Method and system for accurate estimation of delay vector of distortion trailing array array

Abstract

The application discloses a distortion towed array array delay vector accurate estimation method and system, comprising: a line spectrum-based inter-element phase difference weighted least square delay difference estimation method, rough estimation of inter-element delay difference is obtained; taking the rough estimation of inter-element delay difference as an observation sequence, based on the characteristics that the inter-element delay difference changes continuously and slowly in time and space dimensions, a space-time two-dimensional hidden Markov model is constructed; the space-time two-dimensional hidden Markov model is solved, the state sequence corresponding to the maximum posterior probability is calculated, and the state sequence is mapped into a physical delay value, so that the accurate estimation of the array delay vector is obtained. The application fully utilizes the continuous and slow change characteristics of the inter-element delay difference of the multi-line spectrum component of the ship radiation noise in time and space dimensions, carries out space-time-frequency joint processing on the inter-element delay difference of the line spectrum, and significantly improves the estimation accuracy of the distortion towed array array delay vector under the condition that the line spectrum is less and the signal-to-noise ratio is low.

Description

Technical Field

[0001] This invention belongs to the field of data-driven array signal processing technology, specifically relating to a method and system for accurate estimation of time delay vector of distorted towed array, which is particularly suitable for application scenarios of high-fidelity reconstruction of ship radiated noise signals based on data received from towed linear arrays. Background Technology

[0002] Beamforming-based signal enhancement is a key issue in array signal processing, playing a crucial role in feature extraction and target recognition. In passive sonar systems, a significant challenge is extracting enhanced ship-radiated noise signals from received data from hydrophone arrays. This typically requires a large aperture for accurate localization and high array gain. This large aperture is usually achieved by towing a hydrophone array along a nominal straight line behind a towed platform. However, due to unavoidable ocean currents, internal waves, and the tactical maneuvers of towed platforms, the array often deforms or twists, leading to time delay mismatches in beamforming-based signal reconstruction and severely degrading signal enhancement performance.

[0003] A study on the accurate array delay vector estimation of distorted towed hydrophone arrays presents an intuitive approach: installing compasses and depth sensors at several points within the towed array to provide horizontal and vertical information on the local lateral displacement of the array, respectively. While this method directly obtains the array shape, the accuracy and update rate of these auxiliary sensors are limited, making it difficult to accurately estimate the array shape in real time. A generalized cross-correlation estimator, consisting of a pair of pre-filters and a cross-correlator, determines the delay difference by locating the peak value of the cross-correlator output. Notably, large-aperture towed arrays primarily focus on weak targets. However, under low signal-to-noise ratio conditions, the correlation between the broadband components of ship radiated noise received by different hydrophones decreases significantly, severely degrading the delay difference estimation performance of the generalized cross-correlation method.

[0004] Line spectrum components generated by the unavoidable vibrations of mechanical equipment such as diesel generators and air conditioning systems are a very important and useful component of ship radiated noise. Typically, the power of a line spectrum component is several to tens of decibels higher than the power of its neighboring continuous spectrum, making it easy to detect and identify. The phase of these relatively strong line spectrum components contains time delay information from the source to the hydrophone; therefore, these phases can be used to estimate the time delay difference of radiated noise signals received by different hydrophones. For example, a time delay difference estimation algorithm can be used, employing a weighted least squares approach to the phase difference of unambiguous low-frequency line spectra, weighted by a combination of line spectrum frequency and signal-to-noise ratio. However, due to the significant decrease in the source level of ship radiated noise caused by the development of vibration reduction and noise reduction technologies, the requirements of the above algorithms for obtaining accurate estimates of array time delay vectors regarding the number of radiated noise line spectrum components and the signal-to-noise ratio cannot be met.

[0005] In summary, under the condition of array model mismatch, obtaining enhanced array delay vector estimation by measuring the phase difference of ship radiated noise line spectrum components remains an unsolved problem in signal reconstruction based on beamforming, especially when the number of ship radiated noise line spectrum components is small and the signal-to-noise ratio is low. Summary of the Invention

[0006] Purpose of the invention: To address the problems existing in the prior art, the purpose of this invention is to provide a method and system for accurately estimating the time delay vector of a distorted towed array, thereby improving the estimation accuracy of the time delay vector of a distorted towed array target signal array under conditions of limited ship radiated noise line spectrum and low signal-to-noise ratio.

