CN111985342A - Sea clutter time correlation analysis method based on empirical mode decomposition - Google Patents

Sea clutter time correlation analysis method based on empirical mode decomposition Download PDF

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CN111985342A
CN111985342A CN202010716717.1A CN202010716717A CN111985342A CN 111985342 A CN111985342 A CN 111985342A CN 202010716717 A CN202010716717 A CN 202010716717A CN 111985342 A CN111985342 A CN 111985342A
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胡居荣
高放
王丰梅
曾保
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Hohai University HHU
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Abstract

The invention discloses a sea clutter time correlation analysis method based on empirical mode decomposition, which adopts an empirical mode decomposition algorithm to drive by using the data characteristics of the empirical mode decomposition algorithm, decomposes a sea clutter into a plurality of simple waveform components and residual errors, an intrinsic mode function obtained by decomposition has different frequency characteristics, and the frequency of the intrinsic mode function is gradually reduced along with the increase of a decomposition order, so that sea clutter information under different sea conditions is represented. On the basis of an empirical mode function decomposition algorithm, Hilbert transformation is carried out on each obtained simple waveform component to obtain a time-frequency joint energy spectrum of the signal, time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum, finally, the correlation of the decomposed data is calculated by adopting a time intrinsic correlation function, and then the global correlation coefficient of the actually measured data of the sea clutter is estimated through local correlation to obtain the time correlation of the sea clutter.

Description

Sea clutter time correlation analysis method based on empirical mode decomposition
Technical Field
The invention relates to a sea clutter time correlation analysis method based on empirical mode decomposition, belongs to the technical field of signal processing, aims to analyze the characteristics of nonlinear non-stationary signals, obtains the characteristics of original signals of the nonlinear non-stationary signals, analyzes the time correlation of the original signals, and is suitable for the condition that the signals cannot be processed by a priori decomposition analysis method because the basis functions cannot be extracted from the signals.
Background
The sea clutter has a complex structure, is composed of various electromagnetic waves, has the characteristics of nonlinearity and non-stationarity, and is easily influenced by various factors such as wind speed, space floating objects, sea surface roughness, surge, radar wave incident angle and radar polarization mode.
The sea clutter signal is used as a nonlinear and non-stationary signal, when signal processing is carried out, the characteristics of the sea clutter signal are difficult to directly analyze by adopting a once-for-all method, according to a signal processing theory, a complex signal can be thinned, then the thinned signal is analyzed, so that the characteristics of the signal are approximately estimated, and the thinned signal is required to be identical to the original signal after being superposed or a large amount of characteristic information of the original signal is reserved.
Common methods comprise a short-time Fourier transform method, a continuous wavelet transform method, an S transform and the like, which are the most common analysis methods for processing nonlinear and non-stationary signals at present, but all the analysis methods have common characteristics, depend on a priori decomposition basis function and are limited by the Heisenberg inaccurate measurement principle. If the signal to be decomposed cannot extract the decomposition basis functions, the methods cannot be used, so that a plurality of limitations exist in application. According to signal processing theory, it is necessary to find a method that is similar in principle to the above several methods of processing data, but does not need to be based on a priori decomposition.
The sea clutter time correlation analysis is the correlation degree between the data of the same distance gate sea clutter along with the time change, the sea clutter time correlation reflects the clutter fluctuation characteristic, and the information such as the number, the size, the direction, the characteristics and the like of the targets can be judged according to the characteristic. The sea clutter time correlation analysis can provide prior information for setting a threshold value in the constant false alarm detection, and provides a theoretical basis for selecting the number of reference units.
Disclosure of Invention
The invention aims to solve the technical problem of overcoming the defect that the prior art needs to rely on a priori decomposition basis function when processing and calculating the time correlation of a non-linear and non-stationary signal of a sea clutter, and provides a novel sea clutter time correlation analysis method based on empirical mode decomposition and Hilbert-Huang transformation.
