CN115017940A - Target detection method based on empirical mode decomposition and 1(1/2) spectrum analysis - Google Patents
Target detection method based on empirical mode decomposition and 1(1/2) spectrum analysis Download PDFInfo
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Abstract
The invention relates to a target detection method based on empirical mode decomposition and 1(1/2) spectral analysis, which comprises two parts: firstly, decomposing an obtained signal possibly containing a target by using an EMD method, carrying out correlation test on obtained IMF components of each order and environmental noise, and taking the IMF component with weak correlation as an order possibly containing the target and extracting; secondly, adopt
And the spectral analysis method suppresses the environmental noise in the screened IMF components to obtain clearer target components for target detection. When the method is used for detecting the underwater target, the characteristics different from the environmental noise are extracted from the characteristics of the target radiation noise, compared with the traditional mode depending on energy detection, the method is less interfered by the fluctuation of the marine environmental noise and does not need to be carried out for a long timeThe method has good observation and timeliness, and has better adaptability to target detection in various marine environments and various actual conditions.
Description
Technical Field
The invention belongs to the field of underwater acoustic detection, and relates to a target detection method based on empirical mode decomposition and 1(1/2) spectrum analysis, in particular 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 difficulty in detecting the underwater sound target radiation noise is increasing day by day. The conventional passive target detection can improve the detection rate by increasing the observation time and continuously observing the sound energy change of the target water area, but the method has poor timeliness and is easily influenced by environmental fluctuation. The energy of each path of beam output signals can be obtained through a space domain beam forming method to obtain a space spectrum, but the method is limited by the size of a receiving array in actual use, the target resolution is low, and the weak target detection performance is poor. Therefore, with the continuous progress of the underwater target hiding technology and the background noise rise caused by the increasing prosperity of the ocean shipping industry, the underwater target is more and more difficult to detect by the energy-based target detection method. Although the total power of the target radiation noise in water is weakened, there still exist some characteristics for detection and identification. The characteristics of the underwater target are closely related to the power propulsion mode, the propeller structure and the appearance structure of the underwater target, and the characteristics are necessarily existed, so that the target detection method based on the characteristics becomes a new mainstream.
N.e. huang et al proposed a novel time-frequency processing method, Empirical Mode Decomposition (EMD), in 1998. The method is considered as a great breakthrough from linear and steady-state spectrum analysis based on Fourier transform, and the method carries out signal decomposition according to the time scale characteristics of data per se without presetting any basis function. This is fundamentally different from the wavelet decomposition methods that are built on the fourier decomposition of the harmonic basis functions and the wavelet basis functions a priori. Due to the characteristics, the empirical mode decomposition method can be theoretically applied to the decomposition of any type of signals, so that the method has very obvious advantages in processing non-stationary and non-linear data, is suitable for analyzing non-linear and non-stationary signal sequences, and has very high signal-to-noise ratio gain. Therefore, once the empirical mode decomposition method is proposed, the empirical mode decomposition method can be 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 modal parameter identification of a large civil engineering structure.
The high-order statistics refer to statistics with orders greater than the second order, and mainly include contents such as high-order moments, high-order cumulants, high-order cumulant spectrums (short for high-order spectrums). In the late eighties of the twentieth century, with the development of computer technology, high-order statistics have been widely applied in the fields of radar, sonar, communication, oceanography, astronomy, electromagnetism, plasma, crystallography, geophysical, biomedicine, fault diagnosis, vibration analysis and fluid dynamics. Its outstanding advantage has: (1) suppressing the influence of Gaussian color noise; (2) identifying a non-causal, non-minimum phase system or reconstructing a non-minimum phase signal; (3) extracting various information caused by Gaussian deviation; (4) verifying and characterizing nonlinearities in the signal and identifying a nonlinear system; (5) checking and characterizing cyclostationarity in the signal and analyzing and processing the cyclostationary signal. Because the high-order cumulant contains a large amount of abundant information which is not contained in the second-order statistic (power spectrum and correlation function), the high-order cumulant is used for extracting or recovering and enhancing harmonic signals from a noise environment, and the method is a field which is very interested by researchers. In the field of signal processing, high-order cumulant is widely applied to aspects such as 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 method for decomposing and decomposing based on empirical mode
The target detection method of spectral analysis solves the problem that the detection simply by energy can not play a role in actual combat under the environment that underwater target signal level is weaker and interference of ocean environment noise is larger and weaker.
