Weak signal robust detection method under ocean reverberation background

Abstract

The invention discloses a weak signal robust detection method under an ocean reverberation background, and the method comprises the steps: 1, obtaining a receiving signal of a receiver under the reverberation background, employing a novel probability function to represent a probability density function of the receiving signal, and solving a probability density function parameter through the minimization of KL divergence; 2, performing nonlinear transformation on the received signal based on a probability density function; and 3, constructing a test statistic based on the received signal after nonlinear transformation, and comparing the test statistic with a detection threshold to complete weak signal detection under the reverberation background. According to the method, a weak signal robust detector can be constructed, and the influence of the time-varying characteristic of reverberation on the performance of the detector is reduced, so that weak signals can be detected under the condition that the reverberation probability density fluctuates, and the capability of an underwater acoustic detection device for discovering a long-distance underwater acoustic target is improved.

Description

Technical Field

[0001] The invention belongs to the field of underwater acoustic signal detection, and specifically relates to a robust detection method for weak signals under an ocean reverberation background. Background Art

[0002] Detecting weak signals in a reverberation background helps underwater acoustic detection equipment detect distant hydroacoustic targets, which is of great significance for responding to underwater threats and safeguarding maritime rights and interests.

[0003] The main idea of ​​detecting weak signals in the background of ocean reverberation is to first perform probability density modeling on the ocean reverberation to obtain the probability density function of the reverberation, and then build a local optimal detector based on the probability density function. When modeling reverberation, the commonly used probability density models are Gaussian distribution model, mixed Gaussian distribution model and SαS distribution model. However, ocean reverberation is a time-varying signal, which causes its probability density to fluctuate greatly, making it difficult to accurately model it with a single model. Once the model is mismatched, the detection performance of the detector will drop rapidly, that is, the robustness is poor. In view of the time-varying reverberation background, studying the robust detection method of weak signals and applying it to underwater acoustic detection equipment is particularly critical to improving underwater detection capabilities. Summary of the invention

[0004] The present invention aims to solve the deficiencies of the above-mentioned prior art and proposes a robust detection method for weak signals in the background of ocean reverberation, in order to construct a robust detector for weak signals and reduce the influence of the time-varying characteristics of reverberation on the performance of the detector, so that weak signals can be detected when the reverberation probability density fluctuates, thereby improving the ability of underwater acoustic detection equipment to detect long-distance hydroacoustic targets.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme:

[0006] The invention provides a method for robustly detecting weak signals under ocean reverberation background, which is characterized by being performed in the following steps:

[0007] Step 1: Get the signal received by the receiver in the reverberation background { u [ n ] | n = 1 ,..., N } ,in, u [ n ] Represents the reverberation background The received signal at the time instant, and u [ n ] = A s [ n ] + ω [ n ] ,in, s [ n ] Indicates The transmission signal at that moment, Indicates the amplitude of the echo signal, ω [ n ] Indicates The reverberation signal at that moment, Indicates the total time;

[0008] Step 2: Get the received signal { u [ n ] | n = 1 ,..., N } The optimal probability density function f ( u [ n ]) ;

[0009] Step 3: u [ n ] Transform and obtain The received signal after the transformation g [ n ] ;

[0010] Step 4: Use formula (10) to construct the test statistic :

[0011] T = ∑ n = 1 N s [ n ] g [ n ] (10)

[0012] Step 5: If , it means that the receiver receives the target's echo signal at time N, otherwise, it means that it does not receive the target's echo signal; where, It is called the detection threshold.

[0013] The method for robustly detecting weak signals in an ocean reverberation background described in the present invention is also characterized in that step 2 is performed as follows:

[0014] Step 2.1: Get the received signal { u [ n ] | n = 1 ,..., N } Minimum value of and maximum value , and the interval length is , will receive the signal { u [ n ] | n = 1 ,..., N } Divide into equally spaced intervals; is the total number of intervals;

[0015] Step 2.2: Calculate the The center value of the interval , ;

[0016] (1)

[0017] Step 2.3: Use formula (2) to calculate The number of received signals falling within the interval ;

[0018] k i = ∑ n = 1 N φ ( u x i , u [ n ] ) (2)

[0019] In formula (2), φ ( u x i , u [ n ] ) To judge u [ n ] Whether it falls into intervals, and have:

[0020] φ ( u x i , u [ n ] ) = { 1 ， | u [ n ] − u x i | ≤ u maximum − u bad M 0 ， | u [ n ] − u x i | > u maximum − u bad M (3)

[0021] Step 2.4: Calculate using formula (4) The probability of ;

[0022] (4)

[0023] Step 2.5: Use formula (5) to construct the received signal { u [ n ] | n = 1 ,..., N } The initial probability density function f a ( u [ n ] ) ;

[0024] f a ( u [ n ] ) = 1 − ε 2 πσ 2 e x p ( − u [ n ] 2 2 σ 2 ) + ε 2 b e − | u [ n ] | b (5)

[0025] In formula (5), Characterizes the variance of the reverberation signal; Characterize the shape parameters of the reverberation signal; represents the mixing coefficient, and ;

[0026] Step 2.6: Calculate using formula (6) and f a ( u [ n ] ) exist u [ n ] = u x i The KL divergence when ;

[0027] D CL ( p || f a ) = ∑ i = 1 M [ p ( u x i )ln p ( u x i ) − p ( u x i )ln f a ( u x i ) ] (6)

[0028] Step 2.7: Use formula (7) to solve the optimal variance , the optimal shape parameter and the optimal mixing coefficient ;

[0029] (7)

[0030] Step 2.8: Use formula (8) to get the received signal { u [ n ] | n = 1 ,..., N } The optimal probability density function f ( u [ n ] ) ;

[0031] f ( u [ n ] ) = 1 − ε on 2 πσ on 2 e x p ( − u [ n ] 2 2 σ on 2 ) + ε on 2 b e − | u [ n ] | b on (8).

[0032] Further, the step 3 is performed as follows:

[0033] Step 3.1: Calculate the optimal probability density function of the received signal f ( u [ n ] ) The derivative of f ′ ( u [ n ]) ;

[0034] Step 3.2: Use formula (9) to u [ n ] Perform nonlinear transformation to obtain The received signal after nonlinear transformation at time g [ n ] ;

[0035] g [ n ] = { ( 1 − ε on ) u [ n ] 2 π σ on 3 e − u [ n ] 2 2 σ on 2 + ε on 2 b on 2 e − u [ n ] b on 1 − ε on 2 π σ on e − u [ n ] 2 2 σ on 2 + ε on 2 b on e − u [ n ] b on , u [ n ] > 0 0 , u [ n ] = 0 ( 1 − ε on ) u [ n ] 2 π σ on 3 e − u [ n ] 2 2 σ on 2 − ε on 2 b on 2 e − u [ n ] b on 1 − ε on 2 π σ on e − u [ n ] 2 2 σ on 2 + ε on 2 b on e u [ n ] b on , u [ n ] < 0 (9).

[0036] An electronic device of the present invention includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the weak signal robust detection method, and the processor is configured to execute the program stored in the memory.

[0037] The present invention provides a computer-readable storage medium, wherein a computer program is stored on the computer-readable storage medium, and the computer program executes the steps of the weak signal robust detection method when the computer program is executed by a processor.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention adopts a new probability density function to characterize the probability density characteristics of reverberation, and on this basis performs a nonlinear transformation on the received signal to construct a detector, thereby reducing the influence of the fluctuation of the reverberation probability density on signal detection and improving the robustness of weak signal detection in the reverberation background.

[0040] 2. The present invention uses KL divergence to characterize the difference between the new probability density function and the actual probability density function of the received signal, and solves the parameters of the new probability density function by minimizing the KL divergence, thereby reducing the amount of calculation for parameter solution and improving the detection speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A detection structure diagram of the detection method used in the present invention;

[0042] Figure 2 A detection flow chart of the detection method used in the present invention;

[0043] Figure 3 This is the experimental result diagram when the reverberation is assumed to obey the SαS distribution model;

[0044] Figure 4 This is a graph of experimental results when the reverberation is assumed to obey the mixed Gaussian distribution model. DETAILED DESCRIPTION

[0045] In this embodiment, a method for robustly detecting weak signals in the context of ocean reverberation is applied to a receiver of an underwater acoustic detection device. The detection method used in the present invention detects a structure such as Figure 1 As shown, after the transmitter of the detection device transmits a signal, the receiver obtains the received signal, calculates the probability density function of the received signal, performs nonlinear transformation on the received signal, obtains the detection statistic, compares it with the detection threshold, and completes the signal detection. Specifically, Figure 2 As shown, the robust detection method of weak signals under the reverberation background is carried out in the following steps:

[0046] Step 1: Get the signal received by the receiver in the reverberation background { u [ n ] | n = 1 ,..., N } ,in, u [ n ] Represents the reverberation background The received signal at the time instant, and u [ n ] = A s [ n ] + ω [ n ] ,in, s [ n ] Indicates The transmission signal at that moment, Indicates the amplitude of the echo signal, ω [ n ] Indicates The reverberation signal at that moment, represents the total time. For example, when When , it indicates that there is a target echo, which can be regarded as the multiplication of the transmitted signal and the echo amplitude. When , it indicates that there is no echo signal, and there is only reverberation in the received signal. Signal detection is to determine whether there is an echo signal in the received signal.

[0047] Step 2.1: Get the received signal { u [ n ] | n = 1 ,..., N } Minimum value of and maximum value , and the interval length is , will receive the signal { u [ n ] | n = 1 ,..., N } Divide into equally spaced intervals; is the total number of intervals.

[0048] Step 2.2: Calculate the The center value of the interval , ;

[0049] (1)

[0050] Step 2.3: Use formula (2) to calculate Falling within the range u [ n ] number , Reflects u [ n ] Fall into The probability of an interval, The larger the value, the u [ n ] The greater the probability of falling into this range;

[0051] k i = ∑ n = 1 N φ ( u x i , u [ n ] ) (2)

[0052] In formula (2), φ ( u x i , u [ n ] ) To judge u [ n ] Whether it falls into intervals, and have:

[0053] φ ( u x i , u [ n ] ) = { 1 ， | u [ n ] − u x i | ≤ u maximum − u bad M 0 ， | u [ n ] − u x i | > u maximum − u bad M (3)

[0054] Step 2.4: Calculate using formula (4) The probability of ;

[0055] (4) In formula (4), is a discrete value, which represents the The probability of an interval, if the interval is small enough, It can also be regarded as the first The center value of the interval The probability of .

[0056] Step 2.5: Use formula (5) to construct the received signal { u [ n ] | n = 1 ,..., N } The initial probability density function f a ( u [ n ] ) ;

[0057] f a ( u [ n ] ) = 1 − ε 2 πσ 2 e x p ( − u [ n ] 2 2 σ 2 ) + ε 2 b e − | u [ n ] | b (5)

[0058] In formula (5), Characterizes the variance of the reverberation signal; Characterize the shape parameters of the reverberation signal; represents the mixing coefficient, and ; The probability density function shown in formula (5) is given by , as well as It is certain that different parameter values ​​lead to different fitting effects, and the parameter values ​​need to be optimized.

[0059] Step 2.6: Calculate using formula (6) and f a ( u [ n ] ) exist u [ n ] = u x i The KL divergence when , KL divergence can quantitatively express the similarity between two probability density functions;

[0060] D CL ( p || f a ) = ∑ i = 1 M [ p ( u x i )ln p ( u x i ) − p ( u x i )ln f a ( u x i ) ] (6)

[0061] Step 2.7: Minimize the KL divergence value and use formula (7) to solve the optimal variance , the optimal shape parameter and the optimal mixing coefficient ;

[0062] (7)

[0063] Step 2.8: Use formula (8) to get the received signal { u [ n ] | n = 1 ,..., N } The optimal probability density function f ( u [ n ] ) ;

[0064] f ( u [ n ] ) = 1 − ε on 2 πσ on 2 e x p ( − u [ n ] 2 2 σ on 2 ) + ε on 2 b e − | u [ n ] | b on (8)

[0065] Step 3: u [ n ] Transform and obtain The received signal after the transformation g [ n ] ;

[0066] Step 3.1: Calculate the optimal probability density function of the received signal f ( u [ n ] ) The derivative of f ′ ( u [ n ]) ;

[0067] Step 3.2: Use formula (9) to u [ n ] Perform nonlinear transformation to obtain The received signal after nonlinear transformation at time g [ n ] ;