[0007] Technical Solution: To achieve the above objectives, the present invention provides a method for accurately estimating the time delay vector of a distorted towed array, comprising the following steps:

[0008] A weighted least squares method for estimating the time delay difference between array elements based on the phase difference between line spectra is used to obtain a rough estimate of the time delay difference between array elements.

[0009] Using the rough estimate of the time delay difference between array elements as the observation sequence, and based on the characteristic that the time delay difference between array elements changes continuously and slowly in the time and space dimensions, a spatiotemporal two-dimensional hidden Markov model is constructed, which includes multiple discrete array element time delay difference states, time transition probability matrix, space transition probability matrix and observation probability transition matrix.

[0010] The spatiotemporal two-dimensional hidden Markov model is solved to obtain the state sequence corresponding to the maximum a posteriori probability. The state sequence is then mapped to physical time delay values ​​to obtain an accurate estimate of the array time delay vector.

[0011] Furthermore, the time delay difference estimation method based on line spectrum-based weighted least squares of inter-element phase difference obtains a rough estimate of the inter-element time delay difference, including:

[0012] Using array-received data, the inter-element phase difference of the line spectrum detected from the pre-reconstructed target signal is calculated; wherein, for each detected line spectrum, the phase in the received data of each element in each time frame is calculated based on the sine and cosine components of the corresponding line spectrum frequency in the array data.

[0013] The phase difference between array elements of the detected line spectrum is processed by weighted least squares to obtain a rough estimate of the phase difference between array elements; wherein, for each time frame and each array element, the time delay difference corresponding to different line spectrum frequencies is estimated and weighted by averaging according to the signal-to-noise ratio of each line spectrum component at the corresponding array element.

[0014] Furthermore, the construction of the spatiotemporal two-dimensional hidden Markov model includes:

[0015] A rough estimate of the time delay difference between array elements is used as the observed value of the time delay difference between array elements;

[0016] The range of time delay difference between array elements is determined based on the propagation speed of sound waves in water and the spacing between array elements, and the range of values ​​is uniformly discretized to obtain multiple discrete time delay difference states between array elements.

[0017] Based on the characteristic that the time delay difference between array elements changes smoothly between adjacent time frames, the time transition probability matrix of the two-dimensional hidden Markov model is modeled and initialized.

[0018] Based on the characteristic that the time delay difference between array elements changes smoothly between adjacent array elements, the spatial transition probability matrix of the two-dimensional hidden Markov model is modeled and initialized.

[0019] Model and initialize the observation probability transition matrix of the two-dimensional hidden Markov model.

[0020] Furthermore, the time delay difference state between array elements Represented as: ;in For uniform linear array element spacing, Let be the speed at which sound waves travel in water. The time delay interval, The number of discrete states.

[0021] Furthermore, the time transition probability matrix Represented as:

[0022]

[0023] in , These represent time frames respectively. , Array element The hidden state at that location The standard deviation of time transition. Representing the state in the time dimension Transition to state The probability of;

[0024] Spatial transition probability matrix Represented as:

[0025]

[0026] in Indicates time frame Array element The hidden state at that location The standard deviation of the spatial transition matrix. Representing the state in the spatial dimension Transition to state The probability of;

[0027] The observation probability transition matrix B is represented as:

[0028]

[0029] in Indicates time frame Array element Observed time delay difference between array elements To observe the standard deviation of noise, Used to characterize the hidden state as state. Under these conditions, the time delay observation values ​​were obtained. Corresponding discrete state The likelihood probability.

[0030] Furthermore, the spatiotemporal two-dimensional hidden Markov model is solved, including:

[0031] The forward probability from the initial time and initial array element to the current time and current array element is calculated using a forward spatiotemporal weighted recursive formula.

