom that best matches the current signal residual from the dictionary through iteration, and to update the residual until the accuracy requirement is met. Since the target incoming wave direction has sparsity in the spatial domain, here we will use the matching pursuit algorithm to adaptively estimate the number of incoming waves and the incoming wave direction by constructing a spatial sparse dictionary.

[0062] Based on the existing underwater multi-target bearing estimation, there is often a problem that the number of target incoming waves and the direction of target incoming waves cannot be adaptively and accurately estimated, the present application provides an underwater multi-target bearing estimation method based on improved adaptive matching pursuit, as shown in Figure 1 The specific steps are as follows:

[0063] Step 1: complex processing of the target signal data collected by the array;

[0064] In this embodiment, it is assumed that the water depth in the experimental conditions is 100 m, the depths of the transmitting transducers are 20 m, 30 m and 40 m respectively, the 10-element uniform linear array carried by the underwater vehicle is at 30 m below the sea level, the horizontal distance between the transmitting transducer and the receiving array is 1 km, the incoming wave directions are -70°, -15° and 34° respectively, the simulation signal is a single-frequency narrowband signal with a carrier frequency f0=3 kHz, the inter-element spacing d of the receiving array is half the wavelength, and the sound speed is c=1500 m / s. The real signal received by each array element is represented as x(t), and the real signal x(t) is converted into a complex signal

[0065]

[0066] The observation vector obtained after converting the real signals received by each array element under the same snapshot into a complex signal is represented as y;

[0067] Step 2: constructing a spatial dictionary set used by the improved adaptive matching pursuit algorithm;

[0068] When K single-frequency narrowband signals are incident on the M-element array from directions At the same time, considering that the possible incoming wave direction of the signal is limited, a complete incoming wave direction angle set Θ=[θ1, θ2, …, θ N ] can be obtained by using the exhaustive method, so that the signal incident direction A small subset of the set is constructed.

[0069] In this embodiment, the whole spatial domain from -90° to 90° is equally divided into N grids, then the spatial domain can be sampled with an angle interval of 1° and a complete set of Θ C = [-90°, -89°, …, 90°] is constructed. And a spatial domain dictionary set A shown in the following formula is constructed according to the center frequency of the incoming wave signal and the array structure;

[0070]

[0071] Step 3: initialization including algorithm-related parameters such as residual signal, iteration number, step size, stage number and index set;

[0072] Initialize algorithm-related parameters: residual signal r0=y, iteration number t=1, stage number stage=1, index set Step size s=1, number of atom screening L=1;

[0073] Step 4: through the invented algorithm, the dictionary set is adaptively searched, and atom screening is completed according to the change of residual energy;

[0074] Step 4.1: calculate the correlation coefficient of each column vector in the spatial domain dictionary set A and the residual r t-1 , formula as follows:

[0075] u=abs(A T r t-1 ) (3)

[0076] Step 4.2: take the largest 1 value in u(i), and record the sequence number j of this value corresponding to A as the potential index set J;

[0077] Step 4.3: update the index set and the candidate support set respectively, formula as follows:

[0078] Λ t =Λ t-1 ∪J (4)

[0079] A t =A t-1 ∪{a j},j∈J (5)

[0080] Where a j represents the jth column of matrix A.

[0081] Step 4.4: solve the least square solution of matrix A t to express the array received signal y, formula as follows:

[0082]

[0083] Step 4.5: From column vector The values ​​of each element Select the element with the largest value in the first L items, and record the corresponding index as F; and update the residual by the following formula

[0084]

[0085] Step 4.6: Observe the changes in residual energy and make the following judgments:

[0086] If at this time ‖r new ‖2≥‖r t-1 ‖2, then update stage = stage + 1, L = stage * s, and return to the next iteration;

[0087] If at this time || r new ||2<||r t-1 ||2, then update the index set Λ t =F, and record the change in residual value I t =||r t-1 ||2-||r new ||2, at the same time, make the multi-target direction estimation iteration termination judgment, if the number of iterations t≥3, I t <0.7*I t-2 with I t-1 <0.7*I t-2 If both are satisfied, the atomic screening is completed, the iteration is stopped, and the fifth step is entered. Otherwise, take r t =r new , t=t+1, continue iteration;

[0088] Step 5: The number of incoming waves K is estimated as: column vector The direction of arrival of each target is estimated as follows: the pre-constructed complete set of angles of the direction of arrival Θ=[θ1,θ2,…,θ N ]According to the index set Λ t-2 The angle obtained by indexing the element values ​​in , for example: the direction of the incoming wave of the i-th target (i = 1, 2, ..., K) is estimated to be where Λ t-2 (i) represents the index set Λ t-2 The value of the i-th element in .

