CN113866739A - Multi-rotor target parameter estimation method based on GLCT-GPTF - Google Patents
Multi-rotor target parameter estimation method based on GLCT-GPTF Download PDFInfo
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Abstract
The invention discloses a multi-rotor target physical parameter estimation method based on GLCT-GPTF, and aims to solve the problems that in the rotor physical parameter estimation method based on a short-time Fourier transform time-frequency spectrogram in the prior art, the time-frequency spectrogram energy concentration is not high, and a time-frequency spectrogram quantization threshold needs to be preset to influence the rotor physical parameter estimation precision. The invention mainly comprises the following steps: (1) calculating the rotation speed of each rotor wing target; (2) calculating the stability of the signal after the rotation translation by utilizing the generalized linear frequency modulation wavelet transform-generalized parametric time-frequency analysis GLCT-GPTF transform; (3) obtaining a transformation kernel parameter vector matched with the multi-rotor target radar echo signal by using a longicorn swarm optimization algorithm; (4) the blade length of the rotor is calculated. The method has the advantages of more accurately depicting the time-frequency characteristic of the multi-rotor target radar echo signal and improving the rotating speed of the rotor and the estimation precision of the blade length.
Description
Technical Field
The invention belongs to the technical field of radar, and further relates to a multi-rotor target parameter estimation method based on generalized Linear chirp Transform-generalized Parameterized Time-Frequency analysis (GLCT-GPTF) in the technical field of radar target identification. The method can be used for rotor physical parameter estimation of targets with multiple rotors, such as helicopters, proprotors and the like, and the estimated rotor physical parameters can be used for identification of the targets with multiple rotors.
Background
The rotation of the rotor blade can generate a modulation effect on the electromagnetic echo of the radar, a micro Doppler curve in a sine form is shown in a time-frequency spectrogram of the echo, the period of the micro Doppler curve is consistent with the rotation period of the rotor, and the maximum amplitude is determined by the radar wavelength, the length of the rotor blade and the rotating speed of the rotor. Because the physical parameters of the different types of multi-rotor targets are different, the rotor physical parameters can be estimated from the radar echo of the multi-rotor targets, the rotor physical parameters obtained through estimation are compared with the rotor physical parameters in the rotor target knowledge base, and the classification of the multi-rotor targets can be realized. Existing methods can be largely classified into two categories. The first method is a non-parametric method, which mainly extracts the micro Doppler broadening of the rotor blade through image morphological processing, peak detection and other methods on the basis of a time-frequency spectrogram, obtains the rotation speed of the rotor wing by combining a micro-motion period estimation method, and finally realizes the estimation of the length of the rotor blade according to the relationship between the length of the rotor blade, the micro Doppler broadening and the rotation frequency of the rotor wing. The performance of the nonparametric method is limited by the resolution of the time-frequency analysis method, and the estimation precision of the physical parameters of the rotor wing is not high. The parameterization method converts the rotor wing physical parameter estimation problem into a sine micro Doppler curve extraction problem in a time frequency spectrogram, such as Hough transform, inverse Radon transform and the like, however, due to the existence of a plurality of micro Doppler curves in a multi-rotor wing target time frequency diagram, the energy concentration of an echo on the time frequency spectrogram is poor, and the rotor wing physical parameter estimation precision is reduced.
The university of electronic science and technology discloses a method for extracting physical parameters of a multi-rotor unmanned aerial vehicle based on singular vectors in the patent document "method for extracting physical parameters of a multi-rotor unmanned aerial vehicle based on singular vectors" (application number 202011024462.9, application publication number CN 112162273 a). The method comprises the following specific steps: wavelet decomposition is carried out on radar echo signals of the multi-rotor unmanned aerial vehicle, low-frequency components generated by blade rotating parts are extracted, then short-time Fourier transformation is carried out on the components to obtain a time-frequency spectrogram, and physical parameters such as the rotating speed of a rotor and the blade length are extracted through singular vectors corresponding to maximum singular values after the singular values of the time-frequency spectrogram are decomposed. The method has the following defects: when the method is used for estimating the parameters, the energy concentration of the time-frequency spectrogram based on short-time Fourier transform is not high, and the accuracy of singular vector extraction and the accuracy of rotor physical parameter estimation are reduced.
Electronic science and technology university discloses a helicopter rotor physical parameter extraction method based on a time-frequency spectrogram in the patent document 'a helicopter rotor physical parameter extraction method' (application number 201910519253.2, application publication number CN 110133600 a). The method comprises the following specific steps: firstly, filtering a time-frequency spectrogram of a helicopter, carrying out three-value quantization and segmentation on the filtered time-frequency spectrogram according to two thresholds obtained by experience, weakening background noise of the time-frequency spectrogram, improving image definition and accurately extracting time-frequency signal lines; estimating the rotation period of the helicopter rotor by using a least square method; and finally, estimating the length of the paddle according to the relation between the frequency spectrum width and the length of the paddle. The method has the following defects: the threshold for the time-of-flight spectrogram quantification when estimating the parameters by using the method is obtained empirically, and the empirical threshold is difficult to be predetermined for different types of multi-rotor targets and difficult to be directly applied to different types of multi-rotor targets in practice.
Disclosure of Invention
The invention aims to provide a multi-rotor target physical parameter estimation method based on GLCT-GPTF aiming at overcoming the defects of the prior art, and aims to solve the problems that the time-frequency spectrogram energy concentration is not high and the time-frequency spectrogram quantification threshold needs to be preset to influence the estimation precision of the rotor physical parameters in the rotor physical parameter estimation method based on the short-time Fourier transform time-frequency spectrogram in the prior art.
The idea for realizing the purpose of the invention is as follows: according to the method, GLCT-GPTF is used for transforming the multi-rotor target radar echo signals in a rotating and translating manner, and the transform kernel parameter vector matched with the multi-rotor target radar echo signals is obtained by utilizing a