CN115017940B - Target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis - Google Patents
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Abstract
The invention relates to a target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis, which comprises the following two parts: decomposing an obtained signal possibly containing a target by using an EMD method, performing correlation test on the obtained IMF components of each order and environmental noise, and regarding the IMF components with weak correlation as the order possibly containing the target and extracting; and secondly, suppressing environmental noise in the screened IMF component by adopting a spectrum analysis method so as to obtain a clearer target component for target detection. When the method is used for detecting the target in water, the characteristic different from the environmental noise is extracted from the characteristic of the target radiation noise, compared with the traditional mode relying on energy detection, the method is less interfered by the fluctuation of the marine environmental noise, does not need long-time observation, has good timeliness, and is more adaptive to the target detection in various marine environments and various practical conditions.
Description
Technical Field
The invention belongs to the field of underwater sound detection, relates to a target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis, and particularly relates to a target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis.
Background
With the development of submarine silencing materials and silencing technologies, the detection difficulty of underwater sound target radiation noise is increased. Conventional passive target detection can improve the detection rate by increasing the observation time and continuously observing the change of the acoustic energy of a target water area, but the method has poor timeliness and is easily influenced by environmental fluctuation. The spatial spectrum can be obtained by solving the energy of each path of beam output signal by a space domain beam forming method, but the method is limited by the size of a receiving array in actual use, and has low target resolution and poor weak target detection performance. Therefore, with the continuous progress of the underwater target stealth technology and the background noise rise brought by the gradual prosperity of the marine shipping industry, the energy-based target detection method is more and more difficult to detect the underwater target. Although the total power of the target radiation noise in the water is reduced, some characteristics still exist for detection and identification. The characteristics of the targets in the water are closely related to the power propulsion mode, the propeller structure and the appearance structure, and the characteristics are necessarily existed, so the target detection method based on the characteristics is a new mainstream.
A novel time-frequency treatment method, an empirical mode decomposition method (EMPIRICAL MODE DECOMPOSITION, EMD), was proposed by N.E. Huang et al, 1998. This approach is considered a major breakthrough in contrast to fourier transform-based linear and steady-state spectral analysis, which relies on the time-scale characteristics of the data itself to perform signal decomposition without the need for any prior set of basis functions. This is essentially different from the wavelet decomposition method based on the fourier decomposition of the a priori harmonic basis functions and the wavelet basis functions. Because of the characteristics, the empirical mode decomposition method can be theoretically applied to the decomposition of any type of signals, has obvious advantages in processing non-stationary and non-linear data, is suitable for analyzing non-linear and non-stationary signal sequences, and has high signal-to-noise ratio gain. Therefore, once the empirical mode decomposition method is proposed, the empirical mode decomposition method is rapidly and effectively applied to different engineering fields, such as ocean, atmosphere and celestial body observation data and seismic record analysis, mechanical fault diagnosis, damping identification of a dense frequency power system and mode parameter identification of a large civil engineering structure.
The high-order statistics are statistics with orders larger than second order, and mainly include contents such as high-order moment, high-order cumulant, and high-order cumulant spectrum (short for high-order spectrum). In the late eighties of the twentieth century, with the development of computer technology, high order statistics have been widely used in the fields of radar, sonar, communication, oceanography, astronomy, electromagnetics, plasma, crystallography, geophysics, biomedicine, fault diagnosis, vibration analysis, and fluid dynamics. The outstanding advantages are as follows: (1) suppressing the effect of gaussian color noise; (2) Identifying a non-causal, non-minimum phase system or reconstructing a non-minimum phase signal; (3) extracting various information due to gaussian deviation; (4) Checking and characterizing nonlinearities in the signal and identifying a nonlinear system; (5) Cyclostationarity in the signal is checked and characterized and the cyclostationary signal is analyzed and processed. Since the high-order cumulant contains a large amount of abundant information which is not available in the second-order statistics (power spectrum and correlation function), the high-order cumulant is used for extracting or recovering and enhancing harmonic signals from a noise environment, and is a field which is very interesting for researchers. In the field of signal processing, the high-order accumulation is widely applied to the aspects of signal detection, channel equalization, parameter estimation, array processing, disease diagnosis, target classification and identification and the like.
