CN111628750A - Nonlinear filtering method for matching stochastic resonance in trap - Google Patents

Nonlinear filtering method for matching stochastic resonance in trap Download PDF

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CN111628750A
CN111628750A CN202010416149.3A CN202010416149A CN111628750A CN 111628750 A CN111628750 A CN 111628750A CN 202010416149 A CN202010416149 A CN 202010416149A CN 111628750 A CN111628750 A CN 111628750A
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申晓红
董海涛
王海燕
锁健
刘浣琪
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Abstract

The invention provides a nonlinear filtering method for in-trap matching stochastic resonance, which is characterized by establishing a potential well constrained generalized second-order nonlinear model, deducing the matching relation of in-trap nonlinear parameters, establishing a parameter matching optimization method and improving the dynamic range of a filter frequency domain. Compared with the conventional stochastic resonance method, the method can improve the dynamic range of the frequency domain of the filter, breaks through the high sampling limit of the stochastic resonance, can improve the anti-noise performance, and greatly improves the flexibility and feasibility of the stochastic resonance in engineering application, especially for an embedded system with limited operational capability.

Description

Nonlinear filtering method for matching stochastic resonance in trap
Technical Field
The invention relates to the field of signal processing, in particular to a filtering and noise reduction method.
Background
Since the 21 st century, the world countries have increasingly competitive around the marine field in politics, economy and military, and have developed corresponding marine development strategies, and the protection, development and utilization of marine resources have become the focus of common world attention. Currently, the national core interests of China are mainly embodied in two aspects of economic development and safety interests, economic construction is a central task for reforming and opening the world, and ocean rights and interests are fundamentally guaranteed for realizing ocean power in a new period. Therefore, the research of the advanced weak signal processing method has great research value and practical significance for the detection and identification of the target in the long-distance water.
The filter is a general signal processing means for processing noise, and is widely applied in various fields, however, the filtering performance of the commonly used method is limited, and the processing capability for strong background noise is still insufficient. In recent years, a weak signal processing method of stochastic resonance has been drawing attention from domestic and foreign research institutes because of its enhanced characteristics for weak signals. The stochastic resonance is not denoised in a noise filtering way like the traditional weak signal processing method (high-order spectrum analysis, wavelet analysis, empirical mode decomposition analysis and the like), but noise is utilized, and a strong background noise signal is input into a special nonlinear system (resonance system), so that partial energy of the noise is converted into energy of the noise, the signal output is enhanced while the small noise energy is weakened, and the weak small signal detection can be effectively used.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a nonlinear filtering method for in-trap matching stochastic resonance, which is used for establishing a potential well constrained generalized second-order nonlinear model, deducing the matching relation of nonlinear parameters in a trap, establishing a parameter matching optimization method and improving the dynamic range of a filter frequency domain.
The technical scheme adopted by the invention for solving the technical problem comprises the following specific steps:
the first step is as follows: collecting sound signals in the sea by using a sonar, and recording the sound signals as g (t), namely input signals; the input signal simultaneously contains a mixture of a single-frequency line spectrum signal and a noise signal, namely:
g(t)＝s(t)+n(t) (1)
wherein s (t) ═ Acos (2 pi f)0t), A is the input signal amplitude, f0Is the input signal frequency, n (t) is the ocean background noise signal;
the second step is that: and (3) noise intensity estimation, namely respectively estimating the noise variance of each reconstructed signal by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure BDA0002495153400000021
wherein the content of the first and second substances,
Figure BDA0002495153400000022
is an estimated value of noise intensity D, N is the length of signal g (T), and T (x) is the test statistic;
the third step: constructing a second-order duffing nonlinear system:
Figure BDA0002495153400000023
wherein, x is the system output,
Figure BDA0002495153400000024
is the second derivative of x and is,
Figure BDA0002495153400000025
the first derivative of x, gamma is a damping factor, a and b are nonlinear potential parameters, and g (t) is an input signal;
the fourth step: constructing a generalized second-order matching stochastic resonance optimization model of potential well constraint:
Figure BDA0002495153400000026
wherein K is a potential well confinement factor, amatchAnd bmatchFor matching potential parameters, pi is the circumferential ratio, e is a natural constant,
Figure BDA0002495153400000027
and
Figure BDA0002495153400000028
respectively representing the optimal potential well constraint factor and damping factor, wherein the SNRI is the output signal-to-noise ratio gain;
the fifth step: initializing and setting a potential well constraint factor and a damping factor, and setting a parameter search range; wherein the region of the potential well confinement factor is
Figure BDA0002495153400000029
The search interval for the damping factor is
Figure BDA00024951534000000210
And a sixth step: and (3) performing numerical solution on the formula (3) by using a four-order Rungestota method, wherein the initial value is determined to be (0,0), and the step length h is 1/fs，fsObtaining an output sequence x for sampling frequency, calculating a signal-to-noise ratio gain value, optimizing two parameters through a genetic algorithm until the signal-to-noise ratio gain is unchanged or the iteration times are maximum to obtain an optimal value
Figure BDA00024951534000000211
And
Figure BDA00024951534000000212
the seventh step: obtaining the optimal potential well constraint factor and damping factor according to the sixth step
Figure BDA00024951534000000213
And
Figure BDA00024951534000000214
computing optimal nonlinear filter output x using a four-order Runge Kutta methodopt。
In the fourth step, the calculation of the output signal-to-noise ratio gain is as follows:
the signal-to-noise ratio SNR defines: performing N-point Discrete Fourier Transform (DFT) on input g (t) and output x to obtain power S corresponding to each frequencyiAnd i represents an arbitrary value between 1 and N, the signal-to-noise ratio is calculated as follows:
Figure BDA0002495153400000031
wherein
Figure BDA0002495153400000032
Is the frequency f of the signal s (t)0The corresponding power value;
respectively calculating the SNR of the input signal and the system output signal by using the formula (5)inAnd SNRoutThe SNR gain is then represented by the formula SNRI ═ SNRout-SNRinAnd (4) calculating.
The nonlinear filtering method for the in-trap matching stochastic resonance has the advantages that compared with a conventional stochastic resonance method, the dynamic range of a filter frequency domain can be enlarged, the high sampling limit of the stochastic resonance is broken through, the anti-noise performance can be improved, the flexibility and feasibility of the stochastic resonance in engineering application are greatly improved, and particularly, the method is suitable for an embedded system with limited operational capability.
Drawings
Figure 1 is a frequency response curve of the nonlinear filtering of the present invention.
FIG. 2 is a graph of the anti-noise response of the non-linear filtering of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
In order to overcome the defects of the prior art, the invention provides a nonlinear filtering method for in-trap matching stochastic resonance, which is used for establishing a potential well constrained generalized second-order nonlinear model, deducing the matching relation of nonlinear parameters in a trap, establishing a parameter matching optimization method and improving the dynamic range of a filter frequency domain.
The technical scheme adopted by the invention for solving the technical problems is implemented in the following specific steps:
the first step is as follows: collecting sound signals in the sea by using a sonar, and recording the sound signals as g (t), namely input signals; the input signal containing both a single-frequency line-spectrum signal and a noise signal, i.e. mixing
g(t)＝s(t)+n(t) (1)
Wherein s (t) ═ Acos (2 pi f)0t), A is the input signal amplitude, f0For the input signal frequency, n (t) is the ocean background noise signal.
The second step is that: and (3) noise intensity estimation, namely respectively estimating the noise variance of each reconstructed signal by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure BDA0002495153400000033
wherein the content of the first and second substances,
Figure BDA0002495153400000041
is an estimated value of noise intensity D, N is the length of signal g (T), and T (x) is the test statistic;
the third step: constructing a second-order duffing nonlinear system:
Figure BDA0002495153400000042
wherein, x is the system output,
Figure BDA0002495153400000043
is the second derivative of x and is,
Figure BDA0002495153400000044
is the first derivative of x, gamma is the damping factor, a, b are nonlinear potential parameters, and g (t) is the input signal.
The fourth step: constructing a generalized second-order matching stochastic resonance optimization model of potential well constraint:
Figure BDA0002495153400000045
wherein K is a potential well confinement factor, amatchAnd bmatchTo match the potential parameters, π is the circumferential ratio, e is a natural constant, with a value of about 2.71828,
Figure BDA0002495153400000046
and
Figure BDA0002495153400000047
respectively representing the optimal potential well constraint factor and the optimal damping factor, wherein the SNRI is the output signal-to-noise ratio gain, and the output signal-to-noise ratio gain is calculated by the following method:
the signal-to-noise ratio SNR defines: an N-point DFT (discrete Fourier transform) is performed on the input g (t) and the output x to obtain power S corresponding to each frequencyiAnd i represents an arbitrary value between 1 and N, the signal-to-noise ratio is calculated as follows:
Figure BDA0002495153400000048
wherein
Figure BDA0002495153400000049
Is the frequency f of the signal s (t)0The corresponding power value.
Respectively calculating the SNR of the input signal and the output signal of the systeminAnd SNRoutThe SNR gain can be given by the following equation SNRI SNRout-SNRinAnd (4) calculating.
The fifth step: initializing and setting a potential well constraint factor and a damping factor, setting a parameter search range, wherein an empirical interval of the potential well constraint factor is
Figure BDA00024951534000000410
The search interval for the damping factor is
Figure BDA00024951534000000411
And a sixth step: the four-step Runge Kutta method is used for solving the numerical value of the formula (3), the initial value is determined to be (0,0), and the step length is determinedh＝1/fs，fsObtaining an output sequence x for sampling frequency, calculating a signal-to-noise ratio gain value, optimizing two parameters through a genetic algorithm, and obtaining an optimal value when the signal-to-noise ratio gain is unchanged or the iteration times are maximum
Figure BDA00024951534000000412
And
Figure BDA00024951534000000413
the main parameter settings for genetic algorithm optimization are proposed as follows: population: 2. 100 population individuals, 10 maximum iterations, 0.95 cross probability and 0.01 mutation probability.
The seventh step: according to the optimal potential well constraint factor and damping factor
Figure BDA0002495153400000051
And
Figure BDA0002495153400000052
calculating the optimal nonlinear filter output by using a four-order Runge Kutta method, and using xoptAnd (4) showing.
The nonlinear filtering method for matching stochastic resonance in the trap can improve the filtering performance and the anti-noise performance of signals, the frequency response curve of nonlinear filtering is shown in figure 1, compared with the conventional stochastic resonance method, the dynamic range of the frequency domain of a filter can be improved, the high sampling limit of stochastic resonance is broken through, and the noise response curve of nonlinear filtering is shown in figure 2, compared with the conventional stochastic resonance method, the processing gain is improved under different noise intensities. The conventional Stochastic Resonance methods referenced in the figures are Haitao Dong, Haiyan Wang, Xiaohong Shen, et al. effects of second-ordered stored Resonance for Weak Signal Detection [ J ]. IEEEAccess,2018,6:46505-46515.
The method breaks through the high sampling limit of stochastic resonance, can improve the anti-noise performance, and greatly increases the flexibility and feasibility of the stochastic resonance in engineering application, especially for an embedded system with limited computing capability.

