A non-rayleigh sonar array reverberation simulation signal generation method

Abstract

The application discloses a non-Rayleigh sonar array reverberation simulation signal generation method, relates to the technical field of ocean reverberation signal simulation, and mainly comprises the following steps: generating multiple mutually independent uniformly distributed random sequences by using an improved linear congruential generator; obtaining a random sequence of gamma distribution by an exponential distribution summation method; obtaining a sequence subject to Rayleigh distribution; and combining the random sequence of gamma distribution and the sequence subject to Rayleigh distribution to obtain a reverberation signal simulation sequence subject to K distribution. The method is suitable for simulation of reverberation signals in land testing of an active sonar system. The improved linear congruential generator and the exponential distribution summation method are adopted to reduce the calculation amount, generate the reverberation signal simulation sequence of K distribution, adapt to the trend that the reverberation signal deviates from the Rayleigh distribution and is subject to the K distribution along with the improvement of the spatial resolution of the sonar, simulate the characteristics of the reverberation signal generated during actual active sonar operation as much as possible, and improve the accuracy of ocean reverberation signal simulation.

Description

[0001] The application relates to the technical field of ocean reverberation signal simulation, and particularly relates to a non-Rayleigh sonar array reverberation simulation signal generation method. BACKGROUND

[0002] With the increasing attention of countries to marine resources, the importance of sonar technology in underwater detection is also increasing. In the development process of a sonar system, a large amount of financial resources and material resources are consumed in underwater experiments. Therefore, convenient and fast land simulation tests are applied more and more widely in the laboratory design, debugging, verification and other aspects of a sonar system. In order to ensure the accuracy of the simulation test, the echo signal of the sonar system in actual work should be reproduced on land as much as possible. For an active sonar, reverberation is an important part of the echo signal. The reverberation is the sum of all scattered waves received at the receiving point due to the scattering of a large number of irregular scatterers in the ocean to the incident sound signal. The simulation of the reverberation signal is an important part of the land test engineering of an active sonar system, and the quality directly affects the accuracy of the test of the active detection mode of the sonar. Since the scattering sources of the reverberation are numerous and the mechanism is complex, the scattering model is relatively complex and difficult to realize in engineering. At present, in the land test engineering of most sonar systems, Gaussian white noise obeying Rayleigh distribution is generally used to simulate the reverberation signal. However, researches in recent years have found that with the improvement of the spatial resolution of the sonar system, the actually measured reverberation signal gradually deviates from the Rayleigh distribution and obeys the K distribution. SUMMARY

[0003] Therefore, the application provides a non-Rayleigh sonar array reverberation simulation signal generation method, which can generate a reverberation simulation signal obeying the K distribution, can flexibly adjust the distribution parameters according to the simulation needs, adapts to the change trend that the spatial resolution of the sonar gradually improves, and improves the accuracy of the simulation result of the reverberation signal.

[0004] The technical scheme of the application is a non-Rayleigh sonar array reverberation simulation signal generation method, mainly including the following steps:

[0005] (1) generating a plurality of mutually independent uniformly distributed random sequences

[0006] An improved linear congruential generator is used to generate multiple independent uniform distribution random sequences. In order to generate multiple independent uniform distribution random sequences by linear congruential method, multiple traditional linear congruential generators are needed to repeat the iterative calculation, which occupies more resources, the independence between sequences is not high, and the pseudo-randomness is poor. An improved linear congruential generator is proposed. The generator is composed of a traditional linear congruential generator combined with a skip technique. A skip parameter is added in the parameter initialization stage. The initial value of iteration is calculated in advance by using the skip polynomial before the linear congruential method iteration according to the set skip parameter. Adjusting the skip parameter can generate multiple independent uniform distribution random sequences. The improved linear congruential generator used in this method adds a skip technique to the traditional linear congruential generator, replacing multiple traditional linear congruential generators, improving efficiency, saving computing resources, and improving the randomness of the generated sequence and the independence between sequences.

