CN112559973A - Adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT - Google Patents

Adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT Download PDF

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CN112559973A
CN112559973A CN202110209363.6A CN202110209363A CN112559973A CN 112559973 A CN112559973 A CN 112559973A CN 202110209363 A CN202110209363 A CN 202110209363A CN 112559973 A CN112559973 A CN 112559973A
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陈一畅
王万田
汤子跃
孙永健
朱勇
赵园青
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Air Force Early Warning Academy
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Abstract

The invention provides an adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT, which comprises the steps of firstly realizing the optimal transformation order estimation of a linear frequency modulation component signal by a global search method based on a minimum entropy criterion, and estimating the signal amplitude of the linear frequency modulation component; secondly, estimating the instantaneous frequency of the linear frequency modulation component signal through short-time fractional Fourier transform; according to the estimated instantaneous frequency, a polynomial regression method based on linear least square estimation is adopted to realize the rough estimation of the initial frequency and the frequency modulation slope of the linear frequency modulation component signal; and then, obtaining a fine estimation result of the initial frequency and the frequency modulation slope of the linear frequency modulation component signal through frequency modulation removal, low-pass filtering and phase regression processing.

Description

Adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT
Technical Field
The invention relates to the field of communication, in particular to an adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT.
Background
Linear Frequency Modulation (LFM) signals are taken as typical non-stationary signals, have the characteristic of large time-bandwidth product, are taken as transmitting signals, adopt the pulse compression technology, can effectively solve the contradiction between the detection distance and the distance resolution, and are widely applied to the fields of radar, communication, seismic exploration and the like. Therefore, how to accurately perform parameter estimation of LFM signals, especially multi-component LFM signals, has been a major issue in the field of signal processing.
At present, most of the LFM signal parameter estimation methods are linear Time-frequency analysis methods represented by Short Time Fourier Transform (STFT) and bilinear Time-frequency analysis methods represented by Wigner-Ville Distribution (WVD). Although the STFT solves the time-dependent variation of the frequency that cannot describe the signal local in the fourier transform, it is difficult to satisfy both high time domain resolution and high frequency domain resolution, i.e., its time-frequency resolution is not high, and thus the application is limited. The WVD transforms the LFM signal to a time-frequency domain through a quadratic function, has good time-frequency resolution for the LFM signal of a single component, but has inevitable cross-term interference for the LFM signal of a plurality of components, and seriously influences the parameter estimation of the LFM signal of the plurality of components. Although many scholars improve the WVD method by adding a smoothing window function, an adaptive kernel function, and the like in order to suppress the interference of the cross terms, the time-frequency resolution is reduced.
In recent years, many researchers have been dedicated to studying methods for estimating parameters of polynomial phase signals, including the Quasi-maximum likelihood estimation (QML) method based on STFT, which is proposed in 2014 by Igor Djurovi ć et al in IET Signal Processing international journal, volume 8, phase 4, and is proposed in Quasi-maximum-likelihood estimator of polymial phase signals. Compared with the traditional methods such as a high-order fuzzy function and a product high-order fuzzy function, the method has a lower signal-to-noise ratio threshold and reaches the lower boundary of Cramer-Lo when the signal-to-noise ratio is higher, in addition, the LFM signal is used as a simple polynomial phase signal of a second order, parameter estimation can be quickly and accurately realized by the method, but the STFT has lower time-frequency resolution, the parameter estimation performance and the signal-to-noise ratio threshold are influenced, and the method can only be used for realizing the polynomial phase signal of a single component. In a paper "Review of the square-maximum likelihood estimation for a poly phase Signal" published in Digital Signal Processing international journal by Igor Djurovi ć et al in 2017, it is proposed to realize multi-component polynomial phase Signal parameter estimation by combining a STFT-based quasi-maximum likelihood estimation method with sequential elimination of estimated signals, but the method is only limited to the case that the Signal amplitudes of the components are greatly different. When the signal amplitudes of different components are not greatly different, and the instantaneous frequencies of the component signals are estimated by using the STFT, the components with the signal amplitudes which are not greatly different mutually influence, so that the estimation performance of the parameters is seriously deteriorated. In addition, the method defaults that the number of component signals is known, and a decision condition for terminating the signal parameter estimation is not given.
Disclosure of Invention
The present invention aims to provide a parameter estimation method for adaptive multi-component chirp signal based on STFrFT, which can adaptively determine whether parameter estimation is terminated and determine the number of LFM component signals in the signal.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides an adaptive multi-component linear frequency modulation signal parameter estimation method based on STFrFT, which comprises the following steps:
s1, obtaining a multi-component chirp signal
Figure 543733DEST_PATH_IMAGE001
(ii) a Assuming multi-component linear pitchFrequency signal is composed of
Figure 860314DEST_PATH_IMAGE002
The chirp component signal and the background noise component, namely:
Figure 737003DEST_PATH_IMAGE003
Figure 621782DEST_PATH_IMAGE004
wherein the content of the first and second substances,
Figure 951132DEST_PATH_IMAGE005
is shown as
Figure 150033DEST_PATH_IMAGE006
The frequency of the individual chirp component signals,
Figure 22174DEST_PATH_IMAGE007
which is representative of the background noise signal,
Figure 999226DEST_PATH_IMAGE008
、
Figure 753555DEST_PATH_IMAGE009
and
Figure 959409DEST_PATH_IMAGE010
respectively represent
Figure 234243DEST_PATH_IMAGE011
The signal amplitude, the start frequency and the chirp rate,
Figure 460825DEST_PATH_IMAGE012
represents the index of the sample point of the discrete signal, and has,
Figure 702451DEST_PATH_IMAGE013
，
Figure 305470DEST_PATH_IMAGE014
represents the total number of sample points of the discrete signal,
Figure 745679DEST_PATH_IMAGE015
which is indicative of the time of observation of the signal,
Figure 346425DEST_PATH_IMAGE016
which represents the time interval between the sampling of the samples,
Figure 13029DEST_PATH_IMAGE017
the number of the imaginary numbers is represented,
Figure 278795DEST_PATH_IMAGE018
expressed as natural constants
Figure 573510DEST_PATH_IMAGE019
An exponential operation of a base number;
s2, initializing the linear frequency modulation component signal number index
Figure 345157DEST_PATH_IMAGE020
Let the residual signal
Figure 499057DEST_PATH_IMAGE021
；
S3, the calculation corresponds to
Figure 302934DEST_PATH_IMAGE022
A signal of said chirp component
Figure 717735DEST_PATH_IMAGE023
Of the optimal transformation order
Figure 722600DEST_PATH_IMAGE024
(ii) a Firstly, judging whether the residual signal still has the linear frequency modulation component signal, if so, adopting a global search method based on a minimum entropy criterion to realize the optimal transformation order
Figure 160535DEST_PATH_IMAGE025
Otherwise, ending parameter estimation;
s4, estimating the
Figure 909048DEST_PATH_IMAGE026
A signal of said chirp component
Figure 319301DEST_PATH_IMAGE027
Signal amplitude of
Figure 354122DEST_PATH_IMAGE028
(ii) a In fractional Fourier transform, when the order is changed
Figure 341669DEST_PATH_IMAGE029
Equal to said chirp component signal
Figure 565977DEST_PATH_IMAGE030
Of the optimal transformation order
Figure 96316DEST_PATH_IMAGE031
Then, the energy of the component signal is fully accumulated, and the signal amplitude of the component is estimated according to the maximum amplitude value in the fractional Fourier transform result and the total number of signal sampling points
Figure 42318DEST_PATH_IMAGE032
Namely:
Figure 454845DEST_PATH_IMAGE033
