A sparse time domain time reversal deconvolution method for anti-noise underwater target detection

Abstract

The application discloses a kind of sparsity time domain time anti-unwinding noise underwater target detection methods, comprising: by transmitting transducer, transmitting preset transmitting signal, and by receiving transducer, receiving the receiving signal of underwater target reflection containing noise;The autocorrelation function of transmitting signal is calculated;The cross-correlation function of receiving signal and transmitting signal is calculated;Sparsity condition is integrated into Richardson-Lucy algorithm, and sparsity time domain time anti-unwinding is obtained, reaches preset iteration condition, iteration is stopped;When the peak value of output exceeds the threshold value set, it indicates that there is target, the time delay τ of the position where target is located is estimated, the time delay estimation is converted into target distance from transducer, and the position of the target to be detected is obtained.The application ensures sparsity by ensuring that the maximum output occupies the proportion of total energy in the entire processing time window during iteration process, so as to improve the resolution of time delay estimation while greatly improving the anti-noise ability of unwinding algorithm.

Description

Technical Field

[0001] This invention relates to the field of underwater target detection, specifically to a noise-resistant underwater target detection method based on sparse time-domain time-inverse deconvolution. Background Technology

[0002] In the field of underwater target detection, traditional matched filtering is widely used due to its simplicity. Traditional matched filtering methods estimate the time delay parameter by calculating the cross-correlation function between the transmitted and received signals and using the peak value of the cross-correlation function. However, it has several drawbacks: a wide main lobe, low detection resolution, and low signal processing gain. Furthermore, white noise is often present during actual target detection, significantly degrading target detection performance. Additionally, false targets caused by multipath propagation are a significant challenge in underwater target detection.

[0003] In recent years, RL deconvolution algorithms have begun to be used in target detection applications of active sonar or radar. They are applied to improve the resolution of raw images generated by conventional beamformers, matched filters, or a combination of both. A known N-dimensional interest-received signal y(t) can be represented as... Where s(t) is a known M-dimensional real vector, i.e., the transmitted signal, and ρ(t) is an unknown but sparse vector, i.e., the generalized target reflection density function. This represents a copy of the generalized target reflection density function after a time delay τ. Assuming there is only one point target, its location is known, and multipath propagation is ignored, this dimension N is reduced to M, where t is time and τ is the time delay. In this case, it is relatively easy to maintain the stability of RL unconvolution, thus obtaining good image quality. Since the target must usually be located, i.e. Image quality degrades significantly, especially under low signal-to-noise ratio conditions. In such cases, the inversion problem for reconstructing the image becomes ill-conditioned. However, by leveraging the sparsity of targets throughout the processing time window, the desired solution to the equation can be found. Furthermore, the time-reversal concept has been successfully applied to phase-coherent underwater acoustic communication in time-varying multipath marine environments over the past decade. However, the inability to provide a detector source is the biggest obstacle to applying the time-reversal concept to active sonar, where the detector source provides the transfer function. This is straightforward for communication but challenging for active sonar. However, iterative time-reversal allows energy to be focused on the strongest target, solving the multipath propagation problem in underwater target detection. This invention introduces the concepts of sparsity and time-reversal into traditional RL decomposition, iteratively searching for solutions to focus on the target with the strongest reflection, or, under multipath conditions, focusing energy on the path with the strongest reflection, effectively eliminating false targets caused by multipath propagation and thus enhancing target detection performance. Summary of the Invention

[0004] The purpose of this invention is to provide a noise-resistant underwater target detection method with sparse time-domain inverse deconvolution to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: A noise-resistant underwater target detection method based on sparse temporal inverse deconvolution includes: Step 1: The transmitting transducer transmits a preset transmission signal, and the receiving transducer receives the received signal reflected by the underwater target containing noise. Step 2: Calculate the autocorrelation function of the transmitted signal; Step 3: Calculate the cross-correlation function of the received signal and the transmitted signal; Step 4, apply sparsity conditions The Richardson-Lucy algorithm is incorporated, where τ is the time delay and ρ(τ) represents the generalized target reflection density function of a stationary target. This represents the absolute value of the generalized target reflectance density function. This represents a small region near the time delay τ0 of the target location. When the sparsity time domain inverse deconvolution is obtained, the iteration stops when the preset iteration condition is met. Step 5: When the peak value of the output exceeds the set threshold, it indicates that there is a target. The horizontal axis corresponds to the estimated time delay τ of the target's location. The time delay estimate is converted into the distance between the target and the transducer to obtain the position of the target to be detected.