[0007] (2) Obtain a random sequence subject to gamma distribution

[0008] An exponential distribution summation method is used to calculate the random sequence subject to gamma distribution. The specified parameter gamma distribution random sequence is obtained by calculating multiple exponential distribution sequences. In order to solve the problem of complex calculation and large amount of calculation of traditional gamma distribution random sequence generation methods such as scaling method and sampling method, an exponential distribution summation method is proposed. According to the parameters of the gamma distribution sequence to be generated, the specified parameter gamma distribution random sequence is obtained by summing multiple exponential distribution sequences. The method is as follows: according to the shape parameter of the gamma distribution sequence to be generated, generate the same number of independent multiple uniform distribution random sequences; take the logarithm of the generated multiple uniform distribution random sequences and multiply them by the negative value of the scale parameter of the gamma distribution sequence to be generated to obtain multiple random sequences subject to exponential distribution; then add the corresponding elements of the multiple exponential distribution random sequences to obtain a specified parameter gamma distribution random sequence. The calculation formula is as follows:

[0009]

[0010] where γ is the shape parameter, θ is the scale parameter, U i (n)(i=1、2、...、γ) represents the i-th uniform distribution random sequence, and G(n)(n=0, 1, 2, 3,...) represents the gamma distribution random sequence.

[0011] This method can flexibly adjust the gamma distribution parameters by integer multiples while reducing the calculation complexity and the amount of calculation, and improving the efficiency of analog signal generation.

[0012] (3) Obtain a sequence subject to Rayleigh distribution

[0013] The improved linear congruential generator using the jump-in technique in step (1) generates a uniformly distributed random sequence, and two independent Gaussian white noise sequences are obtained by combining any four sequences and performing formula calculation. The two independent Gaussian white noise sequences are squared, and the results are summed and then squared to obtain a sequence that obeys Rayleigh distribution. This method reuses the uniformly distributed random sequence generated in the previous step, improving the efficiency of the simulation signal generation.

[0014] (4) The reverberation simulation signal sequence obeying K distribution is calculated by combining the gamma distribution random sequence and the Rayleigh distribution sequence

[0015] The gamma distribution random sequence is squared and multiplied by the sequence obeying Rayleigh distribution to obtain a sequence obeying K distribution. The sequence obeying K distribution is filtered by a band-pass filter with a specified center frequency and bandwidth, so that the frequency spectrum of the output signal sequence has a certain band expansion with the sonar transmission signal, and a K distribution sequence with Doppler shift is obtained. The amplitude of the K distribution sequence with Doppler shift after the band-pass filter is superimposed on the reverberation signal attenuation envelope, so that the amplitude meets the trend of gradually decaying over time, thereby obtaining a reverberation signal simulation sequence obeying K distribution. The calculation formula is as follows:

[0016]

[0017] Where G(n) is a random sequence obeying gamma distribution, y1(n) and y2(n) are two independent Gaussian white noise sequences, A K (n) is the generated K distribution sequence (n=0, 1, 2, 3,...).

[0018] This method introduces a gamma distribution random sequence based on Rayleigh distribution to simulate the reverberation signal obeying K distribution.

[0019] The technical effect of the present application is that the non-Rayleigh sonar array reverberation simulation signal generation method disclosed in the present application is suitable for simulating the reverberation signal in the land test of the active sonar system. The improved linear congruential generator using the jump-in technique and the exponential distribution summation method are used to efficiently generate the gamma distribution random sequence required for K distribution simulation, and the shape parameter and scale parameter can be flexibly adjusted according to the simulation requirements. The gamma distribution random sequence is introduced based on Rayleigh distribution to generate a reverberation signal obeying K distribution, so as to adapt to the trend of gradually improving the spatial resolution of the sonar, simulate the characteristics of the reverberation signal generated during the actual active sonar operation as much as possible, and improve the accuracy of the reverberation signal simulation. BRIEF DESCRIPTION OF DRAWINGS

[0020] The present application will be further described in detail below with reference to the accompanying drawings and exemplary embodiments.

[0021] Figure 1 This paper presents a flowchart of a method for generating a reverberation simulation signal for a non-Rayleigh sonar array according to an embodiment of this application.