In order to achieve the purpose, the invention provides a sea clutter time correlation analysis method based on empirical mode decomposition, which adopts a decomposition algorithm of an empirical mode function to decompose the sea clutter into a plurality of simple waveform components and residual errors, wherein intrinsic mode functions obtained by sea clutter decomposition have different frequency characteristics;
on the basis of the decomposition algorithm of the empirical mode function, Hilbert transformation is carried out on each simple waveform component to obtain a time-frequency joint energy spectrum of the signal, and the time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum of the signal.
And calculating the correlation between the decomposed simple waveform component and the residual error by adopting a time intrinsic correlation function, and then estimating the global correlation coefficient of No. 54 sea clutter actual measurement data by local correlation to obtain the time correlation of the sea clutter.
The frequency of the eigenmode function decreases gradually as the order of the decomposition increases gradually.
Preferably, the decomposition of the sea clutter into a plurality of simple waveform components and residuals using a decomposition algorithm of empirical mode functions comprises the steps of:
step one, defining the time sequence of the sea wave as T (t), and defining the residual error of decomposition as riDefining the decomposed eigenmode function as ci(t) inputting the sea clutter signal T (t), and initializing the residual error to r0；
Step two, obtaining intrinsic mode quantity h0(t)；
Step three, identifying all extreme points of the simple waveform component, constructing an upper envelope and a lower envelope by cubic spline interpolation, and calculating an upper envelope mean value m and a lower envelope mean value mj(t)；
Step four, judging a decomposition condition SD, if the decomposition condition is met, executing step five, and if the decomposition condition is not met, executing step three;
step five, calculating the next intrinsic mode function and calculating new residual quantity;
and step six, ending if the number of the extreme points is less than 2, and updating the residual error sequence and executing the step two if the number of the extreme points is more than or equal to 2.
Preferably, the standard deviation SD of the two screening conditions is set to determine the decomposition stop condition, and the decomposition stop condition SD during decomposition can be calculated by equation (1):
Figure BDA0002598433940000021
wherein h isj-1(t) is the decomposed i +1 th eigenmode function, hi(t) is the ith eigenmode function.
Preferably, SD is between 0.2 and 0.3.
Preferably, the sea clutter is decomposed into a plurality of simple waveform components, which may be Hilbert transformed according to Hilbert transform formula (2):
Figure BDA0002598433940000022
in the formula (2), wherein cj(t) is the sequence to be transformed, xjFor the sequence after Hilbert transformation, tau is time delay, and t is time variable;
according to the definition of the instantaneous frequency, cj(t) and
Figure BDA0002598433940000031
the composable complex analytic signal is defined as zj(t) which is represented by the formula (3):
Figure BDA0002598433940000032
formula (3) is preferably expressed in exponential form as in formula (4):
Figure BDA0002598433940000033
wherein
Figure BDA0002598433940000034
Figure BDA0002598433940000035
The instantaneous frequency of the signal obtained by differentiating the formula (5) is as shown in formula (7):
Figure BDA0002598433940000036
and the original signal can be expressed as equation (8).
Figure BDA0002598433940000037
Obtaining a Hilbert amplitude expression (9) by transforming the formula (3) to the formula (9):
Figure BDA0002598433940000038
preferably, the calculating the correlation between the decomposed simple waveform component and the residual by using the temporal intrinsic correlation function includes the following steps:
two sea clutter data sets T at different time instants within a given same resolution unit1(T) and sea clutter dataset T2(T) for sea clutter data set T1(T) and sea clutter dataset T2(T) decomposing the data to obtain n IMF modes and a residual error, so as to obtain a sea clutter data set T1(T) and sea clutter dataset T2(t) may be represented by formula (10):
Figure BDA0002598433940000039
wherein i is taken to be 1 and 2,
Figure BDA00025984339400000310
represents Ti(t) a k-th order IMF component, ri(T) is Ti(t) residual after decomposition;
performing correlation solving on IMF components occupying the main characteristics of the sea clutter, wherein the size of a sliding window needs to be divided, and the size of a self-adaptive window is generally determined by using the average period of the IMF components; the average period of each IMF component may be determined according to the maximum value or the number of minimum values of the IMF component or calculated by fourier energy weighted average frequency.