Disclosure of Invention
Technical problem to be solved
In order to avoid the defects of the prior art, the invention provides a target detection method based on empirical mode decomposition and spectrum analysis, which solves the problem that the simple energy detection cannot play a role in actual combat in the environment that the signal level of an underwater target is weaker and the noise interference of the marine environment is greater.
Technical proposal
A target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis is characterized by comprising the following steps:
step 1: the EMD method is adopted to decompose the signal fragments in the water possibly containing the target, the original signal is extracted by the IMF of the n-order and the residual error, and the signal is expressed as follows after being decomposed by the empirical mode:
Wherein: x (t) is an original signal, d (t) is an IMF component obtained by decomposition, and r (t) is a residual error;
the signal to be decomposed satisfies three conditions:
1. the signal has at least two extrema, a maximum and a minimum;
2. the characteristic time scale is determined by the time interval between the extremums;
3. if the data has no extremum but contains inflection points, differentiating the data once or more times to obtain extremum, and obtaining a final result through integration;
The extracted IMF component satisfies two conditions:
1. The number of local extreme points and zero crossings of the signal to be decomposed must be equal or differ by at most one over the whole time range;
2. At any point in time, the average of the envelope of the local maximum, i.e. the upper envelope, and the envelope of the local minimum, i.e. the lower envelope, must be zero;
Step 2: filtering the obtained IMF component of order n to obtain IMF component containing target information,
(1) Solving the correlation coefficient rho of each IMF component and the acquired environmental noise n (t)
(2) The obtained n groups of correlation coefficients are subjected to size judgment, the threshold value is the standard deviation of the group of correlation coefficients, IMF components corresponding to the correlation coefficients with the phase relation number smaller than the standard deviation are regarded as components with targets possibly existing, and the components are added and output;
the standard deviation δ of the correlation coefficient ρ is:
Step 3: performing spectrum analysis on the screened IMF component to obtain a characteristic spectrum of target radiation noise in water, and taking the characteristic spectrum as target detection;
step 4: taking a Nawman-Pearson criterion as an example to perform target detection; under the condition of no target, collecting 100 environmental noise samples, respectively extracting high-order spectral density functions of the environmental noise samples, calculating Gao Jiepu powers in a specified frequency band, sequencing the high-order spectral powers of the 100 samples from large to small, and taking the 5 th high-order spectral power as a detection threshold lambda if a given false alarm is 0.05;
Under the scene with the possible targets, extracting high-order spectrum characteristics from the received signal according to the steps, calculating Gao Jiepu power in a specified frequency band, judging that the targets are present if the power is larger than a threshold lambda, and judging that the targets are not present if the power is smaller than lambda.
The specific process of extracting IMF components from given signals in the EMD method is as follows:
1. fitting all local maximum points through a cubic spline interpolation function to form an upper envelope, and repeating the steps on the local minimum points to generate a lower envelope; calculating the average value of the upper envelope and the lower envelope, and marking the average value as m 1 (t);
2. Subtracting the envelope mean m 1 (t) from the original signal X (t) gives a new sequence h 1 (t):
h1＝X(t)-m1(t)
3. If the new data h 1 (t) generated at this time still has negative local maximum value and positive local minimum value points, repeating the steps by taking h 1 (t) as an original signal; h 1 (t) was noted as m 11 (t) for the upper and lower envelope mean and h 11 (t) for the newly generated sequence:
h11(t)＝h1(t)-m11(t)
The iterative process can be written as:
h1n(t)＝h1(n-1)(t)-m1n(t)
Taking the standard deviation Sd of two continuous processing results as a condition for judging whether iteration of the screening process is ended or not:
For Sd, the value range of Huang is 0.2-0.3;
4. taking h 1n (t) meeting the condition as first-order IMF, marking as d (t), subtracting d (t) from the original signal X (t) to obtain a residual error r (t), repeating the process until the IMF can not be extracted from the signal, and terminating the decomposition process;
The signals after empirical mode decomposition can be expressed as:
I.e. the original signal X (t) is composed of IMF of order n and residual error.