wherein the content of the first and second substances,
Figure 545161DEST_PATH_IMAGE034
is shown as
Figure 789060DEST_PATH_IMAGE035
A signal of a linear frequency-modulated component
Figure 306629DEST_PATH_IMAGE036
Is determined by the signal amplitude estimate of (a),
Figure 144135DEST_PATH_IMAGE037
representing the order of the transformation equal to
Figure 631617DEST_PATH_IMAGE038
Time signal
Figure 198865DEST_PATH_IMAGE039
The fractional order fourier transform result vector of (a);
s5, estimating the
Figure 949652DEST_PATH_IMAGE040
A signal of said chirp component
Figure 258142DEST_PATH_IMAGE041
The instantaneous frequency of (d); obtained according to said S3
Figure 814894DEST_PATH_IMAGE042
A signal of said chirp component
Figure 886581DEST_PATH_IMAGE043
Of the optimal transformation order
Figure 808270DEST_PATH_IMAGE044
Estimating the instantaneous frequency of the signal through short-time fractional Fourier transform, wherein the calculation formula of the short-time fractional Fourier transform is as follows:
Figure 479423DEST_PATH_IMAGE045
wherein the content of the first and second substances,
Figure 590598DEST_PATH_IMAGE046
representing a transformation order of
Figure 522651DEST_PATH_IMAGE047
Time, residual signal
Figure 552924DEST_PATH_IMAGE048
The result of the short-time fractional fourier transform,
Figure 852318DEST_PATH_IMAGE049
representing the window function length of
Figure 485294DEST_PATH_IMAGE050
And has a proper Gaussian window function
Figure 350481DEST_PATH_IMAGE051
When the temperature of the water is higher than the set temperature,
Figure 692601DEST_PATH_IMAGE052
；
Figure 259718DEST_PATH_IMAGE053
representing a discrete time sequence;
Figure 978275DEST_PATH_IMAGE054
a kernel function representing a fractional Fourier transform;
the instantaneous frequency of the signal is estimated by searching for the maximum of the short-time fractional order fourier transform results at different sampling points, namely:
Figure 619341DEST_PATH_IMAGE055
Figure 991416DEST_PATH_IMAGE056
wherein the content of the first and second substances,
Figure 265403DEST_PATH_IMAGE057
is shown as
Figure 318809DEST_PATH_IMAGE058
A signal of a linear frequency-modulated component
Figure 85820DEST_PATH_IMAGE059
The instantaneous frequency of the received signal,
Figure 769742DEST_PATH_IMAGE060
representing a modulo operation;
Figure 249134DEST_PATH_IMAGE061
is a frequency variable;
s6, rough estimation
Figure 902969DEST_PATH_IMAGE062
A signal of said chirp component
Figure 800518DEST_PATH_IMAGE063
Starting frequency of
Figure 639030DEST_PATH_IMAGE064
And chirp rate
Figure 481084DEST_PATH_IMAGE065
；
Estimated signal according to the S5
Figure 79556DEST_PATH_IMAGE066
And roughly estimating the starting frequency by a polynomial regression method based on linear least squares estimation
Figure 815299DEST_PATH_IMAGE067
And chirp rate
Figure 841024DEST_PATH_IMAGE068
The solving formula is as follows:
Figure 29429DEST_PATH_IMAGE069
wherein the content of the first and second substances,
Figure 290646DEST_PATH_IMAGE070
representing the frequency of the start
Figure 162787DEST_PATH_IMAGE071
And chirp rate
Figure 282051DEST_PATH_IMAGE072
The vector of coarse estimates of (a), i.e.:
Figure 239643DEST_PATH_IMAGE073
；
Figure 976655DEST_PATH_IMAGE074
and
Figure 421411DEST_PATH_IMAGE075
respectively represent
Figure 913573DEST_PATH_IMAGE076
A signal of a linear frequency-modulated component
Figure 358460DEST_PATH_IMAGE077
Starting frequency of
Figure 554955DEST_PATH_IMAGE078
And chirp rate
Figure 260743DEST_PATH_IMAGE079
Is determined by the coarse estimation value of (c),
Figure 799172DEST_PATH_IMAGE080
which represents the operation of transposition by means of a transposition operation,
Figure 449465DEST_PATH_IMAGE081
representing an inversion operation, a matrix
Figure 652913DEST_PATH_IMAGE082
Sum vector
Figure 213208DEST_PATH_IMAGE083
Respectively as follows:
Figure 188117DEST_PATH_IMAGE084
Figure 325706DEST_PATH_IMAGE085
Figure 135442DEST_PATH_IMAGE086
Figure 612560DEST_PATH_IMAGE087
s7, fine estimation
Figure 617425DEST_PATH_IMAGE088
A signal of said chirp component
Figure 258622DEST_PATH_IMAGE089
Starting frequency of
Figure 600610DEST_PATH_IMAGE090
And chirp rate
Figure 135497DEST_PATH_IMAGE091
(ii) a Obtaining rough estimated values of the initial frequency and the frequency modulation slope according to the S6
Figure 452209DEST_PATH_IMAGE092
And
Figure 298811DEST_PATH_IMAGE093
the signals are processed by frequency-modulation removal, low-pass filtering and phase regression
Figure 726381DEST_PATH_IMAGE094
Carrying out fine estimation on the initial frequency and the frequency modulation slope;
s8, the first obtained according to the S4
Figure 709250DEST_PATH_IMAGE095
A signal amplitude estimation value of the chirp component signal and the second obtained at said S7
Figure 55917DEST_PATH_IMAGE096
The initial frequency and the fine frequency modulation slope value of the linear frequency modulation component signal are reconstructed
Figure 671706DEST_PATH_IMAGE097
A signal of a linear frequency-modulated component
Figure 621077DEST_PATH_IMAGE098
；
S9, stepping the linear frequency modulation component signal number index
Figure 864976DEST_PATH_IMAGE099
And updates the residual signal to:
Figure 257912DEST_PATH_IMAGE100
Figure 197880DEST_PATH_IMAGE101
represents the reconstructed second
Figure 826308DEST_PATH_IMAGE102
A chirp component signal;
returning to the step S3 to continue execution.
Further, the step S3 includes the following steps:
s3.1, in a half period interval
Figure 331238DEST_PATH_IMAGE103
Inter-search step size
Figure 691813DEST_PATH_IMAGE104
To discretize the transformation order to obtain
Figure 390516DEST_PATH_IMAGE105
A discrete value, i.e.
Figure 744006DEST_PATH_IMAGE106
Wherein
Figure 837864DEST_PATH_IMAGE107
Represents a vector of transform order candidate values,
Figure 556290DEST_PATH_IMAGE108
is referred to as the first
Figure 227443DEST_PATH_IMAGE109
The candidate values of the individual transformation orders are,
Figure 531428DEST_PATH_IMAGE110
which represents a rounding-down operation, the rounding-down operation,
Figure 745372DEST_PATH_IMAGE111
representing a transpose operation; initialization iteration number
Figure 634699DEST_PATH_IMAGE112
；
S3.2, calculating the order of transformation equal to
Figure 793148DEST_PATH_IMAGE113
Time residual signal
Figure 708015DEST_PATH_IMAGE114
Fractional order fourier transform of (a); the calculation formula of the fractional Fourier transform is as follows:
Figure 556891DEST_PATH_IMAGE115
wherein the content of the first and second substances,
Figure 820382DEST_PATH_IMAGE116
representing a transformation order of
Figure 607072DEST_PATH_IMAGE117
Time residual signal
Figure 778160DEST_PATH_IMAGE118
The result of the fractional order fourier transform of (a),
Figure 825750DEST_PATH_IMAGE119
the kernel function of fractional Fourier transform is represented by the following mathematical expression:
Figure 338771DEST_PATH_IMAGE120
Figure 330867DEST_PATH_IMAGE121
Figure 446590DEST_PATH_IMAGE122
which represents an integer number of times,
Figure 489633DEST_PATH_IMAGE123
indicates a rotation angle, and is provided with
Figure 909242DEST_PATH_IMAGE124
Representing a square-on operation;
s3.3, calculating the order of transformation equal to
Figure 404945DEST_PATH_IMAGE125
Time residual signal
Figure 183414DEST_PATH_IMAGE126
Entropy of the fractional fourier transform result of (a); assuming a residual signal
Figure 940018DEST_PATH_IMAGE127
The vector form of (a) is:
Figure 919475DEST_PATH_IMAGE128
wherein the content of the first and second substances,
Figure 27108DEST_PATH_IMAGE129
representing a discretized signal vector; when the transformation order candidate is
Figure 343689DEST_PATH_IMAGE130
Then, the vector form of the signal fractional order fourier transform result is:
Figure 95745DEST_PATH_IMAGE131
Figure 105158DEST_PATH_IMAGE132
the entropy of the fractional fourier transform result can be calculated by:
Figure 434508DEST_PATH_IMAGE133
wherein the content of the first and second substances,
Figure 758042DEST_PATH_IMAGE134
expressed as natural constants
Figure 426921DEST_PATH_IMAGE135
A logarithmic operation of a base number;
s3.4, step iteration number
Figure 816357DEST_PATH_IMAGE136
Judgment of
Figure 492058DEST_PATH_IMAGE137
If the result is true, entering S3.5 if the result is true, otherwise entering S3.2 to continue execution;
s3.5 each transformation order candidate may calculate an entropy value from said S3.2 and said S3.3, from which a vector of candidate values corresponding to the transformation order may be obtained
Figure 291386DEST_PATH_IMAGE138
Vector of entropy values
Figure 18034DEST_PATH_IMAGE139
Comprises the following steps:
Figure 369250DEST_PATH_IMAGE140
s3.6, normalization entropy value vector
Figure 548558DEST_PATH_IMAGE141
The mathematical formula is as follows:
Figure 151578DEST_PATH_IMAGE142
wherein the content of the first and second substances,
Figure 716420DEST_PATH_IMAGE143
represents a vector of normalized entropy values that is,
Figure 254849DEST_PATH_IMAGE144