Preferably, set
Figure BDA0002598433940000041
The average period of the components is
Figure BDA0002598433940000042
The average period of the components is
Figure BDA0002598433940000043
The minimum sliding window width of the correlation can be calculated by equation (11):
Figure BDA0002598433940000044
preferably, the average period of each IMF component is substituted into the TDIC algorithm to calculate the correlation between IMFs, as shown in equation (12):
Figure BDA0002598433940000045
wherein the content of the first and second substances,
Figure BDA0002598433940000046
in order to be a correlation, the correlation is,
Figure BDA0002598433940000047
is an intrinsic mode function.
The invention achieves the following beneficial effects:
the invention aims to analyze the characteristics of the non-linear non-stationary signal of the sea clutter and solve the problem of dependence on the prior decomposition basis function when the time correlation of the non-linear non-stationary signal of the sea clutter is processed and calculated;
the invention adopts an empirical mode decomposition algorithm and takes the data characteristics of the empirical mode decomposition algorithm as driving, sea clutter is decomposed into a plurality of simple waveform components and residual errors, intrinsic mode functions obtained by decomposition have different frequency characteristics, and the frequency of the intrinsic mode functions is gradually reduced along with the increase of the decomposition order, so that the sea clutter information under different sea conditions is represented. On the basis of an empirical mode function decomposition algorithm, Hilbert transform is carried out on each obtained simple waveform component to obtain a time-frequency joint energy spectrum of a signal, time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum, finally, correlation of decomposed data is calculated by adopting a correlation function, and then, the global correlation coefficient of sea clutter measured data is estimated through local correlation to obtain the time correlation of the sea clutter;
by accurately analyzing the time correlation of the sea clutter, the information such as the number of targets, the size of the targets, the judgment direction and the characteristics is obtained, prior information is provided for setting a threshold value in the constant false alarm detection, and an important geographical theory basis is provided for selecting the number of reference units.
Drawings
FIG. 1 is a flow chart of empirical mode decomposition;
fig. 2 is a HHT transformation flow diagram;
FIG. 3 is a flow chart of the invention based on empirical mode decomposition sea clutter time correlation.
Detailed Description
The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Empirical Mode Decomposition (EMPI) is called EMPI Mode Decomposition (EMD), and EMD requires the following conditions:
(1) the data to be decomposed is monotonous and at least has two extreme points, one maximum point and one minimum point;
(2) the time scale between the extreme points uniquely determines the local time domain characteristics of the data;
(3) if the data has no extreme point but has an inflection point, the data can be subjected to differential calculation for extreme value, and then the decomposition result is obtained through integration.
(4) The decomposed IMF had the following characteristics:
(5) the number of the zero crossing points subtracted from the number of the extreme points in the signal is not more than 1;
(6) the average value of the upper envelope and the lower envelope of the signal is zero.
The invention mainly aims to solve the problem of the dependence on a priori decomposition basis function when the time correlation of the non-linear and non-stationary signals of the sea clutter is calculated, firstly, the sea clutter data is processed by using an empirical mode decomposition algorithm, then, the frequency spectrum of the complex signals is analyzed by adopting Hilbert-Huang transform, and finally, the time correlation is analyzed by adopting a time intrinsic correlation method.
The method is characterized in that an empirical mode decomposition algorithm is adopted to drive by using the data characteristics of the method, the sea clutter is decomposed into a plurality of simple waveform components and residual errors, the intrinsic mode functions obtained through decomposition have different frequency characteristics, and the frequency of the intrinsic mode functions is gradually reduced along with the increase of the decomposition order, so that the sea clutter information under different sea conditions is represented. On the basis of an empirical mode function decomposition algorithm, Hilbert transformation is carried out on each obtained simple waveform component to obtain a time-frequency joint energy spectrum of the signal, time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum, finally, the correlation of the decomposed data is calculated by adopting a time intrinsic correlation function, and then the global correlation coefficient of the actually measured data of the sea clutter is estimated through local correlation to obtain the time correlation of the sea clutter.