The spectrum analysis is carried out on the screened IMF components, and the specific process is as follows:
1. dividing the screened IMF component into K sections, wherein the length of each section is M, and marking as:
{x1,x2,…,xN＝KM}
2. De-equalizing each segment;
3. Calculating a diagonal slice c (τ) of the third-order cumulative amount of each segment after the de-equalization:
Where i=1, 2,..k, s 1＝max(0,-τ),s2 =min (M-1, M-1- τ)
4. C (i) (τ) for the K segments is averaged, namely:
5. And carrying out one-dimensional Fourier transform on to obtain a/> -dimensional spectrum of the filtered IMF component.
Advantageous effects
The invention provides a target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis, which comprises the following two parts: decomposing an obtained signal possibly containing a target by using an EMD method, performing correlation test on the obtained IMF components of each order and environmental noise, and regarding the IMF components with weak correlation as the order possibly containing the target and extracting; and secondly, suppressing environmental noise in the screened IMF component by adopting a spectrum analysis method so as to obtain a clearer target component for target detection.
When the method is used for detecting the target in water, the characteristic different from the environmental noise is extracted from the characteristic of the target radiation noise, compared with the traditional mode relying on energy detection, the method is less interfered by the fluctuation of the marine environmental noise, does not need long-time observation, has good timeliness, and is more adaptive to the target detection in various marine environments and various practical conditions.
Drawings
Fig. 1: overall system block diagram
Detailed Description
The invention will now be further described with reference to examples, figures:
The target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis is characterized by comprising the following steps of: (1) Detecting the characteristic difference between the target radiation noise and the environmental noise in water, and being applicable under the condition of low target radiation noise energy; (2) The high-order spectrum analysis method is used for suppressing the environmental noise, so that the detected targets are easier to separate, and the detection probability and the follow-up target classification and identification are improved.
The specific steps of the invention are as follows:
Step one: the EMD method is used to decompose signal fragments that may contain the target.
The IMF component in the EMD method needs to satisfy two conditions: (1) The number of local extreme points and zero crossings of the signal to be decomposed must be equal or differ by at most one over the whole time range; (2) At any point in time, the envelope of the local maxima (upper envelope) and the envelope of the local minima (lower envelope) must be zero on average.
The signal to be decomposed must also satisfy the following three assumptions: (1) The signal has at least two extrema, a maximum and a minimum; (2) The characteristic time scale is determined by the time interval between the extremums; (3) If the data has no extremum at all, but contains an inflection point, it can be differentiated one or more times to find the extremum. The final result may be obtained by integration.
The specific process of extracting IMF components from a given signal in the EMD method is as follows:
(1) After all extreme point positions are determined, all local maximum points are fitted through a cubic spline interpolation function to form an upper envelope. Repeating this step for local minima points to generate a lower envelope; the mean of the upper and lower envelopes was calculated and noted as m 1 (t).
(2) Subtracting the envelope mean value m 1 (t) from the original signal X (t) to obtain a new sequence h 1 (t).
h1＝X(t)-m1(t) (1)
(3) If the new data h 1 (t) generated at this time still has negative local maxima and positive local minima points, the above steps should be repeated using h 1 (t) as the original signal. The average value of the upper envelope and the lower envelope of h 1 (t) is m 11 (t), and the newly generated sequence is h 11 (t).
h11(t)＝h1(t)-m11(t) (2)
If h 11 (t) does not meet the IMF condition, the screening is continued until the requirement is met, and the n iterative processes of the screening can be described as follows:
h1n(t)＝h1(n-1)(t)-m1n(t) (3)
Whether the iteration of the screening process is terminated or not is based on the standard deviation of two consecutive processing results, namely:
for Sd, the recommended value range of Huang is between 0.2 and 0.3.