expressing the operation of solving the maximum value; computing an entropy vector
Figure 967459DEST_PATH_IMAGE145
Variance of (2)
Figure 249536DEST_PATH_IMAGE146
The mathematical expression is as follows:
Figure 668885DEST_PATH_IMAGE147
wherein the content of the first and second substances,
Figure 378215DEST_PATH_IMAGE148
representing vectors of entropy values
Figure 572261DEST_PATH_IMAGE149
And has a mean value of
Figure 658029DEST_PATH_IMAGE150
；
Judging whether the following formula is satisfied:
Figure 931884DEST_PATH_IMAGE151
wherein the content of the first and second substances,
Figure 140012DEST_PATH_IMAGE152
a threshold, here set to 0.02, representing a determination of the presence or absence of a chirp component signal;
if the above formula is true, the residual signal is determined
Figure 577946DEST_PATH_IMAGE153
If there is a chirp component signal, continuing to execute the step S3.7; otherwise, the residual signal is determined
Figure 185514DEST_PATH_IMAGE153
If only a noise signal exists in the signal, terminating the circulation and finishing the parameter estimation;
s3.7 by vector from entropy values
Figure 579455DEST_PATH_IMAGE154
To estimate the entropy corresponding to the second
Figure 630588DEST_PATH_IMAGE155
A signal of a linear frequency-modulated component
Figure 477190DEST_PATH_IMAGE156
The optimal transformation order of (a), namely:
Figure 91711DEST_PATH_IMAGE157
。
further, the pair signal in S7
Figure 481104DEST_PATH_IMAGE158
The initial frequency and the chirp rate are precisely estimated, specifically as follows:
s7.1, frequency modulation removing: first, based on the initial frequency and the rough estimation value of the chirp rate
Figure 895948DEST_PATH_IMAGE159
And
Figure 229846DEST_PATH_IMAGE160
to reconstruct the
Figure 54583DEST_PATH_IMAGE161
A signal of a linear frequency-modulated component
Figure 439428DEST_PATH_IMAGE162
The phase conjugate term of (a), namely:
Figure 816051DEST_PATH_IMAGE163
Figure 981453DEST_PATH_IMAGE164
wherein the content of the first and second substances,
Figure 468935DEST_PATH_IMAGE165
to be reconstructed
Figure 708287DEST_PATH_IMAGE166
A signal of a linear frequency-modulated component
Figure 255812DEST_PATH_IMAGE167
The phase conjugate term of (a);
secondly, according to the reconstructed second
Figure 705248DEST_PATH_IMAGE168
A signal of a linear frequency-modulated component
Figure 12732DEST_PATH_IMAGE169
Phase conjugate term of to the residual signal
Figure 293541DEST_PATH_IMAGE170
And (3) performing frequency modulation removal treatment, wherein the specific formula is as follows:
Figure 152912DEST_PATH_IMAGE171
Figure 700698DEST_PATH_IMAGE172
wherein the content of the first and second substances,
Figure 77453DEST_PATH_IMAGE173
the residual signal after frequency modulation processing is removed;
s7.2, low-pass filtering: in order to improve the signal-to-noise ratio of the target echo, a low-pass filtering process is carried out on the signal after frequency modulation removal by adopting a moving average filter; the specific formula is as follows:
Figure 9505DEST_PATH_IMAGE174
Figure 243041DEST_PATH_IMAGE175
wherein the content of the first and second substances,
Figure 260544DEST_PATH_IMAGE176
，
Figure 909831DEST_PATH_IMAGE177
represents the length of the moving average filter;
Figure 102915DEST_PATH_IMAGE178
represents the result of the low-pass filtering process;
s7.3, phase regression treatment:
firstly, extracting the signal phase after the low-pass filtering processing, wherein the specific formula is as follows:
Figure 366406DEST_PATH_IMAGE179
Figure 933523DEST_PATH_IMAGE180
wherein the content of the first and second substances,
Figure 386501DEST_PATH_IMAGE181
representing the inverse tangent function of the arc tangentIn the calculation, the calculation is carried out,
Figure 371774DEST_PATH_IMAGE182
the imaginary part operation of the signal is expressed,
Figure 602904DEST_PATH_IMAGE183
representing the operation of taking the real part of the signal;
Figure 876891DEST_PATH_IMAGE184
representing the extracted signal phase;
the extracted signal phases are written in vector form
Figure 992615DEST_PATH_IMAGE185
Comprises the following steps:
Figure 946576DEST_PATH_IMAGE186
secondly, the polynomial regression method based on linear least square estimation is adopted to carry out phase matching on the extracted signal
Figure 551870DEST_PATH_IMAGE187
Fitting to estimate the initial frequency of the de-modulated signal
Figure 47573DEST_PATH_IMAGE188
And chirp rate
Figure 888359DEST_PATH_IMAGE189
The solution formula is as follows:
Figure 785908DEST_PATH_IMAGE190
wherein the content of the first and second substances,
Figure 358841DEST_PATH_IMAGE191
representing the estimated phase constant of the signal,
Figure 669736DEST_PATH_IMAGE192
and
Figure 986317DEST_PATH_IMAGE193
respectively representing estimated signal start frequencies
Figure 738372DEST_PATH_IMAGE194
And chirp rate
Figure 888731DEST_PATH_IMAGE195
And rest amount of
Figure 71276DEST_PATH_IMAGE196
，
Figure 207860DEST_PATH_IMAGE197
Matrix of
Figure 798110DEST_PATH_IMAGE198
Expressed as:
Figure 57053DEST_PATH_IMAGE199
wherein the content of the first and second substances,
Figure 608120DEST_PATH_IMAGE200
represents a time variable, and the mathematical expression thereof is as follows:
Figure 813973DEST_PATH_IMAGE201
Figure 461992DEST_PATH_IMAGE202
s7.4, obtaining a precise estimation value: according to the starting frequency
Figure 688574DEST_PATH_IMAGE203
And chirp rate
Figure 851571DEST_PATH_IMAGE204
Coarse estimate and estimated residualThe margin can be used to obtain a fine estimation value of the two parameters, and the solution formula is as follows:
Figure 595536DEST_PATH_IMAGE205
wherein the content of the first and second substances,
Figure 894799DEST_PATH_IMAGE206
and
Figure 682496DEST_PATH_IMAGE207
respectively represent
Figure 349100DEST_PATH_IMAGE208
Multiple multi-component chirp component signal
Figure 755811DEST_PATH_IMAGE209
Starting frequency of
Figure 253788DEST_PATH_IMAGE210
And chirp rate
Figure 687087DEST_PATH_IMAGE211
And (6) fine estimation value.
Further, the step S4
Figure 106567DEST_PATH_IMAGE212
A signal of a linear frequency-modulated component
Figure 910444DEST_PATH_IMAGE213
Signal amplitude estimate of
Figure 466190DEST_PATH_IMAGE214
And the second obtained in said S7.4
Figure 143159DEST_PATH_IMAGE215
A signal of a linear frequency-modulated component
Figure 564782DEST_PATH_IMAGE216
Start frequency ofRate accurate estimation value
Figure 454241DEST_PATH_IMAGE217
Sum chirp slope fine estimate
Figure 723548DEST_PATH_IMAGE218
To reconstruct the first
Figure 86265DEST_PATH_IMAGE219
A signal of a linear frequency-modulated component
Figure 73813DEST_PATH_IMAGE220
The concrete formula is as follows:
Figure 219492DEST_PATH_IMAGE221
Figure 749830DEST_PATH_IMAGE222
wherein the content of the first and second substances,
Figure 96498DEST_PATH_IMAGE223
represents the reconstructed second
Figure 182395DEST_PATH_IMAGE224
A chirp component signal.
The invention has the beneficial effects that: firstly, realizing the optimal transformation order estimation of a Linear Frequency Modulation (LFM) component signal by a global search method based on a minimum entropy criterion, and estimating the signal amplitude of the component; secondly, estimating the instantaneous frequency of the LFM component signal through short-time fractional Fourier transform; according to the estimated instantaneous frequency, a polynomial regression method based on linear least square estimation is adopted to realize the rough estimation of the initial frequency and the frequency modulation slope of the LFM component signal; and then, obtaining a fine estimation result of the initial frequency and the frequency modulation slope of the LFM component signal through frequency modulation removal, low-pass filtering and phase regression processing. And finally, reconstructing the LFM component signal according to the estimated signal amplitude, initial frequency and fine frequency modulation slope estimation value, and sequentially realizing parameter estimation of each LFM component signal by removing the LFM component signal from the multi-component LFM signal and circularly executing the operation. In addition, when the optimal transformation order of the LFM component signal is estimated, whether parameter estimation is terminated or not can be judged in a self-adaptive mode by calculating the variance of the entropy vector and comparing the variance with a fixed threshold value, and the number of the LFM component signals in the signal can be determined. The method is a quasi-maximum likelihood estimation, not only improves the instantaneous frequency estimation of component signals through short-time fractional Fourier transform with higher time-frequency resolution when a time-frequency spectrogram is obtained, but also reduces the influence of noise on parameter estimation through low-pass filtering processing based on a moving average filter, and has a lower signal-to-noise ratio threshold.