[0006] Furthermore, the received signal model in step 1 is as follows: Let the transmitted signal from the transmitting transducer be s(t), and the received signal from the receiving transducer be y(t). The received signal can be represented as a transmitted signal with amplitude and phase variations, time delay, and mixed noise. The expression for the received signal is:

[0007] Where s(t-τ) is the signal after time delay, ρ(τ)s(t-τ) is the echo signal of each propagation path without noise after being reflected by the target, and n(t) represents white noise; The time delay τ is determined by the distance between the transducer and the target and the speed of sound wave propagation, that is: Where R is the one-way distance between the transducer and the target, and c is the speed of sound in water.

[0008] Furthermore, the autocorrelation function in step 2 is: In the formula, The autocorrelation function measures the similarity between the transmitted signal and its delayed replica. This represents the transmitted signal after a time delay τ, and then the conjugate is taken.

[0009] Furthermore, the cross-correlation function in step 3 is: In the formula, This is the cross-correlation function between the received and transmitted signals.

[0010] Furthermore, the expression for the generalized target reflection density function obtained by the sparse time-domain inverse deconvolution in step 4 is:

[0011] Among them, g (r) (τ) is the generalized transfer function obtained in the r-th iteration. , ρ (r) (τ) is the generalized target reflection density function obtained in the r-th iteration, ρ (r+1) (τ) is the generalized target reflection density function obtained in the (r+1)th iteration. Represents convolution. The inverse of the cross-correlation function.

[0012] Furthermore, the termination condition preset in step 4 is simultaneously limited by the number of iterations and a sparsity condition, the sparsity condition being determined by the energy concentration d. r The energy concentration is characterized by the ratio of the total energy in a small area near the target to the total energy within the entire processing time window. When the iteration result exceeds a set condition, that is, when the energy concentration exceeds a set minimum threshold, the iteration automatically stops and the result is output, regardless of whether the specified number of iterations has been reached. The formula for energy concentration is: In the formula, Represents ρ (r) The infinite norm of (τ), Represents ρ (r) The L1 norm of (τ).

[0013] Furthermore, after the iteration in step 5, a function with time delay as the independent variable is obtained. When the peak point exceeds the set threshold, it indicates the presence of a target. The horizontal axis corresponds to the estimated time delay at the target's location. Finally, the time delay estimate is converted into the distance between the target and the transducer, thus obtaining the position of the target to be detected. The formula is as follows: Where R0 is the distance between the target and the transducer.

[0014] Compared with existing technologies, the advantages of this invention are as follows: Traditional matched filtering uses RL deconvolution methods that do not utilize the time-invariant properties of correlation and the sparsity of the target in the time delay estimation process of active sonar. Furthermore, traditional time-reflection detection requires a time-reflection array and a guiding source. To address these issues, this invention utilizes the time-invariant properties of correlation and the sparsity of the target in time delay estimation using active sonar, combining the concepts of sparsity and time-reflection with the RL deconvolution algorithm. It proposes a method to achieve time-reflection processing in the time domain without an array, termed sparse time-domain time-reflection deconvolution. During the iteration process, sparsity is ensured by guaranteeing that the maximum output value accounts for a proportion of the total energy within the entire processing time window. This significantly improves the noise resistance of the deconvolution algorithm while increasing the time delay estimation resolution. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the workflow of a noise-resistant underwater target detection method based on sparse temporal inverse deconvolution according to the present invention.

[0016] Figure 2 This is a graph of the autocorrelation function of the transmitted signal described in an embodiment of the present invention;

[0017] Figure 3 The graph shows the generalized target reflectance density function obtained by performing RL deconvolution on the autocorrelation function as described in this embodiment of the invention.