[0068] g [ n ] = - f ′ ( u [ n ]) f ( u [ n ]) { ( 1 − ε on ) u [ n ] 2 π σ on 3 e − u [ n ] 2 2 σ on 2 + ε on 2 b on 2 e − u [ n ] b on 1 − ε on 2 π σ on e − u [ n ] 2 2 σ on 2 + ε on 2 b on e − u [ n ] b on , u [ n ] > 0 0 , u [ n ] = 0 ( 1 − ε on ) u [ n ] 2 π σ on 3 e − u [ n ] 2 2 σ on 2 − ε on 2 b on 2 e − u [ n ] b on 1 − ε on 2 π σ on e − u [ n ] 2 2 σ on 2 + ε on 2 b on e u [ n ] b on , u [ n ] < 0 (9)

[0069] Step 4: Use formula (10) to construct the test statistic :

[0070] T = ∑ n = 1 N s [ n ] g [ n ] (10)

[0071] Step 5: If , it means that the receiver receives the target's echo signal at time N, otherwise, it means that it does not receive the target's echo signal; where, It is called the detection threshold.

[0072] In this embodiment, an electronic device includes a memory and a processor, wherein the memory is used to store a program that supports the processor to execute the above method, and the processor is configured to execute the program stored in the memory.

[0073] In this embodiment, a computer-readable storage medium stores a computer program on the computer-readable storage medium, and the computer program executes the steps of the above method when executed by a processor.

[0074] Experimental results:

[0075] On December 15, 2024, using the actual ocean reverberation data of underwater detection equipment, artificially adding target echo signals, and conducting signal detection experiments, the experimental results are as follows: Figure 3 , Figure 4 In the experiment, the signal-to-noise ratio was changed by adjusting the amplitude of the echo signal. A total of 1000 experiments were conducted. The number of times the test statistic was greater than the threshold during the 1000 detections was recorded as Md, and the detection probability was Md / 1000. Figure 3 and Figure 4 It can be seen that, regardless of assuming that the ocean reverberation obeys the SαS distribution or the mixed Gaussian distribution, the detection performance of the detection method of the present invention is similar to the performance of the local optimal detector under the model distribution, which reflects the robustness of the detection method of the present invention.

Claims

1. A method for robust detection of weak signals in an ocean reverberation background, characterized in that: Proceed as follows: Step 1: Get the signal received by the receiver in the reverberation background ,in, Represents the background of reverberation The received signal at the time instant, and ,in, Indicates The transmission signal at a certain moment, Indicates the echo signal amplitude, Indicates The reverberation signal at that moment, Indicates the total time; Step 2: Get the received signal The optimal probability density function ; Step 3: Transform and obtain The received signal after the transformation ; Step 4: Use formula (10) to construct the test statistic : (10) Step 5: If , it means that the receiver receives the target's echo signal at time N, otherwise, it means that it does not receive the target's echo signal; where, It is called the detection threshold.

2. The method for robust detection of weak signals in an ocean reverberation background according to claim 1, characterized in that: Described step 2 is carried out as follows: Step 2.1: Get the received signal Minimum value of and maximum value , and the interval length is , will receive the signal Divide into equally spaced intervals; is the total number of intervals; Step 2.2: Calculate the The center value of the interval , ; (1) Step 2.3: Use formula (2) to calculate The number of received signals falling within the interval ; (2) In formula (2), To judge Whether it falls into intervals, and have: (3) Step 2.4: Calculate using formula (4) The probability of ; (4) Step 2.5: Use formula (5) to construct the received signal The initial probability density function ; (5) In formula (5), Characterizes the variance of the reverberation signal; Characterize the shape parameters of the reverberation signal; represents the mixing coefficient, and ; Step 2.6: Calculate using formula (6) and exist The KL divergence when ; (6) Step 2.7: Use formula (7) to solve the optimal variance , the optimal shape parameter and the optimal mixing coefficient ; (7) Step 2.8: Use formula (8) to get the received signal The optimal probability density function ; (8)。 3. The method for robust detection of weak signals in an ocean reverberation background according to claim 2, characterized in that: The step 3 is carried out as follows: Step 3.1: Calculate the optimal probability density function of the received signal The derivative of ; Step 3.2: Use formula (9) to Perform nonlinear transformation to obtain The received signal after nonlinear transformation at time ; (9)。 4. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute any one of the weak signal robust detection methods in claims 1-3, and the processor is configured to execute the program stored in the memory.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the weak signal robust detection method according to any one of claims 1 to 3 are executed.

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