(3) The h 1n (t) output satisfying the condition is denoted as the first order IMF, and is denoted as d (t). Subtracting d (t) from the original signal X (t) to obtain a residual error r (t). This process is repeated until IMFs are no longer extractable from the signal, terminating the decomposition process.
After the signals are decomposed by empirical mode, d (t) can be expressed as:
I.e. the original signal consists of an IMF of order n and a residual error.
Step two: and screening the obtained IMF component of the n order.
The basic idea of the EMD method can be summarized as: a wave with irregular frequency is decomposed into a plurality of wave plus residual waves with single frequency from high to low. The features according to which the object is detected are hidden in the IMF components of the series of different frequencies, so that the obtained IMF components of the series need to be filtered to obtain IMF components that may contain the object information.
The obtained n-order IMF component is screened, and the specific process is as follows:
(1) And solving a correlation coefficient of each IMF component and the acquired environmental noise n (t).
The correlation coefficient is defined as:
(2) The obtained n groups of correlation coefficients are subjected to size determination, and the threshold value of the n groups of correlation coefficients can be taken as the threshold value by the standard deviation of the group of correlation coefficients. The IMF components corresponding to the correlation coefficient smaller than the standard deviation are regarded as components where targets may exist, added and output.
The standard deviation of the correlation coefficient can be defined as:
step three: and performing high-order spectrum analysis on the screened IMF components.
The central limit theorem in statistics states that: under very wide conditions, the distribution of the sum of N statistically independent random variables tends to be Gaussian in the limit of N.fwdarw.infinity. The marine noise is formed by overlapping the radiation noise of a large number of noise sources, and the noise sources are uncorrelated with each other, so that the amplitude distribution of the noise sources is Gaussian. While the target in water is a non-Gaussian nonlinear signal, the high order statistic is a powerful tool for researching the non-Gaussian nonlinear signal, and the calculated amount of the high order statistic can be increased along with the increase of the order, so that the high order statistic has some difficulties in the practical application process. The spectrum is used as a simplified algorithm of double-spectrum analysis in the high-order statistic, so that the advantages of the high-order statistic are maintained, the calculation is simplified, and the practical engineering application is facilitated. The/> spectrum analysis method is used for inhibiting Gaussian distribution environmental noise, so that the characteristic spectrum with the detection signal can be highlighted, and the detection and the identification are convenient.
The third order cumulative amount C 3x(τ1,τ2) of the signal x (t) the one-dimensional fourier transform of the diagonal slice C 3x(τ,τ)(τ1＝τ2 =τ) is defined as the -dimensional spectrum C (ω) of the signal.
Performing spectrum analysis on the screened IMF components, wherein the specific process is as follows:
(1) The IMF component is screened out and divided into K segments, each segment having a length M, denoted { x 1,x2,…,xN＝KM }.
(2) De-equalizing each segment;
(3) Diagonal slice for calculating third-order cumulant of each segment
Where i=1, 2,..k, s 1＝max(0,-τ),s2 =min (M-1, M-1- τ)
(4) C (i) (τ) for k segments is averaged, namely:
(5) And carrying out one-dimensional Fourier transform on to obtain a/> -dimensional spectrum of the screened IMF component.
The characteristic spectrum of the target radiation noise in the water is obtained, and the target detection and subsequent classification recognition work can be completed on the basis of the characteristic spectrum, wherein the detection method can be selected from a Nawman-Pearson criterion, a maximum natural criterion, a Bayesian criterion and the like.
The invention is described in detail below with reference to the drawings and the detailed description. The method comprises the following specific steps:
Step one: collecting an environmental noise signal, and recording the environmental noise signal as n (t); there may be a signal of the target, denoted X (t).
Step two: the signal X (t) where a target may be present is decomposed using the EMD method.