[0018] Figure 4 The graph of the generalized target reflectance density function obtained by performing TTR (transformation and retraction) on the autocorrelation function as described in this embodiment of the invention;

[0019] Figure 5 This is a cross-correlation function graph with a signal-to-noise ratio of 0dB as described in an embodiment of the present invention;

[0020] Figure 6 This is a graph of the generalized target reflection density function obtained by RL deconvolution at a signal-to-noise ratio of 0dB, as described in an embodiment of the present invention.

[0021] Figure 7 This is a graph of the generalized target reflectance density function obtained by the unwinding (TTR) of the present invention at a signal-to-noise ratio of 0dB, as described in an embodiment of the present invention.

[0022] Figure 8 This is a cross-correlation diagram of the direct path described in this embodiment of the invention, where the signal-to-noise ratio is 0dB and the multipath effect is present.

[0023] Figure 9 The graph shows the generalized target reflection density function obtained by RL deconvolution under the conditions of 0dB signal-to-noise ratio for the direct path and multipath effect as described in this embodiment of the invention.

[0024] Figure 10The graph shows the generalized target reflection density function obtained by unwinding (TTR) under the direct path signal-to-noise ratio of 0dB and multipath effect described in this embodiment of the invention. Detailed Implementation

[0025] 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, and 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.

[0026] Please see Figure 1 This invention provides a noise-resistant underwater target detection method with sparse temporal inverse deconvolution, comprising:

[0027] Step 1: The transmitting transducer transmits a preset transmission signal, and the receiving transducer receives the received signal reflected by the underwater target containing noise.

[0028] The transmitted and received signals can be modeled. The specific modeling process is as follows: Let the transmitted signal of the transmitting transducer be s(t), and the received signal of the receiving transducer be y(t). The received signal is represented as the transmitted signal with amplitude and phase changes, time delay, and mixed noise. The received signal can be represented as the convolution of the generalized target reflection density function and the transmitted signal, expressed as:

[0029] (1)

[0030] Where ρ(τ) represents the generalized target reflection density function of a stationary point target, which is affected by factors such as the target reflection coefficient and the ocean channel transfer function; τ represents the time delay; ρ(τ)s(t-τ) is the noise-free echo signal of each propagation path after reflection from the target; s(t-τ) is the signal after the time delay; and n(t) represents white noise. This represents convolution.

[0031] The time delay τ is determined by the distance between the transducer and the target and the speed of sound wave propagation, that is:

[0032]

[0033] Where R is the one-way distance between the transducer and the target, and c is the speed of sound in water.

[0034] The received signal in a multipath channel environment can be modeled as follows:

[0035] (2)

[0036] In the formula, k represents the k-th path, K represents the total number of paths, and ρ k τ represents the amplitude and phase changes of the k-th path caused by the target reflection coefficient and channel propagation. k This represents the delay of the k-th path.

[0037] Comparing (2) and (1), we can see that the generalized target reflection density function of a stationary point target is:

[0038] (3)

[0039] Where δ(·) is the unit impulse response function.

[0040] Step 2, calculate the autocorrelation function of the transmitted signal. The autocorrelation function is:

[0041] (4)

[0042] In the formula, This is the autocorrelation function of the transmitted signal, and also the self-ambiguity function of a stationary target. This represents a copy of the transmitted signal after a time delay τ, then taken as its conjugate. It characterizes the resolution of the transmitted signal in the time delay dimension.

[0043] Step 3: Calculate the cross-correlation function between the received and transmitted signals. The cross-correlation function is as follows:

[0044] (5)

[0045] In the formula, This is the cross-correlation function between the received and transmitted signals.

[0046] The cross-correlation function is the mutual ambiguity function under the specific condition that the target is stationary. Substituting the transmitted signal (1) into (4) and ignoring noise, we can obtain:

[0047] (6)

[0048] In the formula, yes To express the convolution operation, the independent variable t is changed to v. It is a copy of the autocorrelation function after a time delay v.

