A sparse linear array optimization design method based on scene decoupling D3QN

Abstract

The application discloses a sparse linear array optimization design method based on scene decoupling D3QN and belongs to the technical field of cross artificial intelligence and marine science. The application firstly constructs a scene decoupling D3QN network, an initial state space and an action space; then gradually optimizes array elements, constructs a structure reward at each step by using a non-negative differential common array coverage and a non-negative differential common array continuous segment length; obtains a round end reward by weighted sum of a normalized Ziv-Zikai bound, mutual coupling leakage, the non-negative differential common array continuous segment length and a peak side lobe level, and obtains a round total reward by sum of the total structure reward and the round end reward; after training, greedy array generation is performed on GSNR and alpha scene grids, constraint screening and multi-index sorting are performed on candidate arrays, and an optimal sparse linear array is output. The method has good direction finding performance under the influence of pulse noise, low generalized signal-to-noise ratio and array element mutual coupling, and can effectively suppress the interference of scene change on structure learning.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary technology of artificial intelligence and marine technology, specifically involving a sparse linear array optimization design method based on scene decoupling D3QN. Background Technology

[0002] In shallow sea environments, marine biological activity, port operations, ship radiation, and anthropogenic sound sources generate non-Gaussian noise with significant impulse characteristics. Under low generalized signal-to-noise ratio and impulse noise conditions, the impulse component in the received signal can disrupt the stability of traditional second-order statistics, degrading the performance of array processing and direction-of-arrival estimation methods based on Gaussian noise assumptions. Furthermore, small underwater unmanned vehicles typically face strict limitations on array size, element count, and hardware cost, making it difficult to improve direction-finding performance simply by increasing the number of elements. Sparse arrays can expand the equivalent aperture and increase degrees of freedom within a limited element count, but the non-uniform arrangement of element positions increases the difficulty of sidelobe control and array search. Traditional nested arrays, coprime arrays, and other structured sparse arrays usually have fixed geometric forms, with element positions determined by analytical rules, making it difficult to adjust for specific underwater acoustic environments and element coupling conditions.

[0003] Deep reinforcement learning offers a new approach to discrete array element location selection. D3QN, combining a Dueling network structure and the Double DQN objective value calculation method, can suppress... This approach overestimates and enhances the ability to represent state values, making it suitable for stepwise element location construction problems. However, traditional D3QN typically separates array structure information from GSNR and other parameters. When environmental conditions are input into the same value network, the value function simultaneously fits the array geometry and scene difficulty. Differences in reward scale and estimation variance across different scenes can easily contaminate array structure learning due to scene difficulty, leading to convergence instability and biased array selection during training. Furthermore, existing array optimization methods often separate array structure from mutual coupling effects during array design, neglecting issues such as steering vector distortion, sidelobe rise, and increased direction-finding error caused by variations in element spacing. Using only peak sidelobe level or the length of the non-negative differential co-array continuous segment as the optimization objective makes it difficult to simultaneously consider statistical detection performance, angular resolution, and mutual coupling suppression capabilities.

[0004] Therefore, under the combined influence of limited array element quantity and array aperture, low generalized signal-to-noise ratio, impulse noise, and array element mutual coupling, how to construct a reinforcement learning model that can distinguish the value of array structure from the value of environmental scene, and achieve global optimization of sparse linear array, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] This invention addresses the challenges of existing sparse linear array optimization methods under conditions of simultaneous limitations in the number of array elements and array aperture, the combined effects of low generalized signal-to-noise ratio, impulse noise, and element coupling, as well as the problems of unstable training convergence and array selection bias caused by the mixed modeling of array structure information and environmental scene information in traditional D3QN. To address these issues, a sparse linear array optimization design method based on scene-decoupled D3QN is proposed for shallow sea environments. This method first constructs a scene-decoupled D3QN network, its state and action spaces; then, it progressively optimizes... Each array element, in each step, constructs a structural reward based on the non-negative differential co-array coverage and the length of the non-negative differential co-array continuous segment, and applies... The total structural reward is obtained by summing the step-by-step structural rewards; the normalized reward is then calculated. The round-end reward is obtained by weighted summation of boundary, normalized cross-coupling leakage, normalized non-negative differential co-matrix continuous segment length, and normalized peak sidelobe level. The round-end reward is obtained by summing the total structural reward and the round-end reward. After training, ... , A greedy array is generated on the scene grid, and candidate arrays are constrained, filtered, and sorted by multiple indicators to output the optimal sparse linear array.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A sparse linear array optimization design method based on scene decoupling D3QN, using an array element number of The non-uniform linear hydrophone array, to An array aperture is constructed using candidate locations, denoted as the set of candidate locations. ,and Candidate position number, candidate position spacing , For the signal wavelength, in 0 and Two array elements are fixed at one location, and the rest... Individuals from candidate positions The preferred embodiment is characterized by the following steps:

[0008] Step 1: Construct a scene-decoupled D3QN network, which includes scene-independent structure branches and scene-dependent residual branches; set the total number of training rounds to [number missing]. The total number of moves per round is ;