[0032] The backward probability from the current time and the current array element to the end time and the end array element is calculated using a backward spatiotemporal weighted recursive formula;

[0033] By combining the forward and backward probabilities, the posterior probability of each element and each state in each time frame is calculated.

[0034] The maximum a posteriori probability criterion is adopted. For each time frame, each array element selects the state that maximizes the a posteriori probability as the optimal state estimate.

[0035] The optimal state sequence is converted into physical time delay values ​​to obtain an accurate estimate of the time delay difference between array elements.

[0036] The array delay vector is accurately estimated based on the accurate estimation of the delay difference between array elements.

[0037] Furthermore, the forward probability is recursively calculated according to the following forward spatiotemporal weighted recursive formula:

[0038]

[0039] in and The forward probability is adjustable spatiotemporal weighting coefficient, satisfying... ; Indicates time frame Array element Observed time delay difference between array elements Indicates the state Observed under the conditions The probability, Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability;

[0040] Calculate the backward probability using the following backward spacetime weighted recursive formula:

[0041]

[0042] in and The spatiotemporal weighting coefficients are adjustable for backward probability, satisfying... ; Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Indicates time frame Array element Observed time delay difference between array elements Indicates time frame Array element Observed time delay difference between array elements Indicates the state Observed under the conditions The probability, Indicates the state Observed under the conditions The probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability.

[0043] This invention also provides a system for accurately estimating the time delay vector of a distorted towed array, used to implement the aforementioned method for accurately estimating the time delay vector of a distorted towed array. The system includes:

[0044] The preliminary estimation module is used to obtain a rough estimate of the time delay difference between array elements by using a weighted least squares method based on the phase difference between array elements according to the line spectrum.

[0045] The spatiotemporal two-dimensional hidden Markov modeling module is used to construct a spatiotemporal two-dimensional hidden Markov model based on the coarse estimate of the time delay difference between array elements as the observation sequence and the characteristic that the time delay difference between array elements changes continuously and slowly in the time and space dimensions. The spatiotemporal two-dimensional hidden Markov model includes multiple discrete array element time delay difference states, time transition probability matrix, space transition probability matrix and observation probability transition matrix.

[0046] The precise estimation module is used to solve the spatiotemporal two-dimensional hidden Markov model, calculate the state sequence corresponding to the maximum a posteriori probability, and map the state sequence to physical time delay values ​​to obtain a precise estimate of the array time delay vector.

[0047] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the method for accurately estimating the time delay vector of a distorted dragged array.

[0048] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements the steps of the method for accurately estimating the time delay vector of a distorted drag array.

[0049] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0050] 1. This invention adopts a two-step processing framework of weighted least squares preliminary estimation and spatiotemporal two-dimensional hidden Markov model fine estimation. It makes full use of the inherent characteristics of ship radiated noise and the spatiotemporal constraints of array deformation, and realizes high-precision estimation of the time delay vector of the distorted towed array target signal array under the conditions of fewer ship radiated noise line spectra and low signal-to-noise ratio.

[0051] 2. This invention constructs a spatiotemporal two-dimensional Hidden Markov Model, embedding the prior physical knowledge of the continuously and slowly changing time delay difference between array elements of the multi-line spectral component of ship radiated noise in a probabilistic form into the model. During the model solution process, spatiotemporal and frequency joint processing is performed on the time delay difference between the line spectral elements. By finding the state sequence corresponding to the maximum posterior probability, outliers caused by instantaneous noise, interference, or model mismatch can be effectively identified and corrected. Discrete, noisy observations (coarse estimates) are normalized to a smooth trajectory conforming to the laws of physical change, thereby improving the final accuracy of the time delay difference estimation. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of a method for accurately estimating the time delay vector of a distorted dragged array, provided in an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram showing the nominal and actual positions of the distorted drag array in an embodiment of the present invention.

[0054] Figure 3 This is an example of the estimation result of the time delay difference between array elements in the 15th frame in this embodiment of the invention.

[0055] Figure 4 This is an example of the estimation result of the time delay difference between array elements at position 15 in each frame in an embodiment of the present invention.