Drawings
Fig. 1 is a flow chart of the adaptive multi-component chirp signal parameter estimation method based on STFrFT of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Referring to fig. 1, the adaptive multi-component chirp signal parameter estimation method based on STFrFT includes the following steps:
s1, obtaining a multi-component chirp signal
Figure 413656DEST_PATH_IMAGE001
(ii) a Assuming a multi-component chirp signal consisting of
Figure 516611DEST_PATH_IMAGE002
The chirp component signal and the background noise component, namely:
Figure 971863DEST_PATH_IMAGE003
Figure 74948DEST_PATH_IMAGE225
wherein the content of the first and second substances,
Figure 703375DEST_PATH_IMAGE005
is shown as
Figure 660836DEST_PATH_IMAGE006
The frequency of the individual chirp component signals,
Figure 552569DEST_PATH_IMAGE007
which is representative of the background noise signal,
Figure 595480DEST_PATH_IMAGE008
、
Figure 965281DEST_PATH_IMAGE009
and
Figure 324718DEST_PATH_IMAGE010
respectively represent
Figure 246407DEST_PATH_IMAGE011
The signal amplitude, the start frequency and the chirp rate,
Figure 917560DEST_PATH_IMAGE012
represents the index of the sample point of the discrete signal, and has,
Figure 950107DEST_PATH_IMAGE013
，
Figure 23105DEST_PATH_IMAGE014
represents the total number of sample points of the discrete signal,
Figure 918292DEST_PATH_IMAGE015
which is indicative of the time of observation of the signal,
Figure 217686DEST_PATH_IMAGE016
which represents the time interval between the sampling of the samples,
Figure 850662DEST_PATH_IMAGE017
the number of the imaginary numbers is represented,
Figure 981429DEST_PATH_IMAGE018
expressed as natural constants
Figure 323548DEST_PATH_IMAGE019
An exponential operation of a base number;
s2, initializing the linear frequency modulation component signal number index
Figure 703714DEST_PATH_IMAGE020
Let the residual signal
Figure 343643DEST_PATH_IMAGE021
；
S3, the calculation corresponds to
Figure 391233DEST_PATH_IMAGE022
A signal of said chirp component
Figure 746997DEST_PATH_IMAGE023
Of the optimal transformation order
Figure 755404DEST_PATH_IMAGE024
(ii) a Firstly, judging whether the residual signal still has the linear frequency modulation component signal, if so, adopting a global search method based on a minimum entropy criterion to realize the optimal transformation order
Figure 871128DEST_PATH_IMAGE025
Otherwise, ending parameter estimation;
s3.1, in a half period interval
Figure 632279DEST_PATH_IMAGE103
Inter-search step size
Figure 316202DEST_PATH_IMAGE104
To discretize the transformation order to obtain
Figure 936539DEST_PATH_IMAGE105
A discrete value, i.e.
Figure 443569DEST_PATH_IMAGE106
Wherein
Figure 606697DEST_PATH_IMAGE107
Represents a vector of transform order candidate values,
Figure 179630DEST_PATH_IMAGE108
is referred to as the first
Figure 162629DEST_PATH_IMAGE109
The candidate values of the individual transformation orders are,
Figure 620156DEST_PATH_IMAGE110
which represents a rounding-down operation, the rounding-down operation,
Figure 355899DEST_PATH_IMAGE111
representing a transpose operation; initialization iteration number
Figure 381624DEST_PATH_IMAGE112
；
S3.2, calculating the order of transformation equal to
Figure 710974DEST_PATH_IMAGE113
Time residual signal
Figure 831246DEST_PATH_IMAGE114
Fractional order fourier transform of (a); the calculation formula of the fractional Fourier transform is as follows:
Figure 703387DEST_PATH_IMAGE115
wherein the content of the first and second substances,
Figure 618122DEST_PATH_IMAGE116
representing a transformation order of
Figure 575714DEST_PATH_IMAGE117
Time residual signal
Figure 640622DEST_PATH_IMAGE226
The result of the fractional order fourier transform of (a),
Figure 85379DEST_PATH_IMAGE119
the kernel function of fractional Fourier transform is represented by the following mathematical expression:
Figure 452906DEST_PATH_IMAGE120
Figure 756848DEST_PATH_IMAGE121
Figure 349416DEST_PATH_IMAGE122
which represents an integer number of times,
Figure 930570DEST_PATH_IMAGE123
indicates a rotation angle, and is provided with
Figure 593632DEST_PATH_IMAGE124
Representing a square-on operation;
s3.3, calculating the order of transformation equal to
Figure 56975DEST_PATH_IMAGE125
Time residual signal
Figure 322740DEST_PATH_IMAGE126
Entropy of the fractional fourier transform result of (a); assuming a residual signal
Figure 758400DEST_PATH_IMAGE127
The vector form of (a) is:
Figure 716998DEST_PATH_IMAGE227
wherein the content of the first and second substances,
Figure 589008DEST_PATH_IMAGE129
representing a discretized signal vector; when the transformation order candidate is
Figure 674776DEST_PATH_IMAGE130
Then, the vector form of the signal fractional order fourier transform result is:
Figure 89576DEST_PATH_IMAGE131
Figure 953496DEST_PATH_IMAGE228
the entropy of the fractional fourier transform result can be calculated by:
Figure 594693DEST_PATH_IMAGE229
wherein the content of the first and second substances,
Figure 343206DEST_PATH_IMAGE134
expressed as natural constants
Figure 489146DEST_PATH_IMAGE135
A logarithmic operation of a base number;
s3.4, step iteration number
Figure 805858DEST_PATH_IMAGE136
Judgment of
Figure 652460DEST_PATH_IMAGE137
If the result is true, entering S3.5 if the result is true, otherwise entering S3.2 to continue execution;
s3.5 each transformation order candidate may calculate an entropy value from said S3.2 and said S3.3, from which a vector of candidate values corresponding to the transformation order may be obtained
Figure 80030DEST_PATH_IMAGE138
Vector of entropy values
Figure 469423DEST_PATH_IMAGE139
Comprises the following steps:
Figure 409567DEST_PATH_IMAGE140
s3.6, normalization entropy value vector
Figure 25356DEST_PATH_IMAGE141
The mathematical formula is as follows:
Figure 115671DEST_PATH_IMAGE230
wherein the content of the first and second substances,
Figure 218625DEST_PATH_IMAGE143
represents a vector of normalized entropy values that is,
Figure 798511DEST_PATH_IMAGE144
expressing the operation of solving the maximum value; computing an entropy vector
Figure 636017DEST_PATH_IMAGE145
Variance of (2)
Figure 264445DEST_PATH_IMAGE146
The mathematical expression is as follows:
Figure 487485DEST_PATH_IMAGE147
wherein the content of the first and second substances,
Figure 316900DEST_PATH_IMAGE231
representing vectors of entropy values
Figure 427988DEST_PATH_IMAGE232
And has a mean value of
Figure 1052DEST_PATH_IMAGE233
；
Judging whether the following formula is satisfied:
Figure 265549DEST_PATH_IMAGE151
wherein the content of the first and second substances,
Figure 62603DEST_PATH_IMAGE152
a threshold, here set to 0.02, representing a determination of the presence or absence of a chirp component signal;
if the above formula is true, the residual signal is determined
Figure 874702DEST_PATH_IMAGE153
If there is a chirp component signal, continuing to execute the step S3.7; otherwise, the residual signal is determined
Figure 907248DEST_PATH_IMAGE153
If only a noise signal exists in the signal, terminating the circulation and finishing the parameter estimation;
s3.7 by vector from entropy values
Figure 104881DEST_PATH_IMAGE154
To estimate the entropy corresponding to the second
Figure 72837DEST_PATH_IMAGE155
A signal of a linear frequency-modulated component
Figure 231285DEST_PATH_IMAGE156
The optimal transformation order of (a), namely:
Figure 864261DEST_PATH_IMAGE157
。
s4, estimating the
Figure 995028DEST_PATH_IMAGE026
A signal of said chirp component
Figure 190343DEST_PATH_IMAGE027
Signal amplitude of
Figure 773771DEST_PATH_IMAGE028
(ii) a In fractional Fourier transform, when the order is changed
Figure 272754DEST_PATH_IMAGE029
Equal to said chirp component signal
Figure 195711DEST_PATH_IMAGE030
Of the optimal transformation order
Figure 567786DEST_PATH_IMAGE031
Then, the energy of the component signal is fully accumulated, and the signal amplitude of the component is estimated according to the maximum amplitude value in the fractional Fourier transform result and the total number of signal sampling points
Figure 559882DEST_PATH_IMAGE032
Namely:
Figure 816551DEST_PATH_IMAGE033
wherein the content of the first and second substances,
Figure 656331DEST_PATH_IMAGE034
is shown as
Figure 199308DEST_PATH_IMAGE035
A signal of a linear frequency-modulated component
Figure 819645DEST_PATH_IMAGE036
Is determined by the signal amplitude estimate of (a),
Figure 473480DEST_PATH_IMAGE037
representing the order of the transformation equal to
Figure 167767DEST_PATH_IMAGE038
Time signal
Figure 6279DEST_PATH_IMAGE039
The fractional order fourier transform result vector of (a);
s5, estimating the
Figure 989278DEST_PATH_IMAGE040
A signal of said chirp component