[0009] Step Two: For any round Define the normalized generalized signal-to-noise ratio and normalization Distribution stability index ;definition dimensional initial array state space ,in , , Indicates the initial candidate position Not occupied by array elements Indicates the initial candidate position It has already been occupied by the array element, and ;definition Dimensional Action Space ,in Number the action and , ,action Indicates the candidate position Place the array elements at the location;

[0010] Step 3: When the number of steps... At that time, traverse the initial array state space. To satisfy all of Store the set of action numbers from step 1. Define the set of possible actions in step 1. ;

[0011] Step 4: Calculate the set of possible actions from Step 1 Each action Total action value, using Strategies based on probability exist Randomly select an action, with probability Select the action with the highest total action value and denote it as... ; Perform actions and update the array state space. ,in for A dimensional vector, which, excluding actions The element at the corresponding value is 1, and all other elements are 0;

[0012] Step 5: Calculate the structural reward from Step 1 ,in This is the global reward scaling factor. To reward structural weights, For structural mass function;

[0013] Step Six: Repeat steps three through five until the number of steps reaches a certain threshold. Gradually increase from 1 to Afterwards, according to the first Step array state space Obtain a non-uniform linear hydrophone array ;

[0014] Step 7: Compute the array of boundary Mutual coupling leakage Length of continuous segments in nonnegative difference comatrix and peak sidelobe level ; Define normalization boundary Normalized mutual coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level ;

[0015] Step 8: [Regarding...] The total structural reward is obtained by summing the step-by-step structural rewards. ; for normalization boundary Normalized mutual coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level Weighted summation yields end-of-round reward ; Rewards for overall structure End-of-round rewards Summing yields the total reward for each round. ;

[0016] Step Nine: Repeat steps Six through Eight. After the scene decoupling D3QN network training is completed, based on the trained network and the generalized signal-to-noise ratio (GSNR) and... Distribution stability index A greedy array is generated on the constructed scene grid. Candidate arrays are constrained, filtered, and sorted by multiple indicators to output the optimal sparse linear array.

[0017] Furthermore, the specific expression for the normalized generalized signal-to-noise ratio is as follows: ,in The maximum generalized signal-to-noise ratio for the scene. The minimum generalized signal-to-noise ratio for the scene. For the first The generalized signal-to-noise ratio for each round; the normalization The specific expression for the distribution stability index is as follows: ,in For the largest scene Distribution stability index Minimum for the scene Distribution stability index For the first rounds Distribution stability index.

[0018] Furthermore, the first step of the structural reward In and The specific expression is obtained through the following steps:

[0019] According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the set of non-negative difference co-arrays from step 1. ,statistics Total number of elements and define The longest continuous segment length is the length of the continuous segment of the non-negative difference co-matrix in step 1. Define the non-negative difference coverage in step 1. Define the length of the continuous segment of the normalized nonnegative difference comatrix in step 1. ,at this time ,in , These are the weighting coefficients for the normalized nonnegative difference comatrix continuous segment length term and the nonnegative difference coverage term, respectively. Similarly, it can be based on the initial array state space. Repeat the above steps to obtain .

[0020] Furthermore, the aforementioned The specific expression for the boundary is ,in The angular interval between the two incoming wave directions. Indicates the angular interval as The prior amplitude factor of the angle at time, For a given angular interval The probability of detection errors at that time;

[0021] The specific expression for the mutual coupling leakage is: ,in They are mutually coupled matrices. Represents the mutual coupling matrix A diagonal matrix consisting of the main diagonal elements. Denotes the Frobenius norm;

[0022] The length of the continuous segment of the non-negative difference comatrix is ​​determined by the following specific steps:

[0023] According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the nth... Step non-negative difference comatrix set ,definition The longest continuous segment length is the th Length of continuous segment of nonnegative difference comatrix ;

[0024] The specific expression for the peak sidelobe level is as follows: ,in Indicates the side lobe region. Indicates the main lobe region. For pattern functions, This represents the maximum response within the sidelobe region, i.e., the highest sidelobe level. This represents the maximum response within the main lobe region, i.e., the peak level of the main lobe.

[0025] Furthermore, the normalization The specific expression for the boundary is ,in For comparison arrays in the same and Under the conditions The boundary value is the average value, and the comparison array refers to the array with a number of array elements. And the array aperture is Nested sparse linear arrays obtained using a fixed analytical method under certain conditions. and coprime sparse linear array , For array of Boundary logarithmic value, coefficient As a sensitivity modulator, It is the hyperbolic tangent function;

[0026] The specific expression for the normalized cross-coupling leakage is as follows: ,in This is a truncation function;

[0027] The specific expression for the length of the continuous segment of the normalized nonnegative difference coma is as follows: ;

[0028] The specific expression for the normalized peak sidelobe level is as follows: .

[0029] Furthermore, the specific expression for the overall structural reward is as follows: The specific expression for the end-of-round reward is as follows: ,in , , , Normalization The weighting coefficients for boundary, normalized mutual coupling leakage, normalized non-negative differential co-array continuous segment length, and normalized peak sidelobe level, and The specific expression for the total reward of the round is as follows: .

