Synthetic Aperture Sonar Time Delay Estimation Method Based on Micro Neural Network Unwrapping

Abstract

The present invention provides a method for estimating synthetic aperture sonar delay based on micro-neural network dewrapping. The method comprises: receiving time-domain echoes collected by a synthetic aperture sonar array and separating the time-domain echoes into two sub-band signals using a filter; calculating the cross-correlation function between the time-domain echoes of preceding and succeeding frames, and using the cross-correlation function to calculate the warped delay of the two sub-band signals; inputting the warped delay into a pre-established and trained neural network to extract phase-warped integers, and using the warped delay and phase-warped integers to reconstruct the true delay, thereby achieving synthetic aperture sonar delay estimation. This method overcomes the low phase dewrapping accuracy problem of traditional delay estimation methods, achieving high delay estimation accuracy and robustness, a simple network structure, and minimal computational effort. It can provide robust parameter estimation for synthetic aperture sonar motion compensation.

Description

Technical Field

[0001] The present invention relates to the field of underwater acoustic signal processing, and in particular to a synthetic aperture sonar time delay estimation method based on micro neural network unwinding. Background Art

[0002] Currently, synthetic aperture sonar (SAS) has become one of the most important underwater high-resolution imaging devices, with a wide range of applications in both military and civilian fields. SAS utilizes the continuous movement of an array to achieve a virtual large aperture and constant high resolution in azimuth through coherent processing. Coherent processing requires precise information about the carrier's trajectory, often achieving sub-wavelength estimation accuracy. Affected by factors such as wind, waves, currents, and attitude control, the carrier often deviates from the preset track, resulting in motion errors and a decrease in image quality. Currently, motion errors have become the primary factor limiting the improvement of SAS imaging quality, making motion error estimation technology increasingly important in the field of SAS.

[0003] Since GPS systems cannot be used underwater, motion sensors or acoustic transponders are usually used to measure the position of the carrier. However, the accuracy of motion sensors is insufficient to meet the requirements of synthetic aperture sonar imaging; acoustic transponders need to be deployed in advance, which is not convenient for practical application. The precise motion information of the sonar platform can be estimated from its own echo using micro-navigation methods. The offset phase center algorithm is the most commonly used micro-navigation method. The core step of this algorithm is delay estimation. However, due to the influence of noise, phase unwrapping in the delay estimation often leads to errors, resulting in reduced accuracy and robustness of the delay estimation.

[0004] In recent years, deep learning technology has developed rapidly and has been widely used in the field of underwater acoustic signal processing. The time delay in synthetic aperture sonar echoes can be understood as a nonlinear mapping relationship between the echo and the platform motion. Deep learning technology can effectively learn this nonlinear mapping relationship and is insensitive to noise, indicating that deep learning technology can be applied to the problem of synthetic aperture sonar time delay estimation. However, the high performance of deep neural networks depends on deeper network layers and iterative training processes with large amounts of data, which requires large computational overhead and time costs, making it unsuitable for application in synthetic aperture sonar real-time imaging systems. Micro neural networks, also known as lightweight neural networks, still have strong learning capabilities, simple network models, low training data requirements and computational complexity, providing another possibility for robust synthetic aperture sonar time delay estimation.

[0005] In summary, in synthetic aperture sonar motion error estimation, there is an urgent need for a robust, high-precision, and fast delay estimation method to improve the accuracy and real-time performance of subsequent motion compensation. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defect of the instability of phase unwrapping in the prior art and propose a synthetic aperture sonar delay estimation method based on micro neural network unwrapping.

[0007] To achieve the above object, the present invention proposes a synthetic aperture sonar delay estimation method based on micro neural network unwinding, the method comprising:

[0008] Step 1) receiving a time domain echo collected by a synthetic aperture sonar array and dividing the time domain echo into two sub-band signals through a filter;

[0009] Step 2) Calculate the cross-correlation function of the time domain echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function;

[0010] Step 3) The twisted delay is input into a pre-established and trained neural network to extract the phase twisted integer, and the twisted delay and the phase twisted integer are used to reconstruct the true delay, thereby realizing synthetic aperture sonar delay estimation.