[0049] The cross-correlation function is the convolution of the autocorrelation function and the generalized target reflectance density function. The peak value of the cross-correlation corresponds to the time delay of the target's location, and the time delay resolution is determined by the autocorrelation function.

[0050] Step 4, apply sparsity conditions By incorporating the Richardson-Lucy algorithm, a sparse time-domain inverse deconvolution is obtained, and the iteration terminates when the preset iteration conditions are met.

[0051] RL deconvolution incorporating sparsity addresses the following problem:

[0052] (7)

[0053] In the formula, This represents the absolute value of the generalized target reflection density function, i.e., the power of the received signal. This is an estimate of the generalized target reflectance density function. To express the convolution operation, the independent variable is changed from τ to v. argmin takes the minimum value, and subject to is the value under this constraint. It is a small region near the target time delay τ0, that is, the ratio of energy near the target to energy within the entire processing window tends to be 1. The first part of equation (6) is the traditional RL deconvolution, where the output, i.e., the cross-correlation function, is known. The point spread function, also known as the autocorrelation function. Under the given conditions, the input, i.e., the generalized target reflectance density function ρ(τ), is estimated by choosing ρ(τ) to its true value. Its estimated value The Csiszar differential between them is minimized. The latter part guarantees sparsity, constrains the generalized target reflectance density function, and concentrates energy in a very small region near the target. The analytical expression of equation (6) is difficult to obtain, and its iterative solution is:

[0054] (8)

[0055] In the formula, r represents the number of iterations, ρ (r) (v) represents the generalized target reflectance density function estimated in the r-th time, ρ (r+1) (v) represents the generalized target reflectance density function estimated in the (r+1)th time.

[0056] Since the correlation function is time-invariant, equation (8) can be expressed as follows:

[0057] (9)

[0058] in, Let r be the generalized transfer function obtained in the r-th iteration. , Let be the generalized target reflection density function obtained in the r-th iteration. Represents convolution. Equation (9) can be implemented using the concept of time inversion. Since time inversion is implemented in the time domain and the target sparsity is incorporated into RL deconvolution, it is called sparse time-domain time inversion deconvolution.

[0059] The preset termination condition in step 4 is subject to both the number of iterations and the sparsity condition, with the sparsity condition determined by the energy concentration d. r Energy concentration is used to characterize the ratio of the total energy in a small area near the target to the total energy during the entire processing time window. When the iteration result exceeds a set condition, i.e., when the energy concentration exceeds a set minimum threshold, the iteration automatically stops and the result is output, regardless of whether the specified number of iterations has been reached. The formula for energy concentration is:

[0060] (10)

[0061] In the formula, Represents ρ (r) The infinite norm of (τ), Represents ρ (r) The L1 norm of (τ).

[0062] Step 5: The peak value output corresponds to the time delay τ estimation of the location of the target point.

[0063] After iteration, the target's time delay is estimated. This time delay estimate is then converted into the target's distance from the transducer, yielding the target's position. The formula is as follows:

[0064]

[0065] Where R0 is the distance between the target and the transducer, and τ0 is the target time delay.

[0066] Example:

[0067] Figure 1 This diagram illustrates the workflow of a noise-resistant underwater target detection method based on sparse temporal inverse deconvolution. The specific implementation process is as follows:

[0068] First, the type of transmitted signal is determined to be a linear frequency modulated signal, with a transmission duration of 1ms, a center frequency of 12kHz, a bandwidth of 4kHz, a signal sampling frequency of 50kHz, an amplitude of 1, a real time delay of 4ms, and a sound wave propagation speed in water of 1500m / s.

[0069] The autocorrelation function of the transmitted signal is calculated according to equation (4). The autocorrelation function of the transmitted signal in this embodiment is shown in the appendix. Figure 2 As shown, the width of its main lobe represents the resolution of the time delay dimension.