[0030] Furthermore, the mutual coupling matrix adopts a bandwidth of of The dimensional banded Toeplitz mutual coupling matrix, its th Line 1 The elements of the column are as follows:

[0031]

[0032] in, Number the array elements and , and The first The candidate position number corresponding to each array element. For the first Between individual array elements Spacing in units This represents the maximum spacing between array elements where mutual coupling occurs. , The spacing between array elements is The basic mutual coupling strength at time, The exponential decay factor of the mutual coupling strength;

[0033] The specific expression for the pattern function is as follows: ,in For matching weight vectors and Main beam pointing angle, superscript This indicates the conjugate transpose. The scanning angle and ,

[0034] For the guide vector, where For the first The candidate position number corresponding to each array element.

[0035] Compared with the prior art, the present invention, employing the above technical solution, has the following beneficial effects:

[0036] 1. To address the limitations of array size and element count in small underwater unmanned vehicles, this invention employs an array element count of... Non-uniform hydrophone array, with a frequency of 0~35 The array aperture is constructed using discrete candidate locations, with the candidate location spacing... , For the signal wavelength, two array elements are fixed at candidate positions 0 and 35 at the beginning and end, and the remaining 10 array elements are selected from candidate positions 1 to 34, taking into account array size, hardware cost and direction finding performance.

[0037] 2. In view of the problem that the geometric structure of traditional nested arrays and coprime arrays is fixed and difficult to adapt to specific underwater acoustic environments and mutual coupling conditions, this invention does not rely on fixed analytical arrays. Instead, it constructs the selection of array element positions as a sequential constructive Markov decision process. Through reinforcement learning, it optimizes the array element arrangement in discrete candidate positions, thereby obtaining a non-uniform sparse linear array that is adapted to the current scene conditions and multi-index rewards.

[0038] 3. Regarding the traditional D3QN, which combines array structure information with GSNR, When environmental conditions are input into the same value network, the value function simultaneously fits the array geometry quality and scene difficulty. This invention constructs a scene-decoupled D3QN network, which decomposes action value into scene-independent structural branches and scene-dependent residual branches. The scene-independent structural branches focus on learning array geometry value, while the scene-dependent residual branches are responsible for absorbing scene difficulty, thereby suppressing the interference of scene difficulty on structural value learning.

[0039] 4. To address the issue of unstable training convergence caused by differences in reward scale and estimation variance across different scenarios, this invention calculates the structural reward at each step based on the changes in the length of the continuous segment of the normalized non-negative difference comatrix and the non-negative difference coverage, and further calculates the structural reward based on... The training process calculates four sub-rewards: boundary, peak sidelobe level, non-negative differential co-array continuity, and mutual coupling leakage, and then calculates the end-of-round reward. This hierarchical design of structural rewards and end-of-round rewards improves the stability of the training process and the consistency of array selection. Attached Figure Description

[0040] Figure 1 The overall flowchart of a sparse linear array optimization design method based on scene decoupling D3QN provided by the present invention is shown.

[0041] Figure 2 A schematic diagram of the scenario decoupling D3QN network architecture provided by the present invention.

[0042] Figure 3 This is a hydrophone array arrangement diagram of SD-D3QN sparse linear array, D3QN sparse linear array, DDQN sparse linear array, nested sparse linear array and coprime sparse linear array obtained by the array optimization design method of the present invention.

[0043] Figure 4 This is the spatial spectrum of the DOA estimation of the SD-D3QN sparse linear array obtained by the array optimization design method of this invention.

[0044] Figure 5 The RMSE of the SD-D3QN sparse linear array obtained by the array optimization design method of this invention and four contrasting sparse linear arrays varies. Change diagram.

[0045] Figure 6 The graph shows the RMSE of the SD-D3QN sparse linear array and four contrasting sparse linear arrays obtained by the array optimization design method of this invention as a function of GSNR.

[0046] Figure 7 The graph shows the RMSE of the SD-D3QN sparse linear array and four contrasting sparse linear arrays obtained by the array optimization design method of this invention as a function of the number of snapshots.

[0047] Figure 8 The diagram shows the angle measurement success rate of the SD-D3QN sparse linear array obtained by the array optimization design method of this invention and four comparative sparse linear arrays. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings:

[0049] Example 1: Figure 1 This invention provides an overall flowchart of a sparse linear array optimization design method based on scene decoupling D3QN in shallow sea environments. Firstly, this invention uses an array element count of... The non-uniform linear hydrophone array, to An array aperture is constructed using candidate locations, denoted as the set of candidate locations. ,and Candidate position number, candidate position spacing The half-wavelength is 3.75cm, and the signal frequency is... The array aperture is . between 0 and Two array elements are fixed at one location, and the rest... Individuals from candidate positions The best choice among them.