[0011] As an improvement to the above method, step 1) specifically includes:

[0012] The time domain echoes collected by the synthetic aperture sonar array at the pth frame and the p+1th frame are s p (t) and s p+1 (t);

[0013] The echo is divided into two sub-bands by the filter:

[0014]

[0015] Among them, s 1,p (t) and s 2,p (t) are the time domain echo s of the pth frame respectively p (t) the first sub-band signal and the second sub-band signal, s 1,p+1 (t) and s 2,p+1 (t) are the first sub-band signal and the second sub-band signal of the p+1th frame time domain echo, h1(t) and h2(t) are two band-pass filters, Represents the convolution symbol.

[0016] As an improvement to the above method, step 2) specifically includes:

[0017] Calculate the cross-correlation function R of the subband signal of the pth frame and the p+1th frame 1,p (τ) and R 2,p (τ):

[0018]

[0019] Wherein, '*' represents complex conjugation; τ is the time delay between the pth frame and the p+1th frame;

[0020] The cross-correlation function is used to find the time delays τ1 and τ2 of the sub-band signals with phase entanglement:

[0021]

[0022] Wherein, '∠' represents the phase operation, f1 and f2 are the center frequencies of the two sub-band signals;

[0023] As an improvement to the above method, the neural network in step 3) includes an input layer, a hidden layer, and an output layer, wherein the input layer consists of 2 neurons, the hidden layer consists of 5 neurons, and the output layer consists of 2 neurons. The input layer and the output layer use a linear activation function; the hidden layer uses a hyperbolic tangent activation function f(x), which satisfies the following formula:

[0024]

[0025] Among them, x is the function independent variable;

[0026] The input of the i-th neuron in the input layer is a i =τ″ i , the output is x i =g1(a i );

[0027] Where τ″ i is the winding delay received by the i-th neuron, g1 is the activation function of the input layer;

[0028] The input a of the jth neuron in the hidden layer j for:

[0029]

[0030] The output is z j =g2(a j ), where w ij is the weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer, w j0 is the bias of the jth neuron in the hidden layer, and g2 is the activation function of the hidden layer;

[0031] The input a of the kth neuron in the output layer k for:

[0032]

[0033] The output is Among them, w jk is the weight between the jth neuron in the hidden layer and the kth neuron in the output layer, wk0 is the bias of the kth neuron in the output layer, and g3 is the activation function of the output layer.

[0034] As an improvement to the above method, the method further includes a neural network training step; specifically, the steps include:

[0035] Using the relationship between winding delay and real delay, the real delay is generated through simulation:

[0036]

[0037] Among them, τ1 and τ2 represent the winding delay of the two sub-band signals, τ1′ and τ2′ represent the actual delay of the two sub-band signals, represents a phase-wrapped integer;

[0038] Add errors to the real delays in the simulation to improve the generalization ability of the network:

[0039]

[0040] Among them, τ″1 and τ″2 are the real delays with errors, ε1 and ε2 are noises that obey Gaussian distribution, with mean 0 and variance

[0041] Get the training set of the neural network {(τ″1,τ″2),(n1,n2)} train and the test set {(τ″1,τ″2),(n1,n2)} test , where (τ″1,τ″2) is the input data of the neural network, and (n1,n2) is the output data, that is, the label vector;

[0042] The Levenberg-Marquardt back-propagation algorithm and mean square error loss function are used for network training, and the performance of the neural network is verified using the test set to obtain a neural network that meets the training requirements.