A sea clutter time correlation analysis method based on empirical mode decomposition is characterized in that a sea clutter is decomposed into a plurality of simple waveform components and residual errors by adopting a decomposition algorithm of an empirical mode function, and intrinsic mode functions obtained by sea clutter decomposition have different frequency characteristics;
on the basis of the decomposition algorithm of the empirical mode function, Hilbert transformation is carried out on each simple waveform component to obtain a time-frequency joint energy spectrum of the signal, and the time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum of the signal.
And calculating the correlation between the decomposed simple waveform component and the residual error by adopting a time intrinsic correlation function, and then estimating the global correlation coefficient of No. 54 sea clutter actual measurement data by local correlation to obtain the time correlation of the sea clutter. The global correlation coefficient of the sea clutter actual measurement data number 54 is the prior art, and this embodiment is not described.
The frequency of the eigenmode function decreases gradually as the order of the decomposition increases gradually.
Further, the decomposition process is shown as fig. 1, and the decomposition of the sea clutter into a plurality of simple waveform components and residuals by using the decomposition algorithm of the empirical mode function includes the following steps:
step one, defining the time sequence of the sea wave as T (t), and defining the residual error of decomposition as riDefining the decomposed eigenmode function as ci(t) inputting the sea clutter signal T (t), and initializing the residual error to r0；
Step two, obtaining intrinsic mode quantity h0(t)；
Identifying all extreme points of the decomposed signals, constructing an upper envelope and a lower envelope by cubic spline interpolation, and calculating an upper envelope mean value m and a lower envelope mean value mj(t); cubic Spline Interpolation (Spline Interpolation) is abbreviated as Spline Interpolation, and is a process of obtaining a curve function set mathematically by solving a three bending moment equation set through a smooth curve of a series of shape value points;
step four, judging a decomposition condition SD, if the decomposition condition is met, executing step five, and if the decomposition condition is not met, executing step three;
step five, calculating the next intrinsic mode function and calculating new residual quantity;
and step six, ending if the number of the extreme points is less than 2, and updating the residual error sequence and executing the step two if the number of the extreme points is more than or equal to 2.
Furthermore, the decomposition has a filtering function to smooth the waveform, and the process inevitably causes some meaningful information loss, so that an IMF component only subjected to frequency modulation is obtained; in order to reduce the effective information loss and ensure that the frequency and amplitude of the decomposed component have practical significance, the decomposition stop condition can be determined by setting the standard deviation SD of the two screening conditions. The standard deviation SD of the two screening conditions is set to determine the decomposition stopping condition, and the decomposition stopping condition SD in the decomposition process can be calculated by the formula (1):
Figure BDA0002598433940000061
wherein h isj-1(t) is the decomposed i +1 th eigenmode function, hi(t) is the ith eigenmode function.
Two screening conditions refer to: two sets of conditions are required for screening when performing the EMD algorithm.
First screening conditions:
(1) the data to be decomposed is monotonous and at least has two extreme points;
(2) the data on the time dimension between two adjacent polar points uniquely determine the local characteristics of the sea clutter;
(3) data must have an inflection point if there is no extremum.
Second screening conditions:
(1) the absolute value of the number of the extreme points of the component minus the number of the zero crossing points is less than or equal to 1;
(2) the average value of the upper envelope and the lower envelope of the signal is zero.
Further, the value of SD should not be too large, and too large the signal decomposition is not thorough. The SD is not suitable to be too small, excessive decomposition can be caused if the SD is too small, the component decomposed by increasing the workload is not significant, and only resources are wasted. Usually, the decomposition process can be terminated when the value of SD is set between 0.2 and 0.3, and the value of SD in this embodiment is 0.2 or 0.3.