[0050] Under the above conditions, the specific implementation process is as follows:

[0051] Step 1: Construct a scene-decoupled D3QN network, which includes scene-independent structure branches and scene-dependent residual branches; set the total number of training rounds to [number missing]. The total number of moves per round is ;

[0052] For the specific architecture of the decoupled D3QN network in the scenario, please refer to [link / reference needed]. Figure 2 ;

[0053] Step Two: For any round Define the normalized generalized signal-to-noise ratio and normalization Distribution stability index ;definition dimensional initial array state space ,in , , Indicates the initial candidate position Not occupied by array elements Indicates the initial candidate position It has already been occupied by the array element, and ;definition Dimensional Action Space ,in Number the action and , ,action Indicates the candidate position Place the array elements at the location;

[0054] Step 3: When the number of steps... At that time, traverse the initial array state space. To satisfy all of Store the set of action numbers from step 1. Define the set of possible actions in step 1. ;

[0055] Step 4: Calculate the set of possible actions from Step 1 Each action Total action value, using Strategies based on probability exist Randomly select an action, with probability Select the action with the highest total action value and denote it as... ; Perform actions and update the array state space. ,in for A dimensional vector, which, excluding actions The element at the corresponding value is 1, and all other elements are 0;

[0056] Step 5: Calculate the structural reward from Step 1 ,in This is the global reward scaling factor. To reward structural weights, For structural mass function;

[0057] Step Six: Repeat steps three through five until the number of steps reaches a certain threshold. Gradually increase from 1 to Afterwards, according to the first Step array state space Obtain a non-uniform linear hydrophone array ;

[0058] Step 7: Compute the array of boundary Mutual coupling leakage Length of continuous segments in nonnegative difference comatrix and peak sidelobe level ; Define normalization boundary Normalized mutual coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level ;

[0059] Step 8: [Regarding...] The total structural reward is obtained by summing the step-by-step structural rewards. ; for normalization boundary Normalized mutual coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level Weighted summation yields end-of-round reward ; Rewards for overall structure End-of-round rewards Summing yields the total reward for each round. ;

[0060] Step Nine: Repeat steps Six through Eight. After the scene decoupling D3QN network training is completed, based on the trained network and the generalized signal-to-noise ratio (GSNR) and... Distribution stability index A greedy array is generated on the constructed scene grid. Candidate arrays are constrained, filtered, and sorted by multiple indicators to output the optimal sparse linear array.

[0061] Course learning strategies were used during network training. The learning strategy is only effective for the first 1200 rounds. It gradually increases the difficulty of the scenario within these rounds, with each round first calculating... Then according to and Random sampling, with the full range used for the last 800 rounds. , ; The strategy makes the first 1200 rounds The value gradually decreases from 1 to 0.05, and the specific formula is as follows: The last 800 rounds Keep it unchanged at 0.05;

[0062] and Discretization with step sizes of 0.1 and 0.01 respectively yields 101 possible values ​​for GSNR. There are 61 possible values, and the two can be combined to form a total of There are 6161 scene points, which together form a scene grid; based on the trained network, the GSNR and A greedy array generation is performed on the constructed scene mesh. For each scene point in the scene network, the GSNR of the current scene is calculated. Normalize, then start from the initial state (in the initial state, candidate positions are only 0 and 1). Starting with an action occupied by an array element, the set of possible actions is calculated based on the current spatial state of the array. For each action in the set, the array state space and normalized scene conditions are input into the trained network, and the total action value is calculated. The action with the highest total action value is selected, executed, an array element is placed at the corresponding position, and the spatial state of the array is updated. The above steps are repeated. Next, the total number of array elements reached This yields a complete array, which is the candidate array corresponding to the current scene; "greedy" means selecting the action with the highest total action value, instead of using the same approach as during training. The strategy involves random exploration;

[0063] 6161 scenarios will generate 6161 array results, but many of these results are identical, with multiple adjacent GSNRs and Scenes may all generate the same sparse array. Therefore, all results are deduplicated, retaining only the distinct candidate arrays. Assuming that 6161 scenes ultimately generate only 19 distinct candidate arrays, subsequent filtering and evaluation will only be performed on these 19 candidate arrays, instead of repeating the calculation 6161 times. Furthermore, to ensure that the performance of the found arrays is not biased towards any particular reward, the arrays are constrained during the filtering process. The constraints are as follows: , If any of the conditions are not met, the candidate array is directly eliminated. For each candidate array that passes the constraints, the total round reward is calculated across all 6161 scene points. Arrays are then sorted based on their average total round reward. If the average total round rewards are the same, they are further sorted according to the average length of the continuous segment of the non-negative difference co-array. The array is sorted by boundary, and the array with the first sort is taken as the optimal array, and the optimal sparse linear array is output.

[0064] The specific expression for the normalized generalized signal-to-noise ratio is as follows: ,in The maximum generalized signal-to-noise ratio for the scene. The minimum generalized signal-to-noise ratio for the scene. For the first The generalized signal-to-noise ratio for each round; the normalization The specific expression for the distribution stability index is as follows: ,in For the largest scene Distribution stability index Minimum for the scene Distribution stability index For the first rounds Distribution stability index.

[0065] The first step of the structural reward In and The specific expression is obtained through the following steps:

[0066] According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the set of non-negative difference co-arrays from step 1. ,statistics Total number of elements and define The longest continuous segment length is the length of the continuous segment of the non-negative difference co-matrix in step 1. Define the non-negative difference coverage in step 1. Define the length of the continuous segment of the normalized nonnegative difference comatrix in step 1. ,at this time ,in , These are the weighting coefficients for the normalized nonnegative difference comatrix continuous segment length term and the nonnegative difference coverage term, respectively. Similarly, it can be based on the initial array state space. Repeat the above steps to obtain .