[0043] As an improvement to the above method, step 3) specifically includes:

[0044] Input the winding delay into the trained neural network to obtain the estimated value of the phase winding integer and

[0045] The true delay of the two subband signals is reconstructed using the wrapped delay and phase wrapped integer estimates:

[0046]

[0047] in, and are the true delay estimates of the two sub-band signals respectively;

[0048] The average of the actual delay estimates of the two sub-band signals is taken as the final estimate of the actual delay

[0049]

[0050] On the other hand, the present invention proposes a synthetic aperture sonar delay estimation system based on micro neural network unwinding, the system comprising:

[0051] The receiving filter module is used to receive the time domain echo collected by the synthetic aperture sonar array and divide the time domain echo into two sub-band signals through a filter;

[0052] A winding delay calculation module, used to calculate the cross-correlation function of the time domain echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function; and

[0053] The delay estimation module is used to input the entangled delay into a pre-established and trained neural network to extract the phase entangled integer, and use the entangled delay and phase entangled integer to reconstruct the real delay, thereby realizing the synthetic aperture sonar delay estimation.

[0054] Compared with the prior art, the advantages of the present invention are:

[0055] 1. Due to noise interference, phase unwrapping in existing delay estimation methods is prone to errors, resulting in reduced robustness and accuracy of delay estimation. The present invention uses a micro-neural network for phase unwrapping, taking advantage of the neural network's insensitivity to noise. The phase unwrapping effect is more robust and has a higher accuracy, making the final delay estimation result more accurate.

[0056] 2. Use simulation to generate training and test data to complete the training and testing of the neural network, and be able to apply the trained network to real data, avoiding the problem of unknown actual data labels and difficulty in supervised learning;

[0057] 3. Compared with deep neural networks, the micro neural network used in the present invention has a simple structure, with fewer network layers and neurons. It only requires a small amount of training data to learn accurate mapping relationships, greatly reducing computational overhead and time costs. It can be quickly applied to synthetic aperture sonar real-time imaging systems to improve imaging quality in real time. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 This is a flowchart of the overall process of the synthetic aperture sonar delay estimation method based on micro neural network unwinding of the present invention;

[0059] Figure 2 Schematic diagram of extracting two sub-band signals from a complete echo using multi-sub-band technology;

[0060] Figure 3 Schematic diagram of a micro neural network, including input layer, hidden layer and output layer;

[0061] FIG4 is a graph showing the delay estimation results of actual synthetic aperture sonar data, wherein FIG4(a) shows the sub-band wrapping delay of the method of the present invention and the reconstructed delay after dewrapping using a neural network; FIG4(b) shows a comparison of the delay estimation results of the method of the present invention and the step-by-step delay estimation method;

[0062] Figure 5 shows the motion compensation results of actual synthetic aperture sonar data, where Figure 5(a) shows the result without motion compensation; Figure 5(b) shows the result after motion compensation using the delay estimation results of the step-by-step delay estimation method; and Figure 5(c) shows the result after motion compensation using the delay estimation results of the method of the present invention. DETAILED DESCRIPTION

[0063] The technical solution of the present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0064] Example 1

[0065] like Figure 1 As shown, the present invention proposes a synthetic aperture sonar delay estimation method based on micro neural network unwrapping, and its implementation method includes the following steps:

[0066] Step 1: Receive the time-domain echo collected by the synthetic aperture sonar array and separate the echo into two sub-bands through a filter. The specific implementation is as follows:

[0067] Step 1-1) Obtain the received signal s of the synthetic aperture sonar array at the pth frame and the p+1th frame p (t) and s p+1 (t), where the time delay between the two signals is τ and the theoretical center frequency of the received signal is f c , the bandwidth is B.

[0068] Step 1-2) Construct two bandpass filters h1(t) and h2(t) with center frequencies f1 and f2 respectively, satisfying f c -B / 2<f1<f2<f c +B / 2, the bandwidth is b, and b≤B / 2.

[0069] like Figure 2 As shown, the echo is divided into two sub-bands by the filter:

[0070]

[0071] Among them, s 1,p (t) and s 2,p(t) represents the sub-band signal 1 and sub-band signal 2 of the p-th frame echo, s 1,p+1 (t) and s 2,p+1 (t) represents the sub-band signal 1 and sub-band signal 2 of the p+1th frame echo, Represents the convolution symbol.