Figure 446804DEST_PATH_IMAGE041
The instantaneous frequency of (d); obtained according to said S3
Figure 182548DEST_PATH_IMAGE042
A signal of said chirp component
Figure 270590DEST_PATH_IMAGE043
Of the optimal transformation order
Figure 605799DEST_PATH_IMAGE044
Estimating the instantaneous frequency of the signal through short-time fractional Fourier transform, wherein the calculation formula of the short-time fractional Fourier transform is as follows:
Figure 804699DEST_PATH_IMAGE234
wherein the content of the first and second substances,
Figure 535895DEST_PATH_IMAGE046
representing a transformation order of
Figure 450630DEST_PATH_IMAGE047
Time, residual signal
Figure 408222DEST_PATH_IMAGE048
The result of the short-time fractional fourier transform,
Figure 207551DEST_PATH_IMAGE049
representing the window function length of
Figure 855570DEST_PATH_IMAGE050
And has a proper Gaussian window function
Figure 472365DEST_PATH_IMAGE051
When the temperature of the water is higher than the set temperature,
Figure 900941DEST_PATH_IMAGE052
；
Figure 300698DEST_PATH_IMAGE053
representing a discrete time sequence;
Figure 6486DEST_PATH_IMAGE054
a kernel function representing a fractional Fourier transform;
the instantaneous frequency of the signal is estimated by searching for the maximum of the short-time fractional order fourier transform results at different sampling points, namely:
Figure 421548DEST_PATH_IMAGE055
Figure 150469DEST_PATH_IMAGE235
wherein the content of the first and second substances,
Figure 291600DEST_PATH_IMAGE057
is shown as
Figure 710949DEST_PATH_IMAGE058
A signal of a linear frequency-modulated component
Figure 685859DEST_PATH_IMAGE059
The instantaneous frequency of the received signal,
Figure 636497DEST_PATH_IMAGE060
representing a modulo operation;
Figure 581319DEST_PATH_IMAGE061
is a frequency variable;
s6, rough estimation
Figure 855175DEST_PATH_IMAGE062
A signal of said chirp component
Figure 985DEST_PATH_IMAGE063
Starting frequency of
Figure 501237DEST_PATH_IMAGE064
And chirp rate
Figure 984171DEST_PATH_IMAGE065
；
Estimated signal according to the S5
Figure 519057DEST_PATH_IMAGE066
And roughly estimating the starting frequency by a polynomial regression method based on linear least squares estimation
Figure 553878DEST_PATH_IMAGE067
And chirp rate
Figure 682371DEST_PATH_IMAGE068
The solving formula is as follows:
Figure 968996DEST_PATH_IMAGE069
wherein the content of the first and second substances,
Figure 155127DEST_PATH_IMAGE070
representing the frequency of the start
Figure 501794DEST_PATH_IMAGE071
And chirp rate
Figure 982498DEST_PATH_IMAGE072
The vector of coarse estimates of (a), i.e.:
Figure 10496DEST_PATH_IMAGE073
；
Figure 254396DEST_PATH_IMAGE074
and
Figure 365440DEST_PATH_IMAGE075
respectively represent
Figure 468525DEST_PATH_IMAGE076
A signal of a linear frequency-modulated component
Figure 34636DEST_PATH_IMAGE077
Starting frequency of
Figure 398621DEST_PATH_IMAGE078
And chirp rate
Figure 680567DEST_PATH_IMAGE079
Is determined by the coarse estimation value of (c),
Figure 333265DEST_PATH_IMAGE080
which represents the operation of transposition by means of a transposition operation,
Figure 703067DEST_PATH_IMAGE081
representing an inversion operation, a matrix
Figure 655979DEST_PATH_IMAGE082
Sum vector
Figure 515351DEST_PATH_IMAGE083
Respectively as follows:
Figure 311137DEST_PATH_IMAGE084
Figure 671580DEST_PATH_IMAGE236
Figure 738719DEST_PATH_IMAGE237
Figure 768992DEST_PATH_IMAGE238
s7, fine estimation
Figure 786496DEST_PATH_IMAGE088
A signal of said chirp component
Figure 498100DEST_PATH_IMAGE089
Starting frequency of
Figure 566550DEST_PATH_IMAGE090
And chirp rate
Figure 767724DEST_PATH_IMAGE091
(ii) a Obtaining rough estimated values of the initial frequency and the frequency modulation slope according to the S6
Figure 272523DEST_PATH_IMAGE092
And
Figure 725502DEST_PATH_IMAGE093
the signals are processed by frequency-modulation removal, low-pass filtering and phase regression
Figure 835409DEST_PATH_IMAGE094
Carrying out fine estimation on the initial frequency and the frequency modulation slope;
the pair signal in S7
Figure 207484DEST_PATH_IMAGE158
The initial frequency and the chirp rate are precisely estimated, specifically as follows:
s7.1, frequency modulation removing: first, based on the initial frequency and the rough estimation value of the chirp rate
Figure 199580DEST_PATH_IMAGE239
And
Figure 456249DEST_PATH_IMAGE240
to reconstruct the
Figure 358346DEST_PATH_IMAGE241
A signal of a linear frequency-modulated component
Figure 760377DEST_PATH_IMAGE162
The phase conjugate term of (a), namely:
Figure 256081DEST_PATH_IMAGE242
Figure 243671DEST_PATH_IMAGE164
wherein the content of the first and second substances,
Figure 275DEST_PATH_IMAGE165
to be reconstructed
Figure 573207DEST_PATH_IMAGE166
A signal of a linear frequency-modulated component
Figure 821786DEST_PATH_IMAGE167
The phase conjugate term of (a);
secondly, according to the reconstructed second
Figure 279312DEST_PATH_IMAGE168
A signal of a linear frequency-modulated component
Figure 749477DEST_PATH_IMAGE169
Phase conjugate term of to the residual signal
Figure 40781DEST_PATH_IMAGE170
And (3) performing frequency modulation removal treatment, wherein the specific formula is as follows:
Figure 370131DEST_PATH_IMAGE171
Figure 631348DEST_PATH_IMAGE172
wherein the content of the first and second substances,
Figure 96965DEST_PATH_IMAGE173
the residual signal after frequency modulation processing is removed;
s7.2, low-pass filtering: in order to improve the signal-to-noise ratio of the target echo, a low-pass filtering process is carried out on the signal after frequency modulation removal by adopting a moving average filter; the specific formula is as follows:
Figure 277279DEST_PATH_IMAGE174
Figure 359505DEST_PATH_IMAGE243
wherein the content of the first and second substances,
Figure 158833DEST_PATH_IMAGE176
，
Figure 682218DEST_PATH_IMAGE177
represents the length of the moving average filter;
Figure 174380DEST_PATH_IMAGE178
represents the result of the low-pass filtering process;
s7.3, phase regression treatment:
firstly, extracting the signal phase after the low-pass filtering processing, wherein the specific formula is as follows:
Figure 230321DEST_PATH_IMAGE179
Figure 833341DEST_PATH_IMAGE180
wherein the content of the first and second substances,
Figure 476812DEST_PATH_IMAGE181
which represents the operation of the arctan function,
Figure 733349DEST_PATH_IMAGE182
the imaginary part operation of the signal is expressed,
Figure 665533DEST_PATH_IMAGE183
representing the operation of taking the real part of the signal;
Figure 744348DEST_PATH_IMAGE184
representing the extracted signal phase;
the extracted signal phases are written in vector form
Figure 304642DEST_PATH_IMAGE185
Comprises the following steps:
Figure 43666DEST_PATH_IMAGE186
secondly, the polynomial regression method based on linear least square estimation is adopted to carry out phase matching on the extracted signal
Figure 463146DEST_PATH_IMAGE187
Fitting to estimate the initial frequency of the de-modulated signal
Figure 407968DEST_PATH_IMAGE188
And chirp rate
Figure 822769DEST_PATH_IMAGE189
The solution formula is as follows:
Figure 827634DEST_PATH_IMAGE190
wherein the content of the first and second substances,
Figure 265569DEST_PATH_IMAGE191
representing the estimated phase constant of the signal,
Figure 748502DEST_PATH_IMAGE192
and
Figure 289248DEST_PATH_IMAGE193
respectively representing estimated signal start frequencies
Figure 199436DEST_PATH_IMAGE194
And chirp rate
Figure 46038DEST_PATH_IMAGE195
And rest amount of
Figure 270346DEST_PATH_IMAGE244
，
Figure 800684DEST_PATH_IMAGE197
Matrix of
Figure 147352DEST_PATH_IMAGE198
Expressed as:
Figure 684512DEST_PATH_IMAGE199
wherein the content of the first and second substances,
Figure 446932DEST_PATH_IMAGE200
represents a time variable, and the mathematical expression thereof is as follows:
Figure 753148DEST_PATH_IMAGE201
Figure 270718DEST_PATH_IMAGE245
s7.4, obtaining a precise estimation value: according to the starting frequency
Figure 91912DEST_PATH_IMAGE203
And chirp rate
Figure 861285DEST_PATH_IMAGE204
The coarse estimation value and the estimated residual quantity can obtain a fine estimation value of the two parameters, and the solution formula is as follows:
Figure 959691DEST_PATH_IMAGE205
wherein the content of the first and second substances,
Figure 648161DEST_PATH_IMAGE206
and
Figure 97597DEST_PATH_IMAGE207
respectively represent
Figure 382910DEST_PATH_IMAGE208
Multiple multi-component chirp component signal
Figure 460457DEST_PATH_IMAGE209
Starting frequency of
Figure 257511DEST_PATH_IMAGE210
And chirp rate
Figure 69610DEST_PATH_IMAGE211
And (6) fine estimation value.