[0067] The The specific expression for the boundary is ,in The angular interval between the two incoming wave directions. Indicates the angular interval as The prior amplitude factor of the angle at time, For a given angular interval The probability of detection errors at that time;

[0068] The boundary The derivation is as follows:

[0069] Construct a two-hypothesis testing problem, assuming the angular interval is... The two hypotheses to be distinguished are respectively , ,in and These are the signal components corresponding to two adjacent angles. They are mutually coupled matrices. As the guide vector, Let be the signal power. Define the signal difference between the two assumptions as . ,noise use Distributed impulse noise, represented using sub-Gaussian. , To and The positive mixture variable corresponding to the characteristic function of the distribution. For A complex isotropic noise vector has a radial density that satisfies ,in , This represents the 2-norm. In... Under the given conditions, the optimal detection statistic is the log-likelihood ratio. ,when At that time, the judgment was Therefore, given the angular interval The probability of detection error at that time is ,in This represents the conditional probability. To account for the prior distribution of the target angle, we define the angle prior amplitude factor. ,in Let be the cumulative distribution function in the direction of incoming waves. For the angle prior used in this scheme, Determined by the Beta distribution. Ultimately... Boundary The reason why the lower limit is set to 0 is... This represents the angular interval between two incoming wave directions; the angular interval cannot be negative. The upper limit of 2 is because the current code uses normalized prior information about the incoming wave direction. The maximum interval between the two directions is ,when hour ,so Once the value is greater than 2, the prior amplitude factor is already zero, and further integration will not increase the result.

[0070] The specific expression for the mutual coupling leakage is: ,in They are mutually coupled matrices. Represents the mutual coupling matrix A diagonal matrix consisting of the main diagonal elements. Denotes the Frobenius norm;

[0071] The length of the continuous segment of the non-negative difference comatrix is ​​determined by the following specific steps:

[0072] According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the nth... Step non-negative difference comatrix set ,definition The longest continuous segment length is the th Length of continuous segment of nonnegative difference comatrix ;

[0073] The specific expression for the peak sidelobe level is as follows: ,in Indicates the side lobe region. Indicates the main lobe region. For pattern functions, This represents the maximum response within the sidelobe region, i.e., the highest sidelobe level. This represents the maximum response within the main lobe region, i.e., the peak level of the main lobe.

[0074] The normalization The specific expression for the boundary is ,in For comparison arrays in the same and Under the conditions The boundary value is the average value, and the comparison array refers to the array with a number of array elements. And the array aperture is Nested sparse linear arrays obtained using a fixed analytical method under certain conditions. and coprime sparse linear array , For array of Boundary logarithmic value, coefficient As a sensitivity modulator, It is the hyperbolic tangent function;

[0075] The specific expression for the normalized cross-coupling leakage is as follows: ,in This is a truncation function;

[0076] The specific expression for the length of the continuous segment of the normalized nonnegative difference coma is as follows: ;

[0077] The specific expression for the normalized peak sidelobe level is as follows: .

[0078] The specific expression for the overall structural reward is as follows: The specific expression for the end-of-round reward is as follows: ,in Normalization The weighting coefficients for boundary, normalized mutual coupling leakage, normalized non-negative differential co-array continuous segment length, and normalized peak sidelobe level, and The specific expression for the total reward of the round is as follows: .

[0079] The mutual coupling matrix uses a bandwidth of of The dimensional banded Toeplitz mutual coupling matrix, its th Line 1 The elements of the column are as follows:

[0080]

[0081] in, Number the array elements and , and The first The candidate position number corresponding to each array element. For the first Between individual array elements Spacing in units This represents the maximum spacing between array elements where mutual coupling occurs. , The spacing between array elements is The basic mutual coupling strength at time, The exponential decay factor of the mutual coupling strength;

[0082] The specific expression for the pattern function is as follows: ,in For matching weight vectors and ° is the main beam pointing angle, superscript This indicates the conjugate transpose. The scanning angle and ,

[0083] For the guide vector, where For the first The candidate position number corresponding to each array element.

[0084] Furthermore, only the SD-D3QN sparse linear array was obtained using the array optimization design method presented in this paper. The D3QN sparse linear array, compared to the SD-D3QN sparse linear array, did not utilize scene decoupling. The DDQN sparse linear array, compared to the D3QN sparse linear array, lacked the Dueling structure. Nested sparse linear arrays and coprime sparse linear arrays were obtained using a fixed analytical method. Figure 3It can be seen that the five sparse linear array hydrophone arrays are [0,3,4,11,12,15,25,28,29,30,32,35].

[0085] [0,1,4,11,12,13,19,20,22,26,30,35]、[0,10,13,11,12,15,25,28,29,30,32,35]、

[0086] [0,1,2,3,7,11,15,19,23,27,31,35]、[0,5,8,10,15,16,20,24,25,30,32,35].

[0087] The second embodiment addresses the problem of impulse noise causing the failure of traditional second-order statistics in shallow sea environments. This invention employs the PHLOM matrix, Toeplitz reconstruction, and MUSIC peak search for direction-of-arrival estimation, reducing the impact of impulse noise on direction-finding performance. The geometric model of the sparse linear array is then presented, assuming there is... A separate far-field narrowband signal source When incident on the airborne sonar array of a small underwater unmanned vehicle, with the first element as a reference, then... The received signal of a sparse linear array, ignoring element coupling at all times, can be expressed as:

[0088]

[0089] in, The source vector; It is an array manifold matrix; express The corresponding guide vector; For additive Distributed impulse noise.