[0070] The autocorrelation function is a special case of the cross-correlation function. Under specific conditions, namely when the received signal contains no noise and the time delay is 0, the cross-correlation function is the same as the autocorrelation function. This is a very ideal condition. By performing RL unconvolution and sparsity time-domain inverse unconvolution on the autocorrelation function respectively, under the same number of iterations, the resolution and convergence speed of different unconvolution methods under theoretical conditions can be obtained. According to Equation (8), the autocorrelation function is RL unconvolved for 20 iterations to obtain the generalized target reflection density function. This actually corresponds to the case where the target position is known. Theoretically, it is a unit impulse pulse. The generalized target reflection density function of RL unconvolution in this embodiment is shown in the appendix. Figure 3 As shown, it clearly eliminates the blurring caused by the transmitted signal, and the main lobe becomes narrower compared to the autocorrelation function. However, there are two relatively high side lobes around the main lobe, indicating that the number of iterations is insufficient to completely eliminate the blurring caused by the transmitted signal.

[0071] Sparse time-domain inverse time deconvolution (TTR) is performed according to equations (9) and (10) for 20 iterations to obtain the generalized target reflection density function. The generalized target reflection density function obtained by TTR deconvolution in this embodiment is shown in the appendix. Figure 4 As shown, it can also eliminate the ambiguity caused by the transmitted signal and finally obtain an approximate unit impulse function. Under the same number of iterations, it has better energy concentration, a narrower main lobe, and no side lobes, indicating that its convergence speed is faster than RL deconvolution.

[0072] Assuming the point target is located in the time delay At the location where the signal-to-noise ratio is 0dB, the received signal is generated according to equation (1), and then the cross-correlation function is calculated according to equation (6). The processing time window is 7ms. The cross-correlation function under the signal-to-noise ratio of 0dB in this embodiment is shown in the appendix. Figure 5 As shown. The true value is marked with a black circle. Due to the low signal-to-noise ratio, although the cross-correlation function, i.e., the simple matched filtering process, can estimate the true value of the time delay, it contains many spurious peaks.

[0073] RL deconvolution is performed according to equation (8) for 60 iterations to obtain the generalized target reflection density function. The generalized target reflection density function obtained by RL deconvolution in this embodiment with a signal-to-noise ratio of 0dB is shown in the appendix. Figure 6 As shown. The true values ​​are marked with red circles, and the image is filled with peaks due to the search for solutions in a high-dimensional space under low signal-to-noise ratio conditions.

[0074] TTR unwinding is performed according to equations (9) and (10) for 12 iterations to obtain the generalized target reflection density function. The generalized target reflection density function obtained by TTR unwinding in this embodiment with a signal-to-noise ratio of 0dB is shown in the appendix. Figure 7As shown in the figure, thanks to the characteristics of the time reversal method, it can converge to the optimal solution within the entire time window, so a significant peak is shown in the figure, which improves the noise resistance of the time delay estimation.

[0075] If we consider the multipath effect of the signal during propagation, we set the number of paths to 5, and the specific parameters are shown in Table 1. The signal-to-noise ratio of the direct path is 0dB. Substituting the parameters into equation (2) yields the received signal.

[0076] Table 1 Path Parameters

[0077]

[0078] Then calculate the cross-correlation function according to equation (6), such as Figure 8 As shown, the positions of each path are indicated by red circles, demonstrating that it cannot eliminate the effects caused by multipath effects in target detection.

[0079] RL deconvolution is performed according to equation (8) for 60 iterations to obtain the generalized target reflection density function. In this embodiment, the generalized target reflection density function obtained by RL deconvolution under a signal-to-noise ratio of 0dB and multipath effect is shown in the appendix. Figure 9 As shown, the positions of each path are indicated by red circles, demonstrating that it also cannot eliminate the effects caused by multipath propagation in target detection.

[0080] TTR unwinding is performed according to equations (9) and (10) for 12 iterations to obtain the generalized target reflection density function. In this embodiment, the generalized target reflection density function obtained by TTR unwinding under the conditions of 0dB signal-to-noise ratio and multipath effect is shown in the appendix. Figure 10 As shown in the figure, thanks to the characteristics of the time reversal method, it can converge to the optimal solution within the entire time window, so a significant peak is shown in the figure. This improves the noise resistance of time delay estimation and also eliminates the influence of multipath effects in target detection.