S8, the first obtained according to the S4
Figure 305419DEST_PATH_IMAGE095
A signal amplitude estimation value of the chirp component signal and the second obtained at said S7
Figure 378417DEST_PATH_IMAGE096
The initial frequency and the fine frequency modulation slope value of the linear frequency modulation component signal are reconstructed
Figure 408690DEST_PATH_IMAGE097
A signal of a linear frequency-modulated component
Figure 613144DEST_PATH_IMAGE098
；
Obtained according to said S4
Figure 324748DEST_PATH_IMAGE212
A signal of a linear frequency-modulated component
Figure 517832DEST_PATH_IMAGE213
Signal amplitude estimate of
Figure 719006DEST_PATH_IMAGE214
And the second obtained in said S7.4
Figure 364751DEST_PATH_IMAGE215
A signal of a linear frequency-modulated component
Figure 682643DEST_PATH_IMAGE216
Fine estimation of the starting frequency of
Figure 730234DEST_PATH_IMAGE217
Sum chirp slope fine estimate
Figure 961364DEST_PATH_IMAGE218
To reconstruct the first
Figure 32088DEST_PATH_IMAGE219
A signal of a linear frequency-modulated component
Figure 288757DEST_PATH_IMAGE220
The concrete formula is as follows:
Figure 190854DEST_PATH_IMAGE246
Figure 733831DEST_PATH_IMAGE222
wherein the content of the first and second substances,
Figure 88589DEST_PATH_IMAGE223
represents the reconstructed second
Figure 945686DEST_PATH_IMAGE224
A chirp component signal.
S9, stepping the linear frequency modulation component signal number index
Figure 702290DEST_PATH_IMAGE099
And updates the residual signal to:
Figure 416168DEST_PATH_IMAGE100
Figure 523801DEST_PATH_IMAGE101
represents the reconstructed second
Figure 840382DEST_PATH_IMAGE102
A chirp component signal;
returning to the step S3 to continue execution.
1) The quasi-maximum likelihood estimation method based on short-time fractional Fourier transform is provided, the estimation precision of each component instantaneous frequency is improved through higher signal time-frequency resolution, the estimation progress of initial frequency and frequency modulation slope is further improved, and the threshold value of signal-to-noise ratio is lower;
2) because the optimal transformation orders of all LFM component signals are different, only one LFM component signal has higher time-frequency resolution in single cycle estimation by adopting short-time fractional Fourier transform, the mutual influence among all LFM component signals in instantaneous frequency estimation is removed, and a foundation is laid for realizing the parameter estimation of the multi-component LFM signal;
3) when the optimal transformation order of the LFM component signals is estimated, whether parameter estimation is terminated or not can be judged in a self-adaptive mode by calculating the variance of the entropy vector and comparing the variance with a threshold value, and the number of the LFM component signals in the signals is determined;
4) according to the estimated signal amplitude, initial frequency and frequency modulation slope, reconstructing an LFM component signal, subtracting the LFM component signal from a multi-component LFM signal, removing the influence of the LFM component signal with the parameter estimation on the LFM component signal without the parameter estimation, and sequentially realizing the parameter estimation of each LFM component signal.
The above-mentioned embodiments only express the embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.

Claims (4)

1. The adaptive multi-component chirp signal parameter estimation method based on the STFrFT is characterized by comprising the following steps of:
s1, obtaining a multi-component chirp signal
Figure 677459DEST_PATH_IMAGE001
(ii) a Assuming a multi-component chirp signal consisting of
Figure 93397DEST_PATH_IMAGE002
The chirp component signal and the background noise component, namely:
Figure 360430DEST_PATH_IMAGE003
Figure 356068DEST_PATH_IMAGE004
wherein the content of the first and second substances,
Figure 87264DEST_PATH_IMAGE005
is shown as
Figure 408524DEST_PATH_IMAGE006
The frequency of the individual chirp component signals,
Figure 694012DEST_PATH_IMAGE007
which is representative of the background noise signal,
Figure 24499DEST_PATH_IMAGE008
、
Figure 610201DEST_PATH_IMAGE009
and
Figure 571204DEST_PATH_IMAGE010
respectively represent
Figure 140725DEST_PATH_IMAGE011
The signal amplitude, the start frequency and the chirp rate,
Figure 681428DEST_PATH_IMAGE012
represents the index of the sample point of the discrete signal, and has,
Figure 121637DEST_PATH_IMAGE013
，
Figure 784699DEST_PATH_IMAGE014
represents the total number of sample points of the discrete signal,
Figure 310358DEST_PATH_IMAGE015
which is indicative of the time of observation of the signal,
Figure 451490DEST_PATH_IMAGE016
which represents the time interval between the sampling of the samples,
Figure 949467DEST_PATH_IMAGE017
the number of the imaginary numbers is represented,
Figure 783431DEST_PATH_IMAGE018
expressed as natural constants
Figure 61966DEST_PATH_IMAGE019
An exponential operation of a base number;
s2, initializing the linear frequency modulation component signal number index
Figure 747068DEST_PATH_IMAGE020
Let the residual signal
Figure 99552DEST_PATH_IMAGE021
；
S3, the calculation corresponds to
Figure 104417DEST_PATH_IMAGE022
A signal of said chirp component
Figure 604668DEST_PATH_IMAGE023
Of the optimal transformation order
Figure 353182DEST_PATH_IMAGE024
(ii) a Firstly, judging whether the residual signal still has the linear frequency modulation component signal, if so, adopting a global search method based on a minimum entropy criterion to realize the optimal transformation order
Figure 622489DEST_PATH_IMAGE025
Otherwise, ending parameter estimation;
s4, estimating the
Figure 532676DEST_PATH_IMAGE026
A signal of said chirp component
Figure 457907DEST_PATH_IMAGE027
Signal amplitude of
Figure 10111DEST_PATH_IMAGE028
(ii) a In fractional Fourier transform, when the order is changed
Figure 399504DEST_PATH_IMAGE029
Equal to said chirp component signal
Figure 480592DEST_PATH_IMAGE030
Of the optimal transformation order
Figure 627540DEST_PATH_IMAGE031
Then, the energy of the component signal is fully accumulated, and the signal amplitude of the component is estimated according to the maximum amplitude value in the fractional Fourier transform result and the total number of signal sampling points
Figure 983435DEST_PATH_IMAGE032
Namely:
Figure 227334DEST_PATH_IMAGE033
wherein the content of the first and second substances,
Figure 744903DEST_PATH_IMAGE034
is shown as
Figure 707043DEST_PATH_IMAGE035
A signal of a linear frequency-modulated component
Figure 69891DEST_PATH_IMAGE036
Is determined by the signal amplitude estimate of (a),
Figure 433877DEST_PATH_IMAGE037
representing the order of the transformation equal to
Figure 60030DEST_PATH_IMAGE038
Time signal
Figure 243887DEST_PATH_IMAGE039
The fractional order fourier transform result vector of (a);
s5, estimating the
Figure 428004DEST_PATH_IMAGE040
A signal of said chirp component
Figure 584179DEST_PATH_IMAGE041
The instantaneous frequency of (d); obtained according to said S3
Figure 709130DEST_PATH_IMAGE042
A signal of said chirp component
Figure 380282DEST_PATH_IMAGE043
Of the optimal transformation order
Figure 350513DEST_PATH_IMAGE044
Estimating the instantaneous frequency of the signal through short-time fractional Fourier transform, wherein the calculation formula of the short-time fractional Fourier transform is as follows:
Figure 423511DEST_PATH_IMAGE045
wherein the content of the first and second substances,
Figure 391467DEST_PATH_IMAGE046
representing a transformation order of