[0072] Step 2: Calculate the cross-correlation function of the echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function. The specific implementation is as follows:

[0073] Step 2-1) Calculate the cross-correlation function R between the sub-band signals of the p-th frame and the p+1-th frame 1,p (τ) and R 2,p (τ):

[0074]

[0075] The '*' band indicates the complex conjugate.

[0076] Step 2-2) Calculate the phase of the cross-correlation function, and use the relationship between time delay and phase to calculate the time delays τ1 and τ2 of the two sub-band signals with phase entanglement:

[0077]

[0078] Among them, since τ1 and τ2 are time delays with phase entanglement, they are limited to the range of -1 / 2f1<τ1<1 / 2f1 and -1 / 2f2<τ2<1 / 2f2, and the corresponding phase range is (-π,π).

[0079] Step 3: Build a micro neural network, generate training data through simulation, and train the neural network. The specific implementation is as follows:

[0080] Step 3-1) Figure 3 As shown, a 3-layer micro neural network is constructed. The input layer consists of 2 neurons, the hidden layer consists of 5 neurons, and the output layer consists of 2 neurons. The input and output layers use linear activation functions, and the hidden layer uses hyperbolic tangent activation function:

[0081]

[0082] Here, x is the independent variable of the function.

[0083] The input of the i-th, i=1,2-th neuron in the input layer is a i =τ″ i , the output is x i =g1(a i ),

[0084] The input of the jth neuron in the hidden layer, j=1,2,...,5, is:

[0085]

[0086] The output is z j =g2(a j ), where w ij is the weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer, w j0 is the bias of the jth neuron in the hidden layer, which are all learned through training. Similarly, the input of the kth, k=1,2th neurons in the output layer is:

[0087]

[0088] The output is Among them, w jk is the weight between the jth neuron in the hidden layer and the kth neuron in the output layer, w k0 is the bias of the kth neuron in the output layer, g1, g2, and g3 are the activation functions of the input layer, hidden layer, and output layer, respectively.

[0089] Step 3-2) Using the relationship between the winding delay and the real delay, the real delay is generated through simulation. First, the range of the real delays τ1′ and τ2′ is set according to the requirements, and then the value of the winding delay is calculated:

[0090]

[0091] Where τ1 and τ2 represent the winding delays of the two sub-band signals, and τ1′ and τ2′ represent the actual delays of the two sub-band signals.

[0092] Then use the winding delay and the true delay to find the winding integers n1 and n2:

[0093]

[0094] Add errors to the real delays in the simulation to improve the generalization ability of the network:

[0095]

[0096] Where τ″1 and τ″2 are the real delays with errors, ε1 and ε2 are the noises that obey Gaussian distribution, with mean 0 and variance

[0097] Get the training set of the neural network {(τ″1,τ″2),(n1,n2)} train and the test set {(τ″1,τ″2),(n1,n2)} test, where (τ″1,τ″2) is the input data of the neural network, and (n1,n2) is the output data, that is, the label vector.

[0098] Step 3-3) Use the training set data obtained in step 3-2) to train the neural network, set the learning rate to 0.01, and set the number of iterations to 100.

[0099] The training set data is normalized to [-1, 1] before training.

[0100] The mean square error loss function is used to calculate the loss value, and the calculation formula is:

[0101]

[0102] Among them, y k is the output of the neural network, T k is the label data, and w is the network weight matrix.

[0103] The network weight matrix is ​​obtained by minimizing the loss function using the Levenberg-Marquardt backpropagation algorithm:

[0104]

[0105] Denormalize the output of the neural network.

[0106] The performance of the neural network is tested using the test set data obtained in step 3-2).

[0107] Step 4: Input the wrapped delay into the trained neural network to extract the phase wrapped integer, and use the wrapped delay and phase wrapped integer to reconstruct the true delay. The specific implementation is as follows:

[0108] Step 4-1) Input the winding delay into the trained neural network to obtain the estimated value of the phase winding integer and

[0109] Step 4-2) Reconstruct the true delays of the two sub-band signals using the wrapped delay and phase wrapped integer estimates:

[0110]

[0111] in, and are the true delay estimates of the two sub-band signals respectively.