Technical scheme
A target detection method based on empirical mode decomposition and 1(1/2) spectral analysis is characterized by comprising the following steps:
step 1: decomposing a signal fragment possibly containing a target in water by adopting an EMD method, extracting an original signal from n-order IMF and a residual error, and expressing the signal after empirical mode decomposition as follows:
wherein: x (t) is the original signal, d (t) is the IMF component obtained by decomposition, and r (t) is the residual error;
the signal to be decomposed satisfies three conditions:
1. the signal has at least two extreme values, a maximum value and a minimum value;
2. the characteristic time scale is determined by the time interval between the extreme values;
3. if the data has no extreme value at all but contains inflection points, carrying out one or more differentiation on the data to obtain an extreme value, and finally obtaining a result through integration;
the extracted IMF component satisfies two conditions:
1. in the whole time range of the signal to be decomposed, the number of local extreme points and the number of zero-crossing points must be equal, or at most one difference exists;
2. at any time point, the envelope of the local maximum value, namely the upper envelope line, and the envelope of the local minimum value, namely the lower envelope line, must be zero on average;
and 2, step: screening the obtained n-order IMF components to obtain IMF components containing target information,
(1) obtaining the correlation coefficient rho of each order IMF component and the collected environment noise n (t)
(2) Carrying out size judgment on the obtained n groups of correlation coefficients, taking the threshold value as the standard deviation of the group of correlation coefficients, and taking IMF components with the correlation numbers smaller than the standard deviation as components with possible targets to be added and output;
the standard deviation δ of the correlation coefficient ρ is:
and step 3: the screened IMF components are processed
Performing spectrum analysis to obtain a characteristic frequency spectrum of target radiation noise in water, and taking the characteristic frequency spectrum as target detection;
and 4, step 4: taking the Naeman-Pearson criterion as an example to carry out target detection; under the condition of no target, collecting 100 times of environmental noise samples, respectively extracting high-order spectral density functions of the environmental noise samples, calculating high-order spectral power in a specified frequency band, sequencing the high-order spectral power 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 targets, extracting high-order spectral features of the received signals according to the steps, calculating high-order spectral power in the specified frequency band, judging that the targets exist if the high-order spectral power is larger than a threshold lambda, and judging that no target exists if the high-order spectral power is smaller than the threshold lambda.
The specific process of extracting the IMF component from the given signal in the EMD method is as follows:
1. fitting all local maximum values through a cubic spline interpolation function to form an upper envelope, and repeating the step on the local minimum values to generate a lower envelope; calculating the mean value of the upper and lower envelopes, and recording as m 1 (t)；
2. Subtracting the envelope mean m from the original signal X (t) 1 (t) obtaining a new sequence h 1 (t)：
h 1 ＝X(t)-m 1 (t)
3. If new data h is generated at this time 1 (t) there are still negative local maxima and positive local minima points, then h should be assigned 1 (t) repeating the above steps as the original signal; remember h 1 (t) the upper and lower envelope means is m 11 (t), newly generating sequenceIs listed as h 11 (t)：
h 11 (t)＝h 1 (t)-m 11 (t)
This iterative process can be written as:
h 1n (t)＝h 1(n-1) (t)-m 1n (t)
taking the standard deviation Sd of two continuous processing results as a condition for judging whether the iteration of the screening process is terminated:
for Sd, the value range of Huang is 0.2-0.3;
4. h will satisfy the condition 1n (t) outputting a first-order IMF, which is recorded 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;
after empirical mode decomposition, the signal can be expressed as:
namely, the original signal x (t) is composed of an IMF of n-th order and a residual.