Further, the sea clutter is decomposed into a plurality of simple waveform components, and as shown in fig. 2, the simple waveform components may be Hilbert transformed according to Hilbert transform formula (2):
Figure BDA0002598433940000071
in the formula (2), wherein cj(t) is the sequence to be transformed, xjFor the sequence after Hilbert transformation, tau is time delay, and t is time variable;
the instantaneous frequency, defined as the inverse of the analytic signal phase, is physically representative of the rotational speed of the vector argument. In order to define the instantaneous frequency of a signal, the signal x (t) to be analyzed must first be converted into an analytic signal s (t), usually by means of a change in Hilbert, and the signal x (t) to be analyzed must first be converted into an analytic signal s (t), usually by means of a change in Hilbert, i.e. s (t) x (t) + jH [ x (t)]. According to the definition of the instantaneous frequency, cj(t) and
Figure BDA0002598433940000072
the composable complex analytic signal is defined as zj(t) which is represented by the formula (3):
Figure BDA0002598433940000073
further expressing formula (3) in exponential form as shown in formula (4):
Figure BDA0002598433940000074
wherein the content of the first and second substances,
Figure BDA0002598433940000075
Figure BDA0002598433940000076
the instantaneous frequency of the signal obtained by differentiating the formula (5) is as shown in formula (7):
Figure BDA0002598433940000077
the original signal can then be represented by equation (8):
Figure BDA0002598433940000078
obtaining a Hilbert amplitude expression (9) by transforming the formula (3) to the formula (9):
Figure BDA0002598433940000081
further, as shown in the flowchart of fig. 3, the calculating the correlation between the decomposed simple waveform component and the residual by using the time intrinsic correlation function includes the following steps:
two sea clutter data sets T at different time instants within a given same resolution unit1(T) and sea clutter dataset T2(T) for sea clutter data set T1(T) and sea clutter dataset T2(T) decomposing the data to obtain n IMF modes and a residual error, so as to obtain a sea clutter data set T1(T) and sea clutter dataset T2(t) may be represented by formula (10):
Figure BDA0002598433940000082
wherein i is taken to be 1 and 2,
Figure BDA0002598433940000083
represents Ti(t) the k-th IMF componentThe IMF component refers to the intrinsic mode function component, ri(T) is Ti(t) residual after decomposition;
performing correlation solving on IMF components occupying the main characteristics of the sea clutter, wherein the size of a sliding window needs to be divided, and the size of a self-adaptive window is generally determined by using the average period of the IMF components; the average period of each IMF component may be determined according to the maximum value or the number of minimum values of the IMF component or calculated by fourier energy weighted average frequency, which belongs to the prior art, and this embodiment is not specifically described.
Further, let
Figure BDA0002598433940000084
The average period of the components is
Figure BDA0002598433940000085
The average period of the components is
Figure BDA0002598433940000086
The minimum sliding window width of the correlation can be calculated by equation (11):
Figure BDA0002598433940000087
further, the average period of each IMF component is substituted into the TDIC algorithm to calculate the correlation between IMFs, as shown in the following equation (12):
Figure BDA0002598433940000088
wherein the content of the first and second substances,
Figure BDA0002598433940000089
in order to be a correlation, the correlation is,
Figure BDA00025984339400000810
is an intrinsic mode function.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (10)

1. A sea clutter time correlation analysis method based on empirical mode decomposition is characterized in that a sea clutter is decomposed into a plurality of simple waveform components and residual errors by adopting a decomposition algorithm of an empirical mode function, and intrinsic mode functions obtained by sea clutter decomposition have different frequency characteristics;
on the basis of the decomposition algorithm of the empirical mode function, Hilbert transformation is carried out on each simple waveform component to obtain a time-frequency joint energy spectrum of the signal, and the time-frequency energy distribution of the signal can be researched according to the time-frequency joint energy spectrum of the signal.
2. The method according to claim 1, wherein the correlation between the decomposed simple waveform component and the residual is calculated by using a temporal intrinsic correlation function, and then the time correlation of the sea clutter is obtained by estimating a global correlation coefficient of the sea clutter measured data No. 54 through local correlation.
3. The method of claim 1, wherein the frequency of the eigenmode function decreases gradually as the order of the decomposition increases.