[0022] Figure 2 A schematic diagram of a gamma-distributed random sequence generation method according to an embodiment of this application is shown;

[0023] Figure 3 A schematic diagram illustrating a method for generating a K-distributed reverberation signal simulation sequence according to an embodiment of this application is shown. Detailed Implementation

[0024] like Figure 1 The method for generating a reverberation simulation signal for a non-Rayleigh sonar array, as shown, mainly includes four steps: generating multiple independent uniformly distributed random sequences; obtaining a random sequence following a gamma distribution; obtaining a sequence following a Rayleigh distribution; and combining the gamma-distributed random sequence and the Rayleigh-distributed sequence to calculate a reverberation simulation signal sequence following a K-distribution. To more clearly illustrate the simulation signal generation steps and method of this application, each step is described in detail below.

[0025] (1) Generate multiple independent uniformly distributed random sequences

[0026] Based on the requirements of reverberation signal simulation, the shape parameters γ and scale parameters θ of the K-distribution and gamma distribution are determined. Based on the set parameters, an improved linear congruent generator is used to generate γ mutually independent uniformly distributed random sequences.

[0027] An improved linear congruence generator is used to obtain multiple independent uniformly distributed random sequences. This improved generator adds a skipping technique to the traditional linear congruence generator. Before the iterative calculation of the linear congruence method, the initial values ​​of the iteration are pre-calculated using a skipping polynomial. The implementation steps include:

[0028] 1) Parameter initialization phase: Initialize: multiplier a, increment c, modulus m, initial factor X0, jump parameter J;

[0029] 2) The initial values ​​for the iterative calculation using the linear congruential method are pre-calculated using the jump polynomial. The jump polynomial is expressed by the following formula:

[0030] X k =(a J X0+c(a J-1 +a J-2 +...+1))modm

[0031] Here, mod represents the remainder. To improve randomness, m is usually chosen to be a large number that satisfies the following conditions: c and m are coprime, and a-1 is a multiple of the prime factors of m. For example, if m = 2... 32 , a=1664525, c=1013904223;

[0032] 3) Calculate the result X from the jump polynomial. k As the initial value for iteration, it is substituted into the linear congruential method formula for iterative calculation. By changing the value of the jump parameter J, multiple independent uniformly distributed random sequences can be obtained. The value of the jump parameter J should be greater than the length of the previous sequence to ensure the independence between sequences. The iterative calculation formula of the linear congruential method is as follows:

[0033] X n+1 =(aX n +c)modm

[0034] Where mod represents the remainder, X n and X n+1 These represent the nth and (n+1)th elements of the sequence generated by the iterative calculation (n = 0, 1, 2, 3, ...), respectively. The meanings and values ​​of a, c, and m are consistent with those of the jump polynomial.

[0035] (2) Obtain a random sequence that follows a gamma distribution.

[0036] like Figure 2 As shown, the steps of obtaining a random sequence following a gamma distribution using the exponential distribution summation method include:

[0037] 1) Generate mutually independent uniformly distributed random sequences U1(n), U2(n), ..., U... γ Taking the logarithm of each of the n (n = 0, 1, 2, 3, ...) and multiplying it by the negative of the scaling parameter θ, we obtain the γ-path random sequences E1(n), E2(n), ..., E... that follow an exponential distribution. γ (n)(n=0, 1, 2, 3, ...), the calculation formula is as follows:

[0038] E i (n)=-θln(U i (n))(i=1, 2, ..., γ)

[0039] 2) Sum the corresponding elements of the generated γ-path random sequence that follows an exponential distribution to obtain a gamma-distributed random sequence G(n) (n = 0, 1, 2, 3, ...) with shape parameter γ and scale parameter θ. The calculation formula is as follows:

[0040]

[0041]

[0042] G(n)~Gamma(γ,θ).

[0043] (3) Obtain a random sequence that follows a Rayleigh distribution.

[0044] The uniformly distributed random sequence generated in step (1) using the improved linear congruence generator with skipping techniques is used to arbitrarily select four sequences and combine them pairwise using the formula to obtain two independent Gaussian white noise sequences. The two independent Gaussian white noise sequences are then squared, and the sum of the results is followed by a square root operation to obtain a sequence following a Rayleigh distribution. The formula for generating a Gaussian white noise sequence from two uniformly distributed random sequences is as follows:

[0045]

[0046] Where σ represents the mean square error, x1(n) and x2(n) are two uniformly distributed random sequences, and y(n) is the generated Gaussian white noise sequence.