The screened IMF components are processed
The spectrum analysis comprises the following specific processes:
1. dividing the screened IMF components into K segments, wherein the length of each segment is M and is recorded as:
{x 1 ,x 2 ,…,x N＝KM }
2. averaging each segment;
3. calculating the diagonal slice c (τ) of the third-order cumulant of each segment after the averaging:
wherein i is 1,2 1 ＝max(0,-τ),s 2 ＝min(M-1,M-1-τ)
4. C for K fragments (i) (τ) averaging, i.e.:
5. to pair
Performing one-dimensional Fourier transform to obtain IMF components after screening
And (5) performing a dimensional spectrum.
Advantageous effects
The invention provides a target detection method based on empirical mode decomposition and 1(1/2) spectrum analysis, which comprises two parts: firstly, decomposing an obtained signal possibly containing a target by using an EMD method, carrying out correlation test on obtained IMF components of various orders and environmental noise, and taking the IMF components with weak correlation as orders possibly containing the target and extracting; secondly, adopt
And the spectral analysis method suppresses the environmental noise in the screened IMF components to obtain clearer target components for target detection.
When the method is used for detecting the underwater target, the characteristics different from environmental noise are extracted from the characteristics of the target radiation noise, compared with the traditional mode depending on energy detection, the method is less interfered by the fluctuation of the marine environmental noise, does not need to be observed for a long time, has good timeliness, and has better adaptability to the target detection in various marine environments and various practical situations.
Drawings
FIG. 1: general block diagram of system
Detailed Description
The invention will now be further described with reference to the following examples and drawings:
the target detection method based on empirical mode decomposition and 1(1/2) spectral analysis is characterized in that: (1) the method is used for detecting the characteristic difference between target radiation noise and environmental noise in water, and is still suitable for the condition that the target radiation noise energy is low; (2) and a high-order spectrum analysis method is used for inhibiting environmental noise, so that the detected targets are easier to separate, and the detection probability and the subsequent classification and identification of the targets are improved.
The method comprises the following specific steps:
the method comprises the following steps: the EMD method is used to decompose the signal fragment that may contain the target.
The IMF component in the EMD method needs to satisfy two conditions: (1) in the whole time range of the signal to be decomposed, the number of local extreme points and the number of zero-crossing points must be equal, or at most one difference exists; (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, on average, zero.
The signal to be decomposed at the same time must also satisfy the following three assumptions: (1) the signal has at least two extreme values, a maximum value and a minimum value; (2) the characteristic time scale is determined by the time interval between the extreme values; (3) if the data is completely without extreme values but contains inflection points, it can be differentiated one or more times to find the extreme value. The final result can be obtained by integration.
The specific process of extracting the IMF component from the given signal in the EMD method is as follows:
(1) and after all extreme value points are determined, fitting all local maximum value points through a cubic spline interpolation function to form an upper envelope. Repeating this step for the local minima points to generate a lower envelope; calculating the mean value of the upper and lower envelopes, denoted as m 1 (t)。
(2) Subtracting the envelope mean m from the original signal X (t) 1 (t) obtaining a new sequence h 1 (t)。
h 1 ＝X(t)-m 1 (t) (1)
(3) If new data h is generated at this time 1 (t) there are still negative local maxima and positive local minima points, then h should be assigned 1 (t) repeating the above steps as the original signal. Remember h 1 (t) the upper and lower envelope means is m 11 (t) the newly generated sequence is denoted as h 11 (t)。
h 11 (t)＝h 1 (t)-m 11 (t) (2)
If h 11 (t) if the IMF condition is not satisfied, the screening is continued until the IMF condition is satisfied, and the n iterative processes of the screening can be described as:
h 1n (t)＝h 1(n-1) (t)-m 1n (t) (3)
whether the iteration of the screening process is terminated or not is determined according to the standard deviation of two continuous processing results, namely:
for Sd, the recommended value range of Huang is 0.2-0.3.