4. The method according to claim 1, wherein the step of decomposing the sea clutter into a plurality of simple waveform components and residuals by using an empirical mode function decomposition algorithm comprises the following steps:
step one, defining the time sequence of the sea wave as T (t), and defining the residual error of decomposition as riDefining the decomposed eigenmode function as ci(t) inputting the sea clutter signal T (t), initialized residueThe difference being r0；
Step two, obtaining intrinsic mode quantity h0(t)；
Step three, identifying all extreme points of the simple waveform component, constructing an upper envelope and a lower envelope by cubic spline interpolation, and calculating an upper envelope mean value m and a lower envelope mean value mj(t)；
Step four, judging a decomposition condition SD, if the decomposition condition is met, executing step five, and if the decomposition condition is not met, executing step three;
step five, calculating the next intrinsic mode function and calculating new residual quantity;
and step six, ending if the number of the extreme points is less than 2, and updating the residual error sequence and executing the step two if the number of the extreme points is more than or equal to 2.
5. The method according to claim 4, wherein a standard deviation SD of two screening conditions is set to determine a decomposition stop condition, and the decomposition stop condition SD in the decomposition process is calculated by equation (1):
Figure FDA0002598433930000011
wherein h isj-1(t) is the decomposed i +1 th eigenmode function, hi(t) is the ith eigenmode function.
6. The method according to claim 5, wherein the value of SD is between 0.2 and 0.3.
7. The method according to claim 1, wherein the sea clutter is decomposed into a plurality of simple waveform components, and the simple waveform components are Hilbert transformed according to Hilbert transform formula (2):
Figure FDA0002598433930000021
in the formula (2), wherein cj(t) is the sequence to be transformed, xjFor the sequence after Hilbert transformation, tau is time delay, and t is time variable;
according to the definition of the instantaneous frequency, cj(t) and
Figure FDA0002598433930000022
the composable complex analytic signal is defined as zj(t) which is represented by the formula (3):
Figure FDA0002598433930000023
further expressing formula (3) in exponential form as shown in formula (4):
Figure FDA0002598433930000024
wherein
Figure FDA0002598433930000025
Figure FDA0002598433930000026
The instantaneous frequency of the signal obtained by differentiating the formula (5) is as shown in formula (7):
Figure FDA0002598433930000027
the original signal can then be represented by equation (8):
Figure FDA0002598433930000028
obtaining a Hilbert amplitude expression (9) by transforming the formula (3) to the formula (9):
Figure FDA0002598433930000029
8. the method of claim 1, wherein the step of calculating the correlation between the decomposed simple waveform component and the residual using the temporal intrinsic correlation function comprises the following steps:
two sea clutter data sets T at different time instants within a given same resolution unit1(T) and sea clutter dataset T2(T) for sea clutter data set T1(T) and sea clutter dataset T2(T) decomposing the data to obtain n IMF modes and a residual error, so as to obtain a sea clutter data set T1(T) and sea clutter dataset T2(t) may be represented by formula (10):
Figure FDA0002598433930000031
wherein i is taken to be 1 and 2,
Figure FDA0002598433930000032
represents Ti(t) a k-th order IMF component, ri(T) is Ti(t) residual after decomposition;
performing correlation solving on IMF components occupying the main characteristics of the sea clutter, wherein the size of a sliding window needs to be divided, and the size of a self-adaptive window is generally determined by using the average period of the IMF components; the average period of each IMF component may be determined according to the maximum value or the number of minimum values of the IMF component or calculated by fourier energy weighted average frequency.
9. According to claimThe method of claim 8, wherein the method comprises analyzing the time dependence of the sea clutter based on empirical mode decomposition
Figure FDA0002598433930000033
The average period of the components is
Figure FDA0002598433930000034
The average period of the components is
Figure FDA0002598433930000035
The minimum sliding window width of the correlation can be calculated by equation (11):
Figure FDA0002598433930000036
10. the method according to claim 9, wherein the average period of each IMF component is substituted into TDIC algorithm to calculate the correlation between IMFs, as shown in the following equation (12):
Figure FDA0002598433930000037
wherein the content of the first and second substances,
Figure FDA0002598433930000038
in order to be a correlation, the correlation is,
Figure FDA0002598433930000039
is an intrinsic mode function.
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