[0047] (4) The reverberant analog signal sequence following the K distribution is obtained by combining the gamma-distributed random sequence and the Rayleigh distribution sequence.

[0048] like Figure 3 As shown, the steps for calculating a reverberant analog signal sequence following a K-distribution by combining a gamma-distributed random sequence and a Rayleigh distribution sequence include:

[0049] 1) Multiply the square root of a random sequence following a gamma distribution with a sequence following a Rayleigh distribution to obtain a sequence following a K distribution. The calculation formula is as follows:

[0050]

[0051] Where G(n) is a random sequence following a gamma distribution, y1(n) and y2(n) are two independent Gaussian white noise sequences, and A K (n) is the generated K-distributed sequence (n = 0, 1, 2, 3, ...).

[0052] 2) Based on the simulation requirements and the spectrum of the active sonar transmitted signal, design a bandpass filter with the required center frequency and bandwidth. Apply the obtained K-distributed sequence to the bandpass filter so that the spectrum of its output signal sequence has a certain bandwidth extension with the sonar transmitted signal, thus obtaining a K-distributed sequence with Doppler frequency shift.

[0053] 3) The amplitude of the K-distributed sequence with Doppler shift after passing through the bandpass filter is superimposed with the reverberation signal attenuation envelope, so that its amplitude gradually decays over time, thus obtaining a reverberation signal simulation sequence that follows a K-distribution. The formula for the reverberation attenuation envelope is as follows:

[0054]

[0055] Where R is the amplitude control parameter, β is the attenuation coefficient, and m is the power. The larger the values ​​of β and m, the faster the attenuation rate. They can be freely adjusted according to the simulation needs. R is usually taken as 1.

[0056] Through the calculations of the above four steps, the non-Rayleigh sonar array reverberation simulation signal sequence is finally obtained. The various embodiments of this application have been described above, and specific implementation methods of this application are illustrated by example.

Claims

1. A method for generating reverberation simulation signals for a non-Rayleigh sonar array. Its features include the following steps: Step 1: Generate multiple independent uniformly distributed random sequences; By using an improved linear congruence generator, and combining the traditional linear congruence generator with the skip technique, a skip parameter is added during the parameter initialization stage. The initial values ​​of the iteration are pre-calculated using the skip polynomial based on the set skip parameter. By adjusting the skip parameter, multiple independent uniformly distributed random sequences can be generated. Step 2: Obtain a random sequence that follows a gamma distribution; Logarithmic operations are performed on uniformly distributed random sequences to obtain random sequences following exponential distributions. Then, based on parameter settings, the exponential distribution summation method is used to calculate gamma-distributed random sequences with specified parameters from multiple exponentially distributed sequences. The calculation formula is as follows: in, For shape parameters, For scale parameters; Indicates the first A uniformly distributed random sequence, wherein =1,..., ; Denotes a gamma-distributed random sequence, where =0, 1, 2, 3, ...; Step 3: Obtain the sequence that follows a Rayleigh distribution; Step 4: Combine the gamma-distributed random sequence with the Rayleigh distribution sequence to calculate the reverberation analog signal sequence that follows a K-distribution. The steps include: A sequence following a K-distribution is obtained by combining a gamma-distributed random sequence with a Rayleigh-distributed sequence. The obtained K-distributed sequence is passed through a bandpass filter with a specified center frequency and bandwidth to make its spectrum have a certain frequency band extension with the sonar transmission signal, thus obtaining a K-distributed sequence with Doppler frequency shift. The amplitude of the K-distributed sequence with Doppler shift after passing through the bandpass filter is superimposed with the mixing... The reverberation signal attenuation envelope is used to obtain a simulated reverberation signal sequence that follows a K-distribution.

2. The method for generating a reverberation simulation signal for a non-Rayleigh sonar array according to claim 1, characterized in that: When obtaining a sequence that follows a Rayleigh distribution, the uniformly distributed random sequence generated in step 1 is reused to calculate the sequence that follows a Rayleigh distribution.

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