[0056] Figure 5 The figure shows the mean square error of the time delay difference estimation between array elements as the signal-to-noise ratio changes, compared with the existing method and the method of the present invention. Detailed Implementation

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0058] like Figure 1 As shown in the figure, an embodiment of the present invention discloses a method for accurately estimating the time delay vector of a distorted towed array, comprising the following steps:

[0059] Step S1: Based on the weighted least squares time delay difference estimation method of the phase difference between array elements according to the line spectrum, a rough estimate of the time delay difference between array elements is obtained;

[0060] Step S2: Using the rough estimate of the time delay difference between array elements as the observation sequence, based on the characteristic that the time delay difference between array elements changes continuously and slowly in the time and space dimensions, a spatiotemporal two-dimensional hidden Markov model is constructed, which includes multiple discrete array element time delay difference states, time transition probability matrix, space transition probability matrix and observation probability transition matrix.

[0061] Step S3: Solve the spatiotemporal two-dimensional hidden Markov model to calculate the state sequence corresponding to the maximum a posteriori probability, and map the state sequence to the physical time delay value to obtain an accurate estimate of the array time delay vector.

[0062] In this embodiment, in step S1, firstly, the phase difference between array elements of the line spectrum detected from the pre-reconstructed target signal is calculated using array received data. For each detected line spectrum, the phase in the received data of each array element in each time frame is calculated based on the sine and cosine components of the corresponding line spectrum frequency in the array data. Then, the phase difference between array elements of the detected line spectrum is processed by weighted least squares to obtain a rough estimate of the time delay difference between array elements. For each time frame and each array element, the time delay difference estimates corresponding to different line spectrum frequencies are weighted and averaged according to the signal-to-noise ratio of each line spectrum component at the corresponding array element.

[0063] Specifically, step S1 may include the following steps:

[0064] Step S101: Let the frequency of the l-th line spectrum detected from the pre-reconstructed target signal be denoted as . , , The total number of detected line spectra. The number of lines is calculated using the following formula: The first time frame The frequency of the data received by each array element is Phase of the line spectrum :

[0065]

[0066] in For the first The first time frame Data collected by each array element, n=0,1,…N-1, t=1,2,…,T, m=1,2,…,M, where N is the number of array element collection points in a single time frame. This represents the total number of time frames. The number of array elements. denoted as the signal sampling frequency, and arctan2 is the two-parameter arctangent function.

[0067] Step S102: Calculate the frequency. The line spectrum in the first and( +1) inter-element phase difference :

[0068]

[0069] Step S103: Using the phase difference between adjacent array elements The inter-element time delay difference of the l-th line spectrum is estimated using the following formula:

[0070]

[0071] Step S104: Obtain the inter-element time delay difference for each line spectrum using the following formula. We perform weighted least squares to obtain a rough estimate of the time delay difference between array elements. :

[0072]

[0073] in Indicates the first The target radiated noise signal received by each array element is the first Signal-to-noise ratio of the root spectral component.

[0074] For the first Individual Element The amplitude of each spectral component Let V be the variance of the noise.

[0075] In step S2, a spatiotemporal two-dimensional hidden Markov model is constructed, mainly including: using a rough estimate of the time delay difference between array elements as the observed value of the time delay difference between array elements; determining the range of values ​​for the time delay difference between array elements based on the propagation speed of sound waves in water and the spacing between array elements, and uniformly discretizing the range of values ​​to obtain multiple discrete states of the time delay difference between array elements; modeling and initializing the time transition probability matrix of the two-dimensional hidden Markov model based on the characteristic that the time delay difference between array elements changes smoothly between adjacent time frames; modeling and initializing the spatial transition probability matrix of the two-dimensional hidden Markov model based on the characteristic that the time delay difference between array elements changes smoothly between adjacent array elements; and modeling and initializing the observation probability transition matrix of the two-dimensional hidden Markov model.