[0090] In actual arrays, mutual coupling effects exist between array elements, causing deviations between the ideal direction vector and the actual array response. To characterize this effect, a... 3D mutual coupling matrix Then, considering mutual coupling, the array received signal can be expressed as:

[0091]

[0092] in, This is the effective array manifold matrix after mutual coupling correction.

[0093] In an environment with mutually coupled impulse noise, the second-order statistics of the received signal do not exist, and the overall covariance matrix is... Since there is no mathematical definition, the PHLOM matrix is ​​used instead of the traditional covariance matrix. The PHLOM matrix has a first... Each element can be represented as:

[0094]

[0095] in , yes The Each element.

[0096] For complex values , operation Defined as:

[0097]

[0098] in Let be the order of the moment.

[0099] Therefore, the received signal The PHLOM can be represented as ,in The phase fraction low-order correlation matrix of the signal is given by the given information. For incoherent signals, It is a diagonal matrix; It is a scalar, based on the statistical properties of the signal and noise components in the received signal vector.

[0100] Through the By performing vectorization operations, we can deduce that:

[0101]

[0102] and

[0103] in for A vector of order 1, whose elements are matrices. The diagonal elements. yes A submatrix extracted from it, retaining only the continuous and uniform portion of the non-negative difference comatrix. The virtual array signal received in a PHLOM scenario. Find the signal received by a continuous, uniform segment of the virtual array element, where the length of the continuous, uniform segment is... The length of the continuous uniform segment The length of the aforementioned non-negative difference co-matrix continuous segment Consistent.

[0104] Then, the Toeplitz reconstruction method is used to reconstruct the rank, and the recovered data covariance matrix is ​​as follows:

[0105]

[0106] The Toeplitz reconstruction method was applied to obtain the rank-recovered data covariance matrix. Then, the DOA of the input signal is estimated using the MUSIC algorithm.

[0107] Figure 4 To illustrate the spatial spectrum of the DOA estimation for the SD-D3QN sparse linear array obtained using this optimized design method, five far-field narrowband sources were set up in the experiment. The source angles were randomly generated within the range of -60° to 60°, with a minimum interval of 10° between adjacent sources. The actual angles were -50.7°, -14.2°, 21.1°, 39.3°, and 59.3°. Figure 2 Vertical dashed lines are used for labeling; GSNR is fixed at -5dB. The search parameters were fixed at 1.5, the number of snapshots was fixed at 600, the MUSIC search range was -60° to 60°, the search step size was 0.1°, the relative amplitude threshold for peak detection was 0.02, and the minimum distance between adjacent peaks was 1°. For each true angle, the nearest peak within the search range was selected for matching. A matching error of less than 0.8° was considered a successful match for the source. When all five sources were successfully matched, the angle measurement of the five sources was considered successful. This experiment successfully detected five peaks, and all five sources were successfully matched. The detected peaks were -50.6°, -14.0°, 21.3°, 39.3°, and 59.3°, with errors not exceeding 0.2°. This indicates that under multiple source conditions, the sparse linear array obtained by this method has good DOA estimation performance and can effectively distinguish multiple incident signals in space.

[0108] The third embodiment: Figure 5 The RMSE of the SD-D3QN sparse linear array obtained by the optimized design method for this array, and four contrasting sparse linear arrays, varies. The variation graph shows that the GSNR was fixed at -5dB and the number of snapshots was fixed at 600. The horizontal axis is... Starting from 1.5, the value was increased in steps of 0.1 to 1.9, using 10 random seeds and conducting 1000 independent Monte Carlo experiments for each seed. The RMSE curve was obtained by averaging the results. This experiment also calculated the maximum and minimum RMSE values ​​for the five arrays, as well as the difference between the maximum and minimum values. The specific data are as follows:

[0109] SD-D3QN sparse linear array: , , ;

[0110] D3QN sparse linear array: , , ;

[0111] DDQN sparse linear array: , , ;

[0112] Nested sparse linear arrays: , , ;

[0113] Coprime sparse linear array: , , ;

[0114] Depend on Figure 5 And experimental data shows that the SD-D3QN sparse linear array is effective in all... The RMSE remains the lowest and most stable value across all ranges, with the difference between the maximum and minimum RMSE being only 0.0053. Meanwhile, the RMSE of the four contrasting sparse linear arrays varies with... The overall increase is slightly lower and there are fluctuations of varying degrees, which indicates that the optimized array obtained by this method has strong robustness under mutual coupling and moderate intensity impulse noise conditions.