[0089] Reference Figures 2-4As shown in the figure, the analysis results of the experimental data when the signal-to-noise ratio is 20dB, 10dB and 0dB are respectively shown, and the performance of the underwater multi-target direction estimation method based on improved adaptive matching pursuit proposed by the present invention is compared with the classic MUSIC subspace direction estimation method. It can be seen from the experimental result figure that when the MUSIC algorithm estimates the target direction of the coherent signal source, multiple pseudo peaks appear, and the spectrum peak is not sharp enough, making it almost impossible to distinguish the direction of arrival of the source. The method of the present invention can accurately estimate the direction of arrival of the three sources under different signal-to-noise ratios, and successfully realizes the direction of arrival estimation of the coherent signal source. Its advantage is that the direction of arrival estimation method based on compressed sensing does not require eigendecomposition of the data covariance matrix, and thus has a natural decoherence ability, overcoming the deficiency of the subspace algorithm that cannot estimate the coherent source. In addition, in this experiment, the algorithm proposed by the present invention achieves accurate estimation of the direction of arrival using only single snapshot data, proving that the algorithm has a low demand for sampling information and can reduce data storage and computing costs.

[0090] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A method for underwater multi-target position estimation based on improved adaptive matching pursuit, characterized in that The specific steps are as follows: Obtain target signals through array acquisition, and perform complex processing on the acquired target signal data; Based on the incoming direction of the target signal, a spatial dictionary set for improving adaptive matching pursuit is constructed; An adaptive search is performed on the constructed spatial domain dictionary set, and atom screening is completed according to the change of residual energy. The calculation process of the atom screening is as follows: The spatial domain dictionary set and residuals The inner product U expression is: ; The index collection is updated to ; The candidate support set is updated to ; The least squares solution expression is: ; The residual is updated as ; The specific process of judging based on the change of residual energy is as follows: like , then update , , and return to enter the next iteration; like , then update the index set , and record the change in residual value ; At the same time, make the multi-target position estimation iteration termination judgment: if the number of iterations 、 and If both conditions are met, the atomic screening is completed and the iteration is stopped; otherwise, , , continue to iterate; According to the complete set of incoming wave direction angles used when constructing the spatial dictionary set, combined with the index set determined by completing the atomic screening, the number of incoming waves and sparse signals are estimated, and the estimated spatial sparse signals are converted into target orientations.

2. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 1, characterized in that: The method for complexifying the target signal data is to express the real number signal received by each array element as , the real signal Perform Hilbert transform, the expression is as follows: Where, is a complex signal, Hilbert transform result of ; τ represents the integral variable; The result of Hilbert transform of the real signal received by each array element in the same snapshot is expressed as vector To express.

3. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 2, characterized in that: The method for constructing the spatial domain dictionary set is: K real-number signals from K incoming wave directions are received through M array elements; Based on the arrival direction of the real signal, a complete arrival direction angle set is established; Based on the complete set of incoming wave direction angles, the first element of the array is used as a reference point, and the spatial domain dictionary set is designed according to the array structure characteristics. as follows: (2) Where, is the imaginary unit, is the carrier frequency of the incoming signal, The signal angle When incident, it reaches The time delay of the array element relative to the reference point is .

4. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 3, characterized in that: Before the atomic screening, the coherence parameters need to be initialized, that is, the residual signal , number of iterations , number of stages , index set , step length , number of atoms screened .

5. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 4, characterized in that: The specific process of the atomic screening is: Compute the spatial domain dictionary set and residuals The inner product U; Select the largest value from U and assign this value to Serial number Recorded as potential index set ; Update the index set and candidate support set; Solve the updated candidate support set expression array receiving signal The least squares solution of ; Select the first element from the vector of least squares solutions. The element with the largest item value has its corresponding index recorded as ; Update residuals; The change in residual energy is judged. When the number of iterations and the change in residual energy meet the requirements, the atom screening is completed and the iteration is stopped.

6. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 5, characterized in that: The number of incoming waves Estimated as: column vector The dimension of .

7. The underwater multi-target position estimation method based on improved adaptive matching pursuit according to claim 6, characterized in that: The target signal's direction of arrival is estimated by: By index set The angle obtained by indexing the element values ​​in .

8. An underwater multi-target position estimation system based on improved adaptive matching pursuit, used to implement the underwater multi-target position estimation method based on improved adaptive matching pursuit according to any one of claims 1 to 7; characterized in that: It includes array sensor, signal complex processing module, atom screening module and estimation module; Acquire a real signal of a target signal through an array sensor; Converting the real signal into a complex signal through a signal complexification processing module; The spatial domain dictionary set is adaptively searched through the atom screening module, and atom screening is completed according to the change of residual energy. The calculation process of the atom screening is as follows: The spatial domain dictionary set and residuals The inner product U expression is: ; The index collection is updated to ; The candidate support set is updated to ; The least squares solution expression is: ; The residual is updated as ; The specific process of judging based on the change of residual energy is as follows: like , then update , , and return to enter the next iteration; like , then update the index set , and record the change in residual value ; At the same time, make the multi-target direction estimation iteration termination judgment: if the number of iterations 、 and If both conditions are met, the atomic screening is completed and the iteration is stopped; otherwise, , , continue to iterate; The estimation module is used to estimate the number of incoming waves and sparse signals, and convert the estimated spatial sparse signals into target directions.

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