After determining the positions of all extreme points of the signal X (t) possibly with the target, fitting all local maximum points through a cubic spline interpolation function to form an upper envelope. Repeating this step for local minima points to generate a lower envelope; the mean of the upper and lower envelopes was calculated and noted as m 1 (t).
Subtracting the envelope mean m 1 (t) from X (t) gives a new sequence h 1 (t).
h1＝X(t)-m1(t) (11)
If the new data h 1 (t) generated at this time still has negative local maxima and positive local minima points, the above steps should be repeated using h 1 (t) as the original signal. The average value of the upper envelope and the lower envelope of h 1 (t) is m 11 (t), and the newly generated sequence is h 11 (t).
h11(t)＝h1(t)-m11(t) (12)
If h 11 (t) does not meet the IMF condition, the screening is continued until the requirement is met, and the n iterative processes of the screening can be described as follows:
h1n(t)＝h1(n-1)(t)-m1n(t) (13)
Whether the iteration of the screening process is terminated or not is based on the standard deviation of two consecutive processing results, namely:
for Sd, the recommended value range of Huang is between 0.2 and 0.3.
The h 1n (t) output satisfying the condition is denoted as the first order IMF, and is denoted as d (t). Subtracting d (t) from the original signal X (t) to obtain a residual error r (t). This process is repeated until IMFs are no longer extractable from the signal, terminating the decomposition process.
The signal X (t) where a target may be present, after empirical mode decomposition, may represent d (t) as:
I.e. by IMF of order n and residual error.
Step three: and (3) respectively solving correlation coefficients of the acquired environmental noise and the n-order IMF components obtained in the step two.
The obtained n groups of correlation coefficients are subjected to size determination, and the threshold value of the n groups of correlation coefficients can be taken as the threshold value by the standard deviation of the group of correlation coefficients.
The IMF components corresponding to the correlation coefficient smaller than the standard deviation are regarded as components where targets may exist, added and output.
Step four: and performing high-order spectrum analysis on the screened IMF components.
The IMF component is screened out and divided into K segments, each segment having a length M, denoted { x 1,x2,…,xN＝KM }.
De-equalizing each segment;
Diagonal slice for calculating third-order cumulant of each segment
Where i=1, 2,..k, s 1＝max(0,-τ),s2 =min (M-1, M-1- τ)
C (i) (τ) for k segments is averaged, namely:
And carrying out one-dimensional Fourier transform on to obtain a/> -dimensional spectrum of the screened IMF component. Thus, the target characteristic spectrum in the water is obtained, and the target detection and subsequent classification and identification work can be completed. The flow chart of the specific steps of the invention is shown in figure 1.
Step five: and detecting whether the target exists or not according to the obtained high-order spectrum characteristics.
Target detection is here exemplified by the neman-pearson criterion. Under the condition of no target, collecting 100 environmental noise samples, respectively extracting high-order spectral density functions of the environmental noise samples, calculating Gao Jiepu powers in a specified frequency band, sequencing the high-order spectral powers of the 100 samples from large to small, and taking the 5 th high-order spectral power as a detection threshold lambda if a given false alarm is 0.05.
Under the scene with the possible targets, extracting high-order spectrum characteristics from the received signal according to the steps, calculating Gao Jiepu power in a specified frequency band, judging that the targets are present if the power is larger than a threshold lambda, and judging that the targets are not present if the power is smaller than lambda.