[0076] Specifically, step S2 may include the following steps:

[0077] Step S201: Roughly estimate the time delay difference between array elements. As an observation of the time delay difference between array elements Observation sequence It can be defined as:

[0078]

[0079] Step S202: Let the speed of sound in water be... The spacing between elements of the horizontally uniform linear array is The range of values ​​for the time delay difference between array elements is: According to the interval By uniformly discretizing the interval, we obtain The time delay difference state between discrete array elements , can be represented as:

[0080]

[0081] Step S203: Model and initialize the time transition probability matrix of the two-dimensional hidden Markov model according to the following formula. :

[0082]

[0083] in , These represent time frames respectively. , Array element The hidden state at the location (i.e., the time delay difference between array elements). The standard deviation of time transition. Representing the state in the time dimension Transition to state The probability. Model settings. , A positive number is used to control the maximum possible range of change in the time delay difference between adjacent time frames. The smaller the value, the stronger the constraint of the previous frame state on the current frame state, and the smoother the change of the latency difference in the time dimension. The larger the value, the stronger the randomness of the state transition, allowing for larger temporal jumps.

[0084] Step S204: Model and initialize the spatial transition probability matrix of the two-dimensional hidden Markov model. :

[0085]

[0086] in Indicates time frame Array element The hidden state at that location The standard deviation of the spatial transition matrix. Representing the state in the spatial dimension Transition to state The probability. Model settings. , It is a positive number used to control the maximum possible range of changes in the time delay difference between adjacent time frames. Quantify the maximum reasonable range of change in the time delay difference between adjacent array elements within the same time frame. The smaller the value, the stronger the spatial constraint of the previous array element state on the current array element state, and the more continuous the distribution of the time delay difference in the spatial dimension. The larger the value, the stronger the randomness of the spatial state transition, allowing for larger time delay jumps between adjacent array elements.

[0087] Step S205: Model and initialize the observation probability transition matrix B of the two-dimensional hidden Markov model according to the following formula:

[0088]

[0089] in Indicates time frame Array element Observed time delay difference between array elements The standard deviation of the observed noise. Used to characterize the hidden state as state. Under these conditions, the time delay observation values ​​were obtained. Corresponding discrete state The likelihood probability, which can be simplified as... Model settings , The values ​​are positive, and a statistical description of the rough estimation error is provided. The smaller the value, the closer the observed value obtained by weighted least squares is to the true time delay difference, and the higher the reliability of the observation. The larger the value, the more severe the noise interference with the observation, and the lower the reliability of the observation.

[0090] In step S3, the spatiotemporal two-dimensional hidden Markov model is solved, mainly including: calculating the forward probability from the starting time and the starting array element to the current time and the current array element using a forward spatiotemporal weighted recursive formula; calculating the backward probability from the current time and the current array element to the ending time and the ending array element using a backward spatiotemporal weighted recursive formula; combining the forward and backward probabilities to calculate the posterior probability for each time frame, each array element, and each state; using the maximum a posteriori probability criterion, selecting the state that maximizes the posterior probability for each time frame and each array element as the optimal state estimate; converting the optimal state sequence into physical time delay values ​​to obtain an accurate estimate of the time delay difference between array elements; and obtaining an accurate estimate of the array time delay vector based on the obtained accurate estimate of the time delay difference between array elements.

[0091] Specifically, step S3 may include the following steps:

[0092] Step S301, Forward probability variable Define the current state Current observation value and the joint probability of "past" observations, when It can be initialized as:

[0093]

[0094] in Indicates the initial state as state. The probability of.

[0095] Step S302, when or When recursively calculating the forward probability :

[0096]

[0097] in and The forward probability is adjustable spatiotemporal weighting coefficient, satisfying... ; Default settings In practical applications where there are many hydrophones and the total number of frames is short, the number of frames can be appropriately increased. The coefficient should be increased appropriately if the coefficient is large, and vice versa. Size. Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability.