(3) H will satisfy the condition 1n (t) output as first order IMF, denoted d (t). Subtracting d (t) from the original signal X (t) to obtain a residual error r (t). This process is repeated until no more IMF can be extracted from the signal, terminating the decomposition process.
After empirical mode decomposition, the signal can be expressed as d (t) is:
i.e. the original signal is composed of an IMF of order n and a residual.
Step two: and screening the obtained n-order IMF components.
The basic idea of the EMD method can be summarized as follows: a wave with irregular frequency is decomposed into a plurality of waves with single frequency from high to low and a residual wave. The characteristics of the target detection basis of the invention are hidden in the IMF components of the series of different frequencies, so that the obtained IMF components of the series need to be screened to obtain the IMF components possibly containing target information.
Screening the obtained n-order IMF components, wherein the specific process is as follows:
(1) and (3) calculating a correlation coefficient between each order IMF component and the acquired environmental noise n (t).
The correlation coefficient is defined as:
(2) the obtained n sets of correlation coefficients are subjected to size determination, and the threshold value of the obtained n sets of correlation coefficients can be defined as a standard deviation of the set of correlation coefficients. And adding and outputting the IMF components corresponding to the relation numbers smaller than the standard deviation as components in which the target possibly exists.
The standard deviation of the correlation coefficient can be defined as:
step three: and performing high-order spectral analysis on the screened IMF components.
The central limit theorem in statistics states that: under very broad conditions, the distribution of the sum of N statistically independent random variables tends to be gaussian with the limit of N → ∞. The marine environmental noise is formed by overlapping radiation noise of a large number of noise sources, and the noise sources are not related with each other, so that the amplitude distribution of the marine environmental noise is Gaussian. The target in water is a non-Gaussian nonlinear signal, and the high-order statistic is a powerful tool for researching the non-Gaussian nonlinear signal, but the calculation amount of the non-Gaussian nonlinear signal increases along with the increase of the order, so that some difficulties exist in the practical application process.
The spectrum is used as a simplified algorithm of double-spectrum analysis in the high-order statistics, so that the advantages of the high-order statistics are reserved, the calculation is simplified, and the practical engineering application is facilitated. By using
The spectrum analysis method inhibits the environmental noise of Gaussian distribution, can highlight the characteristic spectrum with detection signals and is convenient to detect and identify.
Third order cumulant C of signal x (t) 3x (τ 1 ,τ 2 ) Diagonal slice C 3x (τ,τ)(τ 1 ＝τ 2 τ) is defined as the one-dimensional fourier transform of the signal
The dimension spectrum C (ω).
The screened IMF components are processed
The spectrum analysis comprises the following specific processes:
(1) dividing the screened IMF components into K segments, wherein the length of each segment is M, and marking as { x 1 ,x 2 ,…,x N＝KM }。
(2) Averaging each segment;
(3) diagonal slice for calculating third-order cumulant of each segment
Wherein i is 1,2 1 ＝max(0,-τ),s 2 ＝min(M-1,M-1-τ)
(4) C for k segments (i) (τ) averaging, i.e.:
(5) to pair
Making a one-dimensional FourierTransforming to obtain IMF components after screening
And (5) performing a dimensional spectrum.
Thus, the characteristic frequency spectrum of the target radiation noise in the water is obtained, and target detection and subsequent classification and identification can be completed on the basis of the characteristic frequency spectrum.
The invention is described in detail below with reference to the figures and the specific embodiments. The method comprises the following specific steps:
the method comprises the following steps: collecting an environmental noise signal, which is recorded as n (t); there may be a signal of interest, denoted x (t).
Step two: the EMD method is used to decompose the signal x (t) where the target may be present.