[0112] The average of the estimated true delay values ​​of the two sub-band signals is taken as the final estimated true delay value:

[0113]

[0114] Example 2

[0115] Embodiment 2 of the present invention proposes a synthetic aperture sonar delay estimation system based on micro-neural network unwinding, which is implemented based on the method of embodiment 1. The system includes:

[0116] The receiving filter module is used to receive the time domain echo collected by the synthetic aperture sonar array and divide the time domain echo into two sub-band signals through a filter;

[0117] The winding delay calculation module is used to calculate the cross-correlation function of the time domain echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function;

[0118] The delay estimation module is used to input the entangled delay into a pre-established and trained neural network to extract the phase-entangled integer, and use the entangled delay and phase-entangled integer to reconstruct the real delay, thereby realizing synthetic aperture sonar delay estimation.

[0119] Experimental data

[0120] The method and beneficial effects of the present invention are further described in detail below with reference to the embodiment diagram.

[0121] Experimental conditions and parameters: The data processing platform was Windows, using an Intel Core i7-10700 @ 2.90 GHz processor. Echo signals were acquired from a synthetic aperture sonar lake test, with a center frequency of 110 kHz and a bandwidth of 20 kHz. Using multi-subband technology, two subband signals were generated, each with a center frequency of 105 kHz and a bandwidth of 10 kHz. Simulations were used to train and test the micro-neural network using 7200 training data points and 720 test data points, respectively. The learning rate was set to 0.01, the number of iterations was set to 100, and the training time was 1.07 seconds. The test data accuracy was 99.86%.

[0122] Figure 4 shows the delay estimation results obtained by processing experimental data using the method of the present invention. Figure 4(a) shows the entangled delay of the two subband signals and the estimated value of the true delay reconstructed using a neural network. Figure 4(b) compares the delay estimation results of the method of the present invention and the step-by-step delay estimation method. It can be seen that the method of the present invention accurately estimates the corresponding delay from the echo without phase unwrapping errors, while the step-by-step delay estimation method produces more phase unwrapping errors, resulting in more outliers in the delay estimation results, reducing the accuracy and robustness of the delay estimation.

[0123] In order to further verify the accuracy of the delay estimation results of the method of the present invention, the delay estimation results were used to perform motion compensation on the synthetic aperture sonar data and the corresponding image contrast was calculated. The imaging results are shown in Figure 5. The contrasts of the three images are 1.03, 1.04 and 1.15, respectively. Among them, Figure 5(a) shows the imaging results without compensation, Figure 5(b) shows the results of delay compensation using the step-by-step delay estimation method, and Figure 5(c) shows the results of delay compensation using the method of the present invention. It can be seen that when the images of the two targets are not compensated, there is obvious azimuth defocus. After the delay compensation using the step-by-step method, the defocus is suppressed to a certain extent, but there is still obvious azimuth blur. After the delay compensation using the method of the present invention, the defocus is well suppressed, and the image focusing effect is good.

[0124] Finally, it should be noted that the above embodiments are intended only to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention and are intended to be encompassed by the claims of the present invention.

Claims

1. A method for estimating synthetic aperture sonar delay based on micro-neural network unwinding, the method comprising: Step 1) receiving a time domain echo collected by a synthetic aperture sonar array and dividing the time domain echo into two sub-band signals through a filter; Step 2) Calculate the cross-correlation function of the time domain echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function; Step 3) Inputting the wrapping delay into a pre-established and trained neural network to extract the phase wrapping integer, and reconstructing the true delay using the wrapping delay and the phase wrapping integer, thereby realizing synthetic aperture sonar delay estimation; The neural network in step 3) includes an input layer, a hidden layer, and an output layer, wherein the input layer consists of 2 neurons, the hidden layer consists of 5 neurons, and the output layer consists of 2 neurons. The input layer and the output layer use linear activation functions; the hidden layer uses a hyperbolic tangent activation function f(x), which satisfies the following formula: Among them, x is the function independent variable; The input of the i-th neuron in the input layer is a i =τ i ″, the output is x i =g1(a i ); Among them, τ i ″ is the winding delay received by the i-th neuron, g1 is the activation function of the input layer; The input a of the jth neuron in the hidden layer j for: The output is z j =g2(a j ), where w ij is the weight between the i-th neuron in the input layer and the j-th neuron in the hidden layer, w j0 is the bias of the jth neuron in the hidden layer, and g2 is the activation function of the hidden layer; The input a of the kth neuron in the output layer k for: The output is Among them, w jk is the weight between the jth neuron in the hidden layer and the kth neuron in the output layer, w k0 is the bias of the kth neuron in the output layer, and g3 is the activation function of the output layer; The method also includes a neural network training step; specifically, including: Using the relationship between winding delay and real delay, the real delay is generated through simulation: Among them, τ1 and τ2 represent the winding delay of the two sub-band signals, τ1′ and τ2′ represent the actual delay of the two sub-band signals, represents a phase-wrapped integer; Add errors to the real delays in the simulation to improve the generalization ability of the network: Among them, τ1″ and τ2″ are the real delays with errors, ε1 and ε2 are noises that obey Gaussian distribution, with mean 0 and variance of Get the training set of the neural network {(τ″1,τ″2),(n1,n2)} train and the test set {(τ″1,τ″2),(n1,n2)} test , where (τ″1,τ″2) is the input data of the neural network, and (n1,n2) is the output data, that is, the label vector; The Levenberg-Marquardt back-propagation algorithm and mean square error loss function are used for network training, and the performance of the neural network is verified using the test set to obtain a neural network that meets the training requirements.

2. The method for estimating time delay of synthetic aperture sonar based on micro neural network unwinding according to claim 1, characterized in that: The step 1) specifically includes: The time domain echoes collected by the synthetic aperture sonar array at the pth frame and the p+1th frame are s p (t) and s p+1 (t); The echo is divided into two sub-bands by the filter: Among them, s 1,p (t) and s 2,p (t) are the time domain echo s of the pth frame respectively p (t) the first sub-band signal and the second sub-band signal, s 1,p+1 (t) and s 2,p+1 (t) are the first sub-band signal and the second sub-band signal of the p+1th frame time domain echo, h1(t) and h2(t) are two band-pass filters, Represents the convolution symbol.

3. The method for estimating time delay of synthetic aperture sonar based on micro neural network unwinding according to claim 2, characterized in that: The step 2) specifically includes: Calculate the cross-correlation function R of the subband signal of the pth frame and the p+1th frame 1,p (τ) and R 2,p (τ): Wherein, '*' represents complex conjugation; τ is the time delay between the pth frame and the p+1th frame; The cross-correlation function is used to find the time delays τ1 and τ2 of the sub-band signals with phase entanglement: Wherein, '∠' represents a phase operation, and f1 and f2 are the center frequencies of the two sub-band signals.

4. The method for synthetic aperture sonar delay estimation based on micro neural network unwinding according to claim 1, characterized in that: The step 3) specifically includes: Input the winding delay into the trained neural network to obtain the estimated value of the phase winding integer and The true delay of the two subband signals is reconstructed using the wrapped delay and phase wrapped integer estimates: in, and are the true delay estimates of the two sub-band signals respectively; The average of the actual delay estimates of the two sub-band signals is taken as the final estimate of the actual delay 5. A synthetic aperture sonar delay estimation system based on micro-neural network unwinding, implemented according to any one of claims 1 to 4, characterized in that: The system comprises: The receiving filter module is used to receive the time domain echo collected by the synthetic aperture sonar array and divide the time domain echo into two sub-band signals through a filter; A winding delay calculation module, used to calculate the cross-correlation function of the time domain echoes of the previous and next frames, and calculate the winding delay of the two sub-band signals through the cross-correlation function; and The delay estimation module is used to input the entangled delay into a pre-established and trained neural network to extract the phase-entangled integer, and use the entangled delay and phase-entangled integer to reconstruct the real delay, thereby realizing synthetic aperture sonar delay estimation.

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