[0098] Step S303: Define the backward probability variable For future observations given the current state The conditional probability when Initialize to:

[0099]

[0100] Step S304, when or At that time, the backward probability is calculated using a spatiotemporal weighted recursive formula:

[0101]

[0102] in and The spatiotemporal weighting coefficients are adjustable for backward probability, satisfying... ; Default settings In practical applications where there are many hydrophones and the total number of frames is short, the number of frames can be appropriately increased. The coefficient should be increased appropriately if the coefficient is large, and vice versa. Size. Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Indicates time frame Array element Observed time delay difference between array elements Indicates time frame Array element Observed time delay difference between array elements Indicates the state Observed under the conditions The probability, Indicates the state Observed under the conditions The probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability.

[0103] Step S305: Calculate each time frame Each array element Each state Posterior probability:

[0104]

[0105] Step S306: Using the maximum a posteriori probability criterion, apply the following formula to each position. Choose the state that maximizes the posterior probability as the optimal state estimate:

[0106]

[0107] Step S307: Decode the optimal state sequence Converting this to physical time delay values ​​yields an accurate estimate of the time delay difference between array elements:

[0108]

[0109] in It is the optimal hidden state selected by the maximum a posteriori probability at time frame t and array element m. The corresponding discrete array element delay difference physical value is the delay difference result that restores the state index to a value that can be directly used in engineering.

[0110] Step S308: Based on the accurate estimation results of the time delay difference between all adjacent array elements in each time frame (a total of T time frames), the array time delay vector of the corresponding time frame is obtained through cumulative reconstruction, and finally T array time delay vectors are output, each vector having a dimension of 1×M. Based on the obtained accurate estimation of the time delay difference between array elements... Obtain accurate estimation of array delay vector for frame t : ,in The definition is as follows:

[0111]

[0112] The following simulation examples demonstrate the effectiveness and advantages of this invention.

[0113] Simulation Example 1: The simulation parameters for ship radiated noise are set as follows: power spectral line frequencies of 200 Hz, 350 Hz, and 700 Hz, and the number of array elements is... =32, the element spacing is d=0.8m, and the distorted dragged array is as follows: Figure 2 As shown, the speed of sound underwater is c = 1500 m / s, the line spectrum signal-to-noise ratio is set to 7 dB, and the sampling frequency is [missing information]. =20kHz, array data frame number T is 30 frames, each frame duration is 1s, and the angle at which the ship's radiated noise is incident on the towed linear array is 60°.

[0114] According to step S1, line spectrum detection is performed on the pre-reconstructed target signal, and a total of 5 line spectra are detected with frequencies of 200 Hz, 350 Hz and 700 Hz, respectively, thereby obtaining the phase of the acquired line spectra. The phase difference between line spectrum elements is obtained by subtracting the phases of adjacent array elements. Through the phase difference between line spectrum array elements Line spectrum frequency Signal-to-noise ratio of narrowband line spectrum in array data A rough estimate of the time delay difference between array elements. .

[0115] Based on step S2, a rough estimate is made based on the time delay difference between array elements. Calculate the parameters of the spatiotemporal two-dimensional hidden Markov model , , B. In this simulation example, the resolution of the time delay difference between array elements is set. s, i.e. =214. In this simulation, we assume that all initial states occur with equal probability. Assuming the time and spatial domains are equal in proportion, that is... In the simulation experiment, the standard deviation of the transition probability is set. Standard deviation of observation noise .

[0116] Based on step S3, using the constructed and calculated spatiotemporal two-dimensional hidden Markov model, the forward probabilities are calculated respectively. With backward variables Finally, the state sequence with the highest posterior probability is selected. Transform into accurate time delay estimation The final calculation shows that, using the line spectrum phase difference weighted least squares method, the root mean square error of the time delay difference between array elements is: s; and the root mean square error of the time delay difference between array elements proposed in this invention is The root mean square error was reduced by 7.06 times. The estimation results of the inter-element delay difference in the 15th frame are as follows: Figure 3 As shown, the estimation results of the time delay difference between array elements in each frame of array element 15 are as follows: Figure 4 As shown.