Figure 284336DEST_PATH_IMAGE047
Time, residual signal
Figure 323837DEST_PATH_IMAGE048
The result of the short-time fractional fourier transform,
Figure 516921DEST_PATH_IMAGE049
representing the window function length of
Figure 452515DEST_PATH_IMAGE050
And has a proper Gaussian window function
Figure 98260DEST_PATH_IMAGE051
When the temperature of the water is higher than the set temperature,
Figure 675872DEST_PATH_IMAGE052
；
Figure 785780DEST_PATH_IMAGE053
representing a discrete time sequence;
Figure 220172DEST_PATH_IMAGE054
a kernel function representing a fractional Fourier transform;
the instantaneous frequency of the signal is estimated by searching for the maximum of the short-time fractional order fourier transform results at different sampling points, namely:
Figure 87634DEST_PATH_IMAGE055
Figure 209217DEST_PATH_IMAGE056
wherein the content of the first and second substances,
Figure 111314DEST_PATH_IMAGE057
is shown as
Figure 575662DEST_PATH_IMAGE058
A signal of a linear frequency-modulated component
Figure 461578DEST_PATH_IMAGE059
The instantaneous frequency of the received signal,
Figure 115414DEST_PATH_IMAGE060
representing a modulo operation;
Figure 137596DEST_PATH_IMAGE061
is a frequency variable;
s6, rough estimation
Figure 851474DEST_PATH_IMAGE062
A signal of said chirp component
Figure 693528DEST_PATH_IMAGE063
Starting frequency of
Figure 151055DEST_PATH_IMAGE064
And chirp rate
Figure 27744DEST_PATH_IMAGE065
；
Estimated signal according to the S5
Figure 850206DEST_PATH_IMAGE066
And roughly estimating the starting frequency by a polynomial regression method based on linear least squares estimation
Figure 241873DEST_PATH_IMAGE067
And chirp rate
Figure 503090DEST_PATH_IMAGE068
The solving formula is as follows:
Figure 228427DEST_PATH_IMAGE069
wherein the content of the first and second substances,
Figure 284107DEST_PATH_IMAGE070
representing the frequency of the start
Figure 100754DEST_PATH_IMAGE071
And chirp rate
Figure 165662DEST_PATH_IMAGE072
The vector of coarse estimates of (a), i.e.:
Figure 751364DEST_PATH_IMAGE073
；
Figure 712366DEST_PATH_IMAGE074
and
Figure 281888DEST_PATH_IMAGE075
respectively represent
Figure 884908DEST_PATH_IMAGE076
A signal of a linear frequency-modulated component
Figure 325116DEST_PATH_IMAGE077
Starting frequency of
Figure 50496DEST_PATH_IMAGE078
And chirp rate
Figure 576155DEST_PATH_IMAGE079
Is determined by the coarse estimation value of (c),
Figure 982866DEST_PATH_IMAGE080
which represents the operation of transposition by means of a transposition operation,
Figure 12001DEST_PATH_IMAGE081
representing an inversion operation, a matrix
Figure 111544DEST_PATH_IMAGE082
Sum vector
Figure 124500DEST_PATH_IMAGE083
Respectively as follows:
Figure 137498DEST_PATH_IMAGE084
Figure 614616DEST_PATH_IMAGE085
Figure 744115DEST_PATH_IMAGE086
Figure 306683DEST_PATH_IMAGE087
s7, fine estimation
Figure 117513DEST_PATH_IMAGE088
A signal of said chirp component
Figure 386821DEST_PATH_IMAGE089
Starting frequency of
Figure 562587DEST_PATH_IMAGE090
And chirp rate
Figure 284555DEST_PATH_IMAGE091
(ii) a Obtaining rough estimated values of the initial frequency and the frequency modulation slope according to the S6
Figure 836760DEST_PATH_IMAGE092
And
Figure 226153DEST_PATH_IMAGE093
the signals are processed by frequency-modulation removal, low-pass filtering and phase regression
Figure 324819DEST_PATH_IMAGE094
Carrying out fine estimation on the initial frequency and the frequency modulation slope;
s8, the first obtained according to the S4
Figure 861980DEST_PATH_IMAGE095
A signal amplitude estimation value of the chirp component signal and the second obtained at said S7
Figure 952296DEST_PATH_IMAGE096
The initial frequency and the fine frequency modulation slope value of the linear frequency modulation component signal are reconstructed
Figure 196195DEST_PATH_IMAGE097
A signal of a linear frequency-modulated component
Figure 448185DEST_PATH_IMAGE098
；
S9, stepping the linear frequency modulation component signal number index
Figure 410325DEST_PATH_IMAGE099
And updates the residual signal to:
Figure 38752DEST_PATH_IMAGE100
Figure 402737DEST_PATH_IMAGE101
represents the reconstructed second
Figure 153525DEST_PATH_IMAGE102
A chirp component signal;
returning to the step S3 to continue execution.
2. The STFrFT-based adaptive multi-component chirp signal parameter estimation method of claim 1, wherein the S3 comprises the following implementation steps:
s3.1, in a half period interval
Figure 337381DEST_PATH_IMAGE103
Inter-search step size
Figure 769500DEST_PATH_IMAGE104
To discretize the transformation order to obtain
Figure 722412DEST_PATH_IMAGE105
A discrete value, i.e.
Figure 847363DEST_PATH_IMAGE106
Wherein
Figure 518516DEST_PATH_IMAGE107
Represents a vector of transform order candidate values,
Figure 494605DEST_PATH_IMAGE108
is referred to as the first
Figure 567603DEST_PATH_IMAGE109
The candidate values of the individual transformation orders are,
Figure 660193DEST_PATH_IMAGE110
which represents a rounding-down operation, the rounding-down operation,
Figure 943276DEST_PATH_IMAGE111
representing a transpose operation; initialization iteration number
Figure 654880DEST_PATH_IMAGE112
；
S3.2, calculating the order of transformation equal to
Figure 582385DEST_PATH_IMAGE113
Time residual signal
Figure 783559DEST_PATH_IMAGE114
Fractional order fourier transform of (a); the calculation formula of the fractional Fourier transform is as follows:
Figure 429304DEST_PATH_IMAGE115
wherein the content of the first and second substances,
Figure 69232DEST_PATH_IMAGE116
representing a transformation order of
Figure 851244DEST_PATH_IMAGE117
Time residual signal
Figure 404410DEST_PATH_IMAGE118
The result of the fractional order fourier transform of (a),
Figure 537452DEST_PATH_IMAGE119
the kernel function of fractional Fourier transform is represented by the following mathematical expression:
Figure 653175DEST_PATH_IMAGE120
Figure 555272DEST_PATH_IMAGE121
Figure 894987DEST_PATH_IMAGE122
which represents an integer number of times,
Figure 780903DEST_PATH_IMAGE123
indicates a rotation angle, and is provided with
Figure 497055DEST_PATH_IMAGE124
Representing a square-on operation;
s3.3, calculating the order of transformation equal to
Figure 253658DEST_PATH_IMAGE125
Time residual signal
Figure 233116DEST_PATH_IMAGE126
Entropy of the fractional fourier transform result of (a); assuming a residual signal
Figure 75170DEST_PATH_IMAGE127
The vector form of (a) is:
Figure 532696DEST_PATH_IMAGE128
wherein the content of the first and second substances,
Figure 143806DEST_PATH_IMAGE129
representing a discretized signal vector; when the transformation order candidate is
Figure 294165DEST_PATH_IMAGE130
Then, the vector form of the signal fractional order fourier transform result is:
Figure 691691DEST_PATH_IMAGE131
Figure 952908DEST_PATH_IMAGE132
the entropy of the fractional fourier transform result can be calculated by:
Figure 746421DEST_PATH_IMAGE133
wherein the content of the first and second substances,
Figure 802101DEST_PATH_IMAGE134
expressed as natural constants
Figure 743381DEST_PATH_IMAGE135
A logarithmic operation of a base number;
s3.4, step iteration number
Figure 542710DEST_PATH_IMAGE136
Judgment of
Figure 66095DEST_PATH_IMAGE137
If the result is true, entering S3.5 if the result is true, otherwise entering S3.2 to continue execution;
s3.5 each transformation order candidate may calculate an entropy value from said S3.2 and said S3.3, from which a vector of candidate values corresponding to the transformation order may be obtained
Figure 558257DEST_PATH_IMAGE138
Vector of entropy values