[0081] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A noise-resistant underwater target detection method based on sparse temporal inverse deconvolution, characterized in that, include: Step 1: The transmitting transducer transmits a preset transmission signal, and the receiving transducer receives the received signal reflected by the underwater target containing noise. Step 2: Calculate the autocorrelation function of the transmitted signal; Step 3: Calculate the cross-correlation function of the received signal and the transmitted signal; Step 4, apply sparsity conditions The Richardson-Lucy algorithm is incorporated, where τ is the time delay and ρ(τ) represents the generalized target reflection density function of a stationary target. This represents the absolute value of the generalized target reflectance density function. This represents a small region near the time delay τ0 of the target location. When the sparsity time domain inverse deconvolution is obtained, the iteration stops when the preset iteration condition is met. Step 5: When the peak value of the output exceeds the set threshold, it indicates that there is a target. The horizontal axis corresponds to the estimated time delay τ of the target's location. The time delay estimate is converted into the distance between the target and the transducer to obtain the location of the target to be detected.

2. The method for noise-resistant underwater target detection with sparse temporal inverse deconvolution according to claim 1, characterized in that, The received signal modeling in step 1 is as follows: Let the transmitted signal from the transmitting transducer be s(t), and the received signal from the receiving transducer be y(t). The received signal can be represented as a transmitted signal with amplitude and phase variations, time delay, and mixed noise. The expression for the received signal is: Where s(t-τ) is the signal after time delay, ρ(τ)s(t-τ) is the echo signal of each propagation path without noise after being reflected by the target, and n(t) represents white noise; The time delay τ is determined by the distance between the transducer and the target and the speed of sound wave propagation, that is: Where R is the one-way distance between the transducer and the target, and c is the speed of sound in water.

3. The method for noise-resistant underwater target detection with sparse temporal inverse deconvolution according to claim 2, characterized in that, The autocorrelation function in step 2 is: In the formula, The autocorrelation function measures the similarity between the transmitted signal and its delayed replica. This represents the transmitted signal after a time delay τ, and then the conjugate is taken.

4. The method for noise-resistant underwater target detection with sparse time-domain inverse deconvolution according to claim 3, characterized in that, The cross-correlation function in step 3 is: In the formula, This is the cross-correlation function between the received and transmitted signals.

5. The method for noise-resistant underwater target detection with sparse temporal inverse deconvolution according to claim 4, characterized in that, The expression for the generalized target reflection density function obtained from the sparse time-domain inverse deconvolution in step 4 is as follows: Among them, g (r) (τ) is the generalized transfer function obtained in the r-th iteration. , ρ (r) (τ) is the generalized target reflection density function obtained in the r-th iteration, ρ (r+1) (τ) is the generalized target reflection density function obtained in the (r+1)th iteration. Represents convolution. The inverse of the cross-correlation function.

6. The method for noise-resistant underwater target detection with sparse temporal inverse deconvolution according to claim 5, characterized in that, The termination condition preset in step 4 is subject to both the number of iterations and the sparsity condition. The sparsity condition is determined by the energy concentration d. r The energy concentration is characterized by the ratio of the total energy in a small area near the target to the total energy within the entire processing time window. When the iteration result exceeds a set condition, that is, when the energy concentration exceeds a set minimum threshold, the iteration automatically stops and the result is output, regardless of whether the specified number of iterations has been reached. The formula for energy concentration is: In the formula, Represents ρ (r) The infinite norm of (τ), Represents ρ (r) The L1 norm of (τ).

7. The method for noise-resistant underwater target detection with sparse temporal inverse deconvolution according to claim 6, characterized in that, After the iteration in step 5, a function with time delay as the independent variable is obtained. When the peak point exceeds the set threshold, it indicates the presence of a target. The horizontal axis corresponds to the estimated time delay at the target's location. Finally, the time delay estimate is converted into the distance between the target and the transducer, thus obtaining the position of the target to be detected. The formula is as follows: Where R0 is the distance between the target and the transducer.

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