After all extreme point positions of the signal X (t) where the target possibly exists are determined, all local maximum point positions are fitted through a cubic spline interpolation function to form an upper envelope. Repeating this step for the local minima points to generate a lower envelope; calculating the mean value of the upper and lower envelopes, and recording as m 1 (t)。
Subtracting the envelope mean m from X (t) 1 (t), a new sequence h can be obtained 1 (t)。
h 1 ＝X(t)-m 1 (t) (11)
If new data h is generated at this time 1 (t) there are still negative local maxima and positive local minima points, then h should be assigned 1 (t) repeating the above steps as the original signal. Remember h 1 (t) the upper and lower envelope means is m 11 (t) the newly generated sequence is denoted as h 11 (t)。
h 11 (t)＝h 1 (t)-m 11 (t) (12)
If h 11 (t) if the IMF condition is not satisfied, the screening is continued until the IMF condition is satisfied, and the n iterative processes of the screening can be described as:
h 1n (t)＝h 1(n-1) (t)-m 1n (t) (13)
whether the iteration of the screening process is terminated or not is determined according to the standard deviation of two continuous processing results, namely:
for Sd, the recommended value range of Huang is 0.2-0.3.
H will satisfy the condition 1n (t) output as first order IMF, denoted d (t). Subtracting d (t) from the original signal X (t) to obtain a residual error r (t). This process is repeated until no more IMF can be extracted from the signal, terminating the decomposition process.
The signal x (t) where the target may be present may be empirically represented as d (t) as:
i.e. consisting of an IMF of order n and a residual.
Step three: and respectively solving the correlation coefficients of the acquired environmental noise for the n-order IMF components obtained in the step two.
The obtained n sets of correlation coefficients are subjected to size determination, and the threshold value of the obtained n sets of correlation coefficients can be defined by the standard deviation of the set of correlation coefficients.
And adding and outputting the IMF components corresponding to the relation numbers smaller than the standard deviation as components in which the target possibly exists.
Step four: and performing high-order spectral analysis on the screened IMF components.
Dividing the screened IMF components into K segments, wherein the length of each segment is M and is marked as { x 1 ,x 2 ,…,x N＝KM }。
Averaging each segment;
diagonal slice for calculating third-order cumulant of each segment
Wherein i is 1,2 1 ＝max(0,-τ),s 2 ＝min(M-1,M-1-τ)
C for k segments (i) (τ) averaging, i.e.:
to pair
Performing one-dimensional Fourier transform to obtain IMF components after screening
And (5) performing a dimensional spectrum. Thus, the target characteristic frequency spectrum in water is obtained, and target detection and subsequent classification and identification can be completed. The flow chart of the above specific steps of the present invention is shown in fig. 1.
Step five: and detecting whether the target exists or not according to the obtained high-order spectrum characteristics.
Target detection is here performed using the neman-pearson criterion as an example. Under the condition of no target, 100 times of environmental noise samples are collected, high-order spectral density functions of the environmental noise samples are respectively extracted, high-order spectral power in a specified frequency band is calculated, the high-order spectral power of the 100 samples is sorted from large to small, and if a given false alarm is 0.05, the 5 th high-order spectral power is taken as a detection threshold lambda.
Under the scene with targets, extracting high-order spectral features of the received signals according to the steps, calculating high-order spectral power in the specified frequency band, judging that the targets exist if the high-order spectral power is larger than a threshold lambda, and judging that no target exists if the high-order spectral power is smaller than the threshold lambda.