Figure 862199DEST_PATH_IMAGE139
Comprises the following steps:
Figure 199639DEST_PATH_IMAGE140
s3.6, normalization entropy value vector
Figure 905427DEST_PATH_IMAGE141
The mathematical formula is as follows:
Figure 240594DEST_PATH_IMAGE142
wherein the content of the first and second substances,
Figure 94149DEST_PATH_IMAGE143
represents a vector of normalized entropy values that is,
Figure 439809DEST_PATH_IMAGE144
expressing the operation of solving the maximum value; computing an entropy vector
Figure 103DEST_PATH_IMAGE145
Variance of (2)
Figure 834067DEST_PATH_IMAGE146
The mathematical expression is as follows:
Figure 847023DEST_PATH_IMAGE147
wherein the content of the first and second substances,
Figure 854162DEST_PATH_IMAGE148
representing vectors of entropy values
Figure 331279DEST_PATH_IMAGE149
And has a mean value of
Figure 336145DEST_PATH_IMAGE150
；
Judging whether the following formula is satisfied:
Figure 836396DEST_PATH_IMAGE151
wherein the content of the first and second substances,
Figure 381647DEST_PATH_IMAGE152
a threshold, here set to 0.02, representing a determination of the presence or absence of a chirp component signal;
if the above formula is true, the residual signal is determined
Figure 916533DEST_PATH_IMAGE153
If there is a chirp component signal, continuing to execute the step S3.7; otherwise, the residual signal is determined
Figure 92300DEST_PATH_IMAGE153
If only a noise signal exists in the signal, terminating the circulation and finishing the parameter estimation;
s3.7 by vector from entropy values
Figure 85707DEST_PATH_IMAGE154
To estimate the entropy corresponding to the second
Figure 434649DEST_PATH_IMAGE155
A signal of a linear frequency-modulated component
Figure 558462DEST_PATH_IMAGE156
The optimal transformation order of (a), namely:
Figure 905130DEST_PATH_IMAGE157
。
3. the STFrFT-based adaptive multi-component chirp signal parameter estimation method of claim 2, wherein the S7 is for a signal
Figure 379974DEST_PATH_IMAGE158
The initial frequency and the chirp rate are precisely estimated, specifically as follows:
s7.1, frequency modulation removing: first, based on the initial frequency and the rough estimation value of the chirp rate
Figure 470289DEST_PATH_IMAGE159
And
Figure 714189DEST_PATH_IMAGE160
to reconstruct the
Figure 90813DEST_PATH_IMAGE161
A signal of a linear frequency-modulated component
Figure 52952DEST_PATH_IMAGE162
The phase conjugate term of (a), namely:
Figure 681380DEST_PATH_IMAGE163
Figure 45365DEST_PATH_IMAGE164
wherein the content of the first and second substances,
Figure 468256DEST_PATH_IMAGE165
to be reconstructed
Figure 855375DEST_PATH_IMAGE166
A signal of a linear frequency-modulated component
Figure 468585DEST_PATH_IMAGE167
The phase conjugate term of (a);
secondly, according to the reconstructed second
Figure 421497DEST_PATH_IMAGE168
A signal of a linear frequency-modulated component
Figure 280869DEST_PATH_IMAGE169
Phase conjugate term of to the residual signal
Figure 952022DEST_PATH_IMAGE170
And (3) performing frequency modulation removal treatment, wherein the specific formula is as follows:
Figure 187831DEST_PATH_IMAGE171
Figure 323146DEST_PATH_IMAGE172
wherein the content of the first and second substances,
Figure 353419DEST_PATH_IMAGE173
the residual signal after frequency modulation processing is removed;
s7.2, low-pass filtering: in order to improve the signal-to-noise ratio of the target echo, a low-pass filtering process is carried out on the signal after frequency modulation removal by adopting a moving average filter; the specific formula is as follows:
Figure 511868DEST_PATH_IMAGE174
Figure 285789DEST_PATH_IMAGE175
wherein the content of the first and second substances,
Figure 213293DEST_PATH_IMAGE176
，
Figure 414468DEST_PATH_IMAGE177
represents the length of the moving average filter;
Figure 122530DEST_PATH_IMAGE178
represents the result of the low-pass filtering process;
s7.3, phase regression treatment:
firstly, extracting the signal phase after the low-pass filtering processing, wherein the specific formula is as follows:
Figure 440422DEST_PATH_IMAGE179
Figure 488012DEST_PATH_IMAGE180
wherein the content of the first and second substances,
Figure 860088DEST_PATH_IMAGE181
which represents the operation of the arctan function,
Figure 993129DEST_PATH_IMAGE182
the imaginary part operation of the signal is expressed,
Figure 108852DEST_PATH_IMAGE183
representing the operation of taking the real part of the signal;
Figure 10949DEST_PATH_IMAGE184
representing the extracted signal phase;
the extracted signal phases are written in vector form
Figure 553926DEST_PATH_IMAGE185
Comprises the following steps:
Figure 971001DEST_PATH_IMAGE186
secondly, the polynomial regression method based on linear least square estimation is adopted to carry out phase matching on the extracted signal
Figure 890415DEST_PATH_IMAGE187
Fitting to estimate the initial frequency of the de-modulated signal
Figure 771652DEST_PATH_IMAGE188
And chirp rate
Figure 485530DEST_PATH_IMAGE189
The solution formula is as follows:
Figure 593164DEST_PATH_IMAGE190
wherein the content of the first and second substances,
Figure 130585DEST_PATH_IMAGE191
representing the estimated phase constant of the signal,
Figure 866329DEST_PATH_IMAGE192
and
Figure 16687DEST_PATH_IMAGE193
respectively representing estimated signal start frequencies
Figure 283721DEST_PATH_IMAGE194
And chirp rate
Figure 544938DEST_PATH_IMAGE195
And rest amount of
Figure 10554DEST_PATH_IMAGE196
，
Figure 394131DEST_PATH_IMAGE197
Matrix of
Figure 210777DEST_PATH_IMAGE198
Expressed as:
Figure 72423DEST_PATH_IMAGE199
wherein the content of the first and second substances,
Figure 658125DEST_PATH_IMAGE200
represents a time variable, and the mathematical expression thereof is as follows:
Figure 150286DEST_PATH_IMAGE201
Figure 188649DEST_PATH_IMAGE202
s7.4, obtaining a precise estimation value: according to the starting frequency
Figure 859845DEST_PATH_IMAGE203
And chirp rate
Figure 565633DEST_PATH_IMAGE204
The coarse estimation value and the estimated residual quantity can obtain a fine estimation value of the two parameters, and the solution formula is as follows:
Figure 963116DEST_PATH_IMAGE205
wherein the content of the first and second substances,
Figure 754355DEST_PATH_IMAGE206
and
Figure 895486DEST_PATH_IMAGE207
respectively represent
Figure 455780DEST_PATH_IMAGE208
Multiple multi-component chirp component signal
Figure 24165DEST_PATH_IMAGE209
Starting frequency of
Figure 302700DEST_PATH_IMAGE210
And chirp rate
Figure 247522DEST_PATH_IMAGE211
And (6) fine estimation value.
4. The STFrFT-based adaptive multi-component chirp signal parameter estimation method of claim 3, wherein: obtained according to said S4
Figure 662323DEST_PATH_IMAGE212
A signal of a linear frequency-modulated component
Figure 667188DEST_PATH_IMAGE213
Signal amplitude estimate of
Figure 167439DEST_PATH_IMAGE214
And the second obtained in said S7.4
Figure 650373DEST_PATH_IMAGE215
A line ofFrequency modulated component signal
Figure 185260DEST_PATH_IMAGE216
Fine estimation of the starting frequency of
Figure 157764DEST_PATH_IMAGE217
Sum chirp slope fine estimate
Figure 201769DEST_PATH_IMAGE218
To reconstruct the first
Figure 550711DEST_PATH_IMAGE219
A signal of a linear frequency-modulated component
Figure 877787DEST_PATH_IMAGE220
The concrete formula is as follows:
Figure 224455DEST_PATH_IMAGE221
Figure 699298DEST_PATH_IMAGE222
wherein the content of the first and second substances,
Figure 586352DEST_PATH_IMAGE223
represents the reconstructed second
Figure 17202DEST_PATH_IMAGE224
A chirp component signal.
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