[0117] Simulation Example 2: The line spectrum signal-to-noise ratio setting was changed, while other conditions remained the same as in Simulation Example 1. The time delay estimation error of the proposed method and the estimation error obtained by weighted least squares of the line spectrum phase difference are as follows: Figure 5 As shown, within the signal-to-noise ratio range, the root mean square error of the inter-array delay difference estimation is reduced by 6.15 times compared to the weighted least squares average of existing methods.

[0118] This invention also discloses a system for accurately estimating the time delay vector of a distorted towed array, used to implement the method for accurately estimating the time delay vector of a distorted towed array as described in any of the preceding embodiments. The system includes: a preliminary estimation module, used to obtain a rough estimate of the time delay difference between array elements based on a weighted least squares method of phase difference between array elements using line spectra; a spatiotemporal two-dimensional hidden Markov modeling module, used to construct a spatiotemporal two-dimensional hidden Markov model based on the observation sequence of the rough estimate of the time delay difference between array elements and the characteristic of the time delay difference between array elements changing continuously and slowly in the time and space dimensions, the spatiotemporal two-dimensional hidden Markov model including multiple discrete array element time delay difference states, time transition probability matrices, spatial transition probability matrices, and observation probability transition matrices; and an accurate estimation module, used to solve the spatiotemporal two-dimensional hidden Markov model, calculate the state sequence corresponding to the maximum a posteriori probability, and map the state sequence to physical time delay values ​​to obtain an accurate estimate of the array time delay vector.

[0119] This invention also discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of a method for accurately estimating the time delay vector of a distorted drag array according to any of the foregoing embodiments.

[0120] This invention also discloses a computer program product, including a computer program that, when executed by a processor, implements the steps of a method for accurately estimating the time delay vector of a distorted dragged array according to any of the foregoing embodiments.

[0121] Any aspects of this invention not described in detail are well-known to those skilled in the art.

[0122] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for accurately estimating the time delay vector of a distorted dragged array, characterized in that, Includes the following steps: A weighted least squares method for estimating the time delay difference between array elements based on the phase difference between line spectra is used to obtain a rough estimate of the time delay difference between array elements. Using the rough estimate of the time delay difference between array elements as the observation sequence, and based on the characteristic that the time delay difference between array elements changes continuously and slowly in the time and space dimensions, a spatiotemporal two-dimensional hidden Markov model is constructed, which includes multiple discrete array element time delay difference states, time transition probability matrix, space transition probability matrix and observation probability transition matrix. The spatiotemporal two-dimensional hidden Markov model is solved to obtain the state sequence corresponding to the maximum a posteriori probability, and the state sequence is mapped to the physical time delay value to obtain an accurate estimate of the array time delay vector. Solving the spatiotemporal two-dimensional hidden Markov model includes: The forward probability from the initial time and initial array element to the current time and current array element is calculated using a forward spatiotemporal weighted recursive formula. The backward probability from the current time and the current array element to the end time and the end array element is calculated using a backward spatiotemporal weighted recursive formula; By combining the forward and backward probabilities, the posterior probability of each element and each state in each time frame is calculated. The maximum a posteriori probability criterion is adopted. For each time frame, each array element selects the state that maximizes the a posteriori probability as the optimal state estimate. The optimal state sequence is converted into physical time delay values ​​to obtain an accurate estimate of the time delay difference between array elements. The array delay vector is accurately estimated based on the accurate estimation of the inter-element delay difference. The forward probability is recursively calculated using the following forward spatiotemporal weighted recursive formula: ； in and The forward probability is adjustable spatiotemporal weighting coefficient, satisfying ; Indicates time frame Array element Observed time delay difference between array elements Indicates the state Observed under the conditions The probability, Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability, Represents time frame Array element ,state The forward probability, The number of discrete states, This represents the total number of time frames. The number of array elements; Calculate the backward probability using the following backward spacetime weighted recursive formula: ； in and The spatiotemporal weighting coefficients are adjustable for backward probability, satisfying... ; Representing the state in the time dimension Transition to state The probability, Representing the state in the spatial dimension Transition to state The probability, Indicates time frame Array element Observed time delay difference between array elements Indicates time frame Array element Observed time delay difference between array elements Indicates the state Observed under the conditions The probability, Indicates the state Observed under the conditions The probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability, Represents time frame Array element ,state The backward probability.