Claims (3)
1. A target detection method based on empirical mode decomposition and 1 (1/2) spectrum analysis is characterized by comprising the following steps:
Step 1: the EMD method is adopted to decompose the signal fragments in the water possibly containing the target, the original signal is extracted by the IMF of the n-order and the residual error, and the signal is expressed as follows after being decomposed by the empirical mode:
Wherein: x (t) is an original signal, d (t) is an IMF component obtained by decomposition, and r (t) is a residual error;
the signal to be decomposed satisfies three conditions:
1. the signal has at least two extrema, a maximum and a minimum;
2. the characteristic time scale is determined by the time interval between the extremums;
3. if the data has no extremum but contains inflection points, differentiating the data once or more times to obtain extremum, and obtaining a final result through integration;
The extracted IMF component satisfies two conditions:
1. The number of local extreme points and zero crossings of the signal to be decomposed must be equal or differ by at most one over the whole time range;
2. At any point in time, the average of the envelope of the local maximum, i.e. the upper envelope, and the envelope of the local minimum, i.e. the lower envelope, must be zero;
Step 2: filtering the obtained IMF component of order n to obtain IMF component containing target information,
(1) Solving the correlation coefficient rho of each IMF component and the acquired environmental noise n (t)
(2) The obtained n groups of correlation coefficients are subjected to size judgment, the threshold value is the standard deviation of the group of correlation coefficients, IMF components corresponding to the correlation coefficients with the phase relation number smaller than the standard deviation are regarded as components with targets possibly existing, and the components are added and output;
the standard deviation δ of the correlation coefficient ρ is:
Step 3: performing spectrum analysis on the screened IMF component to obtain a characteristic spectrum of target radiation noise in water, and taking the characteristic spectrum as target detection;
Step 4: taking a Nawman-Pearson criterion as an example to perform target detection; under the condition of no target, collecting 100 environmental noise samples, respectively extracting high-order spectral density functions of the environmental noise samples, calculating Gao Jiepu powers in a specified frequency band, sequencing the high-order spectral powers of the 100 samples from large to small, and taking the 5 th high-order spectral power as a detection threshold lambda if a given false alarm is 0.05;
Under the scene with the possible targets, extracting high-order spectrum characteristics from the received signal according to the steps, calculating Gao Jiepu power in a specified frequency band, judging that the targets are present if the power is larger than a threshold lambda, and judging that the targets are not present if the power is smaller than lambda.
2. The method for detecting the target based on empirical mode decomposition and 1 (1/2) spectrum analysis according to claim 1, wherein: the specific process of extracting IMF components from given signals in the EMD method is as follows:
1. fitting all local maximum points through a cubic spline interpolation function to form an upper envelope, and repeating the steps on the local minimum points to generate a lower envelope; calculating the average value of the upper envelope and the lower envelope, and marking the average value as m 1 (t);
2. Subtracting the envelope mean m 1 (t) from the original signal X (t) gives a new sequence h 1 (t):
h1＝X(t)-m1(t)
3. if the new data h 1 (t) generated at this time still has negative local maximum value and positive local minimum value points, repeating the steps by taking h 1 (t) as an original signal; h 1 (t) was noted as m 11 (t) for the upper and lower envelope mean and h 11 (t) for the newly generated sequence:
h11(t)＝h1(t)-m11(t)
The iterative process can be written as:
h1n(t)＝h1(n-1)(t)-m1n(t)
Taking the standard deviation Sd of two continuous processing results as a condition for judging whether iteration of the screening process is ended or not:
For Sd, the value range of Huang is 0.2-0.3;
4. taking h 1n (t) meeting the condition as first-order IMF, marking as d (t), subtracting d (t) from the original signal X (t) to obtain a residual error r (t), repeating the process until the IMF can not be extracted from the signal, and terminating the decomposition process;
The signals after empirical mode decomposition can be expressed as:
I.e. the original signal X (t) is composed of IMF of order n and residual error.
3. The method for detecting the target based on empirical mode decomposition and 1 (1/2) spectrum analysis according to claim 1, wherein: the spectrum analysis is carried out on the screened IMF components, and the specific process is as follows:
1. dividing the screened IMF component into K sections, wherein the length of each section is M, and marking as:
{x1,x2,…,xN＝KM}
2. De-equalizing each segment;
3. Calculating a diagonal slice c (τ) of the third-order cumulative amount of each segment after the de-equalization:
Where i=1, 2,..k, s 1＝max(0,-τ),s2 =min (M-1, M-1- τ)
4. C (i) (τ) for the K segments is averaged, namely:
5. And carrying out one-dimensional Fourier transform on to obtain a/> -dimensional spectrum of the filtered IMF component.
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