Claims (3)
1. A target detection method based on empirical mode decomposition and 1(1/2) spectral analysis is characterized by comprising the following steps:
step 1: decomposing a signal fragment possibly containing a target in water by adopting an EMD method, extracting an original signal from n-order IMF and a residual error, and expressing the signal after empirical mode decomposition as follows:
wherein: x (t) is the original signal, d (t) is the IMF component obtained by decomposition, and r (t) is the residual error;
the signal to be decomposed satisfies three conditions:
1. the signal has at least two extreme values, a maximum value and a minimum value;
2. the characteristic time scale is determined by the time interval between the extreme values;
3. if the data has no extreme value at all but contains inflection points, carrying out one or more differentiation on the data to obtain an extreme value, and finally obtaining a result through integration;
the extracted IMF component satisfies two conditions:
1. in the whole time range of the signal to be decomposed, the number of local extreme points and the number of zero-crossing points must be equal, or at most one difference exists;
2. at any time point, the envelope of the local maximum value, namely the upper envelope line, and the envelope of the local minimum value, namely the lower envelope line, must be zero on average;
step 2: screening the obtained n-order IMF components to obtain IMF components containing target information,
(1) obtaining the correlation coefficient rho of each order IMF component and the collected environment noise n (t)
(2) Carrying out size judgment on the obtained n groups of correlation coefficients, taking the threshold value as the standard deviation of the group of correlation coefficients, and taking IMF components with the correlation numbers smaller than the standard deviation as components with possible targets to be added and output;
the standard deviation δ of the correlation coefficient ρ is:
and step 3: the screened IMF components are processed
Performing spectrum analysis to obtain a characteristic frequency spectrum of target radiation noise in water, and taking the characteristic frequency spectrum as target detection;
and 4, step 4: target detection is carried out by taking a Neyman-Pearson criterion as an example; under the condition of no target, collecting 100 environmental noise samples, respectively extracting high-order spectral density functions of the environmental noise samples, calculating high-order spectral power in a specified frequency band, sequencing the high-order spectral power 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 targets, extracting high-order spectral characteristics from the received signal according to the steps, calculating high-order spectral power in the designated frequency band, if the high-order spectral characteristics are larger than a threshold lambda, judging that the target exists, and if the high-order spectral characteristics are smaller than the threshold lambda, judging that the target does not exist.
2. The method for target detection based on empirical mode decomposition and 1(1/2) spectral analysis of claim 1, wherein: the specific process of extracting the IMF component from the given signal in the EMD method is as follows:
1. fitting all local maximum value points through a cubic spline interpolation function to form an upper envelope, and repeating the step on the local minimum value points to generate a lower envelope; calculating the mean value of the upper and lower envelopes, and recording as m 1 (t)；
2. Subtracting the envelope mean m from the original signal X (t) 1 (t) obtaining a new sequence h 1 (t)：
h 1 ＝X(t)-m 1 (t)
3. If new data h is generated at this time 1 (t) there are still negative local maxima and positive local minima points, then h should be assigned 1 (t) repeating the above steps as the original signal; remember h 1 (t) the upper and lower envelope means is m 11 (t) the newly generated sequence is denoted as h 11 (t)：
h 11 (t)＝h 1 (t)-m 11 (t)
This iterative process can be written as:
h 1n (t)＝h 1(n-1) (t)-m 1n (t)
taking the standard deviation Sd of two continuous processing results as a condition for judging whether the iteration of the screening process is terminated:
for Sd, the value range of Huang is 0.2-0.3;
4. h will satisfy the condition 1n (t) outputting a first-order IMF, which is recorded 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;
after empirical mode decomposition, the signal can be expressed as:
namely, the original signal x (t) is composed of an IMF of n-th order and a residual.
3. The method for object detection based on empirical mode decomposition and 1(1/2) spectral analysis of claim 1, wherein: the screened IMF components are processed
The spectrum analysis comprises the following specific processes:
1. dividing the screened IMF components into K segments, wherein the length of each segment is M and is recorded as:
{x 1 ,x 2 ,…,x N＝KM }
2. averaging each segment;
3. calculating the diagonal slice c (τ) of the third-order cumulant of each segment after the averaging:
wherein i is 1,2 1 ＝max(0,-τ),s 2 ＝min(M-1,M-1-τ)
4. C for K fragments (i) (τ) averaging, i.e.:
5. to pair
Performing one-dimensional Fourier transform to obtain IMF components after screening
And (5) performing a dimensional spectrum.
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