Claims (2)

1. A method of nonlinear filtering of in-trap matched stochastic resonance, comprising the steps of:
the first step is as follows: collecting sound signals in the sea by using a sonar, and recording the sound signals as g (t), namely input signals; the input signal simultaneously contains a mixture of a single-frequency line spectrum signal and a noise signal, namely:
g(t)＝s(t)+n(t) (1)
wherein s (t) ═ Acos (2 pi f)0t), A is the input signal amplitude, f0Is the input signal frequency, n (t) is the ocean background noise signal;
the second step is that: and (3) noise intensity estimation, namely respectively estimating the noise variance of each reconstructed signal by adopting a maximum likelihood estimation method, wherein the calculation formula is as follows:
Figure FDA0002495153390000011
wherein the content of the first and second substances,
Figure FDA0002495153390000012
is an estimated value of noise intensity D, N is the length of signal g (T), and T (x) is the test statistic;
the third step: constructing a second-order duffing nonlinear system:
Figure FDA0002495153390000013
wherein, x is the system output,
Figure FDA0002495153390000014
is the second derivative of x and is,
Figure FDA0002495153390000015
the first derivative of x, gamma is a damping factor, a and b are nonlinear potential parameters, and g (t) is an input signal;
the fourth step: constructing a generalized second-order matching stochastic resonance optimization model of potential well constraint:
Figure FDA0002495153390000016
wherein K is a potential well confinement factor, amatchAnd bmatchFor matching potential parameters, pi is the circumferential ratio, e is a natural constant,
Figure FDA0002495153390000017
and
Figure FDA0002495153390000018
respectively representing the optimal potential well constraint factor and damping factor, wherein the SNRI is the output signal-to-noise ratio gain;
the fifth step: initializing and setting a potential well constraint factor and a damping factor, and setting a parameter search range; wherein the region of the potential well confinement factor is
Figure FDA0002495153390000019
The search interval for the damping factor is
Figure FDA00024951533900000110
And a sixth step: and (3) performing numerical solution on the formula (3) by using a four-order Rungestota method, wherein the initial value is determined to be (0,0), and the step length h is 1/fs，fsObtaining an output sequence x for sampling frequency, calculating a signal-to-noise ratio gain value, optimizing two parameters through a genetic algorithm until the signal-to-noise ratio gain is unchanged or the iteration times are maximum to obtain an optimal value
Figure FDA00024951533900000111
And
Figure FDA00024951533900000112
the seventh step: obtaining the optimal potential well constraint factor and damping factor according to the sixth step
Figure FDA0002495153390000021
And
Figure FDA0002495153390000022
computing optimal nonlinear filter output x using a four-order Runge Kutta methodopt。
2. The method of claim 1, wherein the method comprises:
in the fourth step, the calculation of the output signal-to-noise ratio gain is as follows:
the signal-to-noise ratio SNR defines: performing N-point Discrete Fourier Transform (DFT) on input g (t) and output x to obtain power S corresponding to each frequencyiAnd i represents an arbitrary value between 1 and N, the signal-to-noise ratio is calculated as follows:
Figure FDA0002495153390000023
wherein Sf0Is the frequency f of the signal s (t)0The corresponding power value;
respectively calculating the SNR of the input signal and the system output signal by using the formula (5)inAnd SNRoutThe SNR gain is then represented by the formula SNRI ═ SNRout-SNRinAnd (4) calculating.
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