[0115] Fourth example: Figure 6 The RMSE of the SD-D3QN sparse linear array and four contrasting sparse linear arrays obtained from the optimized design method of this array are shown in the GSNR graph. Experiments will be conducted on this array. The value was fixed at 1.5, the number of snapshots was fixed at 600, the x-axis was GSNR, starting from -10dB and increasing in steps of 2dB to 0dB. Ten random seeds were used, and each random seed underwent 1000 independent Monte Carlo experiments. The RMSE curve was obtained by averaging the results. Figure 6 It can be seen that when When the GSNR is 1.5, as the GSNR increases from -10dB to 0dB, the RMSE of all five arrays decreases significantly. The SD-D3QN sparse linear array maintains the lowest RMSE across all GSNR values, exhibiting the fastest RMSE decrease in the -10dB to -6dB GSNR range, reaching only 0.274° at -6dB. This indicates that the optimized array obtained using this method, compared to the other arrays, demonstrates the best estimation performance under conditions of mutual coupling, moderate-intensity impulse noise, and low generalized signal-to-noise ratio, exhibiting a more significant advantage and meeting the anti-interference requirements of new marine equipment such as small underwater unmanned vehicles in shallow sea environments.

[0116] Fifth example: Figure 7 The graph shows the RMSE variation with snapshot number for the SD-D3QN sparse linear array and four contrasting sparse linear arrays obtained from the optimized array design method. The experiment fixed the GSNR at -5dB. The value is fixed at 1.5, with the horizontal axis representing the number of snapshots, starting from 100 and increasing in increments of 100 to 600. Ten random seeds are used, and each seed is used to conduct 1000 independent Monte Carlo experiments. The RMSE curve is obtained by averaging the results. Figure 7 It can be seen that when When the frame count is 1.5, the RMSE of all five arrays decreases significantly as the number of snapshots increases from 100 to 600. However, with 100 snapshots, the RMSE of the SD-D3QN sparse linear array is slightly lower than that of the D3QN sparse linear array due to the limited available samples. The SD-D3QN sparse linear array maintains the lowest RMSE for all snapshot counts except 100, reaching only 0.345° at 400 snapshots. This indicates that the optimized array obtained by this method exhibits the best estimation performance compared to other arrays under conditions of mutual coupling, moderate impulse noise, and varying snapshot counts, demonstrating a more significant advantage and meeting the high sample utilization requirements of new marine equipment such as small underwater unmanned vehicles in shallow sea environments.

[0117] 6th embodiment: Figure 8 The success rate diagram of angle measurement for the SD-D3QN sparse linear array obtained by the optimized design method of this array is shown in the figure, compared with four contrasting sparse linear arrays. Two far-field narrowband sources were used in the experiment. The angular interval between these two sources, the angle of the first source. Between -30° and 30° Randomly generated within the range, the second source angle is GSNR is fixed at -5dB, and the number of snapshots is fixed at 600. The x-axis is fixed at 1.5, and the x-axis represents the angle interval, which is 1°, 1.5°, 2°, 2.5°, 3°, 4°, 5°, 6°, 7°, 8°, 9°, 10°, 11°, 12°, and 13°. If the error between any two paired angles exceeds 0.8°, the trial is considered a failure. Ten random seeds are used, and each random seed is used to conduct 1000 independent Monte Carlo experiments. The average is then taken to obtain the angle measurement success rate curve. Figure 8It can be seen that as the angle interval increases from 1° to 13°, the angle measurement success rate of all five arrays increases significantly, eventually approaching 100%. When the angle interval is 1°, the angle measurement success rate of all five arrays is close to 0. When the angle interval is 1.5°, the angle measurement success rate of the SD-D3QN sparse linear array is slightly lower than that of the DDQN sparse linear array. The SD-D3QN sparse linear array maintains the highest angle measurement success rate for all angle intervals except for the 1° to 1.5° range. Its angle measurement success rate increases the fastest in the 1.5° to 2.5° range, and reaches 98.3% when the angle interval is 2.5°. This indicates that the optimized array obtained by this method has the best estimation performance compared to the other arrays under conditions of mutual coupling and moderate-intensity impulse noise, with more obvious advantages, meeting the high stability requirements of new marine equipment such as small underwater unmanned vehicles in shallow sea environments.

[0118] Although some embodiments of the present invention have been shown and described, those skilled in the art will recognize that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and all such solutions fall within the scope of protection of the present invention.

Claims

1. A sparse linear array optimization design method based on scene decoupling D3QN, using an array element number of... The non-uniform linear hydrophone array, to An array aperture is constructed using candidate locations, denoted as the set of candidate locations. ,and Candidate position number, candidate position spacing , For the signal wavelength, in 0 and Two array elements are fixed at one location, and the rest... Individuals from candidate positions The selection is characterized by, The method includes the following steps: Step 1: Construct a scene-decoupled D3QN network, which includes scene-independent structure branches and scene-dependent residual branches; Set the total number of training rounds to [number]. The total number of moves per round is ; Step Two: For any round Define the normalized generalized signal-to-noise ratio and normalization Distribution stability index ;definition dimensional initial array state space ,in , , Indicates the initial candidate position Not occupied by array elements Indicates the initial candidate position It has already been occupied by the array element, and ;definition Action space ,in Number the action and , ,action Indicates the candidate position Place the array elements at the location; Step 3: When the number of steps... At that time, traverse the initial array state space. To satisfy all of Store the set of action numbers from step 1. Define the set of possible actions in step 1. ; Step 4: Calculate the set of possible actions from Step 1 Each action Total action value, using Strategies based on probability exist Randomly select an action, with probability Select the action with the highest total action value and denote it as... ; Perform actions and update the array state space. ,in for A dimensional vector, which, excluding actions The element at the corresponding value is 1, and all other elements are 0; Step 5: Calculate the structural reward from Step 1 ,in This is the global reward scaling factor. To reward structural weights, For structural mass function; Step Six: Repeat steps three through five until the number of steps reaches a certain threshold. Gradually increase from 1 to Afterwards, according to the first Step array state space Obtain a non-uniform linear hydrophone array ; Step 7: Compute the array of boundary Mutual coupling leakage Length of continuous segments in nonnegative difference comatrix and peak sidelobe level ; Define normalization boundary Normalized cross-coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level ; Step 8: [Regarding...] The total structural reward is obtained by summing the step-by-step structural rewards. ; for normalization boundary Normalized cross-coupling leakage Normalized nonnegative difference comatrix continuous segment length and normalized peak sidelobe level Weighted summation yields end-of-round reward ; Rewards for overall structure End-of-round rewards Summing yields the total reward for each round. ; Step Nine: Repeat steps Six through Eight. After the scene decoupling D3QN network training is completed, the trained network is then analyzed using the generalized signal-to-noise ratio (GSNR) and... Distribution stability index A greedy array is generated on the constructed scene grid. The candidate arrays are constrained, filtered, and sorted by multiple indicators to output the optimal sparse linear array.

2. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 1, characterized in that, The specific expression for the normalized generalized signal-to-noise ratio is as follows: ,in The maximum generalized signal-to-noise ratio for the scene. The minimum generalized signal-to-noise ratio for the scene. For the first The generalized signal-to-noise ratio for each round; the normalization The specific expression for the distribution stability index is as follows: ,in For the largest scene Distribution stability index Minimum for the scene Distribution stability index For the first rounds Distribution stability index.

3. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 1, characterized in that, The first step of the structural reward In and The specific expression is obtained through the following steps: According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the set of non-negative difference co-arrays from step 1. ,statistics Total number of elements and define The longest continuous segment length is the length of the continuous segment of the non-negative difference co-matrix in step 1. Define the non-negative difference coverage in step 1. Define the length of the continuous segment of the normalized nonnegative difference comatrix in step 1. ,at this time ,in , These are the weighting coefficients for the normalized nonnegative difference comatrix continuous segment length term and the nonnegative difference coverage term, respectively. ; Similarly, it can be based on the initial array state space Repeat the above steps to obtain .

4. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 1, characterized in that, The The specific expression for the boundary is ,in The angular interval between the two incoming wave directions. Indicates the angular interval as The prior amplitude factor of the angle at time, For a given angular interval The probability of detection errors at that time; The specific expression for the mutual coupling leakage is: ,in They are mutually coupled matrices. Represents the mutual coupling matrix A diagonal matrix consisting of the main diagonal elements. Denotes the Frobenius norm; The length of the continuous segment of the non-negative difference comatrix is ​​determined by the following specific steps: According to the Step array state space Extract all candidate position numbers occupied by array elements, calculate the non-negative difference between any two occupied candidate position numbers, and remove duplicates from all non-negative differences to obtain the nth... Step non-negative difference comatrix set ,definition The longest continuous segment length is the th Length of continuous segment of nonnegative difference comatrix ; The specific expression for the peak sidelobe level is as follows: ,in Indicates the side lobe region. Indicates the main lobe region. For pattern functions, This represents the maximum response within the sidelobe region, i.e., the highest sidelobe level. This represents the maximum response within the main lobe region, i.e., the peak level of the main lobe.

5. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 1, characterized in that, The normalization The specific expression for the boundary is ,in For comparison arrays in the same and Under the conditions The boundary value is the average value, and the comparison array refers to the array with a number of array elements. And the array aperture is Nested sparse linear arrays obtained using a fixed analytical method under certain conditions. and coprime sparse linear array , For array of Boundary logarithmic value, coefficient As a sensitivity modulator, It is the hyperbolic tangent function; The specific expression for the normalized cross-coupling leakage is as follows: ,in This is a truncation function; The specific expression for the length of the continuous segment of the normalized nonnegative difference coma is as follows: ; The specific expression for the normalized peak sidelobe level is as follows: .

6. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 1, characterized in that, The specific expression for the overall structural reward is as follows: The specific expression for the end-of-round reward is as follows: ,in , , , Normalization The weighting coefficients for boundary, normalized mutual coupling leakage, normalized non-negative differential co-array continuous segment length, and normalized peak sidelobe level, and The specific expression for the total reward of the round is as follows: .

7. The sparse linear array optimization design method based on scene decoupling D3QN as described in claim 4, characterized in that, The mutual coupling matrix uses a bandwidth of of The dimensional banded Toeplitz mutual coupling matrix, its th Line 1 The elements of the column are as follows: in, Number the array elements and , and The first The candidate position number corresponding to each array element. For the first Between individual array elements Spacing in units This represents the maximum spacing between array elements that allows for mutual coupling. , The spacing between array elements is The basic mutual coupling strength at time, The exponential decay factor of the mutual coupling strength; The specific expression for the pattern function is as follows: ,in For matching weight vectors and Main beam pointing angle, superscript This indicates the conjugate transpose. The scanning angle and , For the guide vector, where For the first The candidate position number corresponding to each array element.

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