2. The method for accurately estimating the time delay vector of a distorted towed array according to claim 1, characterized in that, The time delay difference estimation method based on line spectrum and weighted least squares of phase difference between array elements obtains a rough estimate of the time delay difference between array elements, including: Using array-received data, the inter-element phase difference of the line spectrum detected from the pre-reconstructed target signal is calculated; wherein, for each detected line spectrum, the phase in the received data of each element in each time frame is calculated based on the sine and cosine components of the corresponding line spectrum frequency in the array data. The phase difference between array elements of the detected line spectrum is processed by weighted least squares to obtain a rough estimate of the phase difference between array elements; wherein, for each time frame and each array element, the time delay difference corresponding to different line spectrum frequencies is estimated and weighted by averaging according to the signal-to-noise ratio of each line spectrum component at the corresponding array element.

3. The method for accurately estimating the time delay vector of a distorted towed array according to claim 1, characterized in that, The construction of the spatiotemporal two-dimensional hidden Markov model includes: A rough estimate of the time delay difference between array elements is used as the observed value of the time delay difference between array elements; The range of time delay difference between array elements is determined based on the propagation speed of sound waves in water and the spacing between array elements, and the range of values ​​is uniformly discretized to obtain multiple discrete time delay difference states between array elements. Based on the characteristic that the time delay difference between array elements changes smoothly between adjacent time frames, the time transition probability matrix of the two-dimensional hidden Markov model is modeled and initialized. Based on the characteristic that the time delay difference between array elements changes smoothly between adjacent array elements, the spatial transition probability matrix of the two-dimensional hidden Markov model is modeled and initialized. Model and initialize the observation probability transition matrix of the two-dimensional hidden Markov model.

4. The method for accurately estimating the time delay vector of a distorted towed array according to claim 1, characterized in that, Inter-element delay difference state Represented as: ;in For uniform linear array element spacing, Let be the speed at which sound waves travel in water. The time delay interval, The number of discrete states.

5. The method for accurately estimating the time delay vector of a distorted towed array according to claim 1, characterized in that, Time transition probability matrix Represented as: ； in , These represent time frames respectively. , Array element The hidden state at that location The standard deviation of time transition. Representing the state in the time dimension Transition to state The probability of; Spatial transition probability matrix Represented as: ； in Indicates time frame Array element The hidden state at that location The standard deviation of the spatial transition matrix. Representing the state in the spatial dimension Transition to state The probability of; The observation probability transition matrix B is represented as: ； in Indicates time frame Array element Observed time delay difference between array elements To observe the standard deviation of noise, Used to characterize the hidden state as state. Under these conditions, the time delay observation values ​​were obtained. Corresponding discrete state The likelihood probability.

6. A system for accurately estimating the time delay vector of a distorted towed array, used to implement the method for accurately estimating the time delay vector of a distorted towed array according to any one of claims 1-5, characterized in that, The system includes: The preliminary estimation module is used to obtain a rough estimate of the time delay difference between array elements by using a weighted least squares method based on the phase difference between array elements according to the line spectrum. The spatiotemporal two-dimensional hidden Markov modeling module is used to construct a spatiotemporal two-dimensional hidden Markov model based on the coarse estimate of the time delay difference between array elements as the observation sequence and the characteristic that the time delay difference between array elements changes continuously and slowly in the time and space dimensions. The spatiotemporal two-dimensional hidden Markov model includes multiple discrete array element time delay difference states, time transition probability matrix, space transition probability matrix and observation probability transition matrix. The precise estimation module is used to solve the spatiotemporal two-dimensional hidden Markov model, calculate the state sequence corresponding to the maximum a posteriori probability, and map the state sequence to physical time delay values ​​to obtain a precise estimate of the array time delay vector.

7. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for accurately estimating the time delay vector of a distorted dragged array according to any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for accurately estimating the time delay vector of a distorted dragged array according to any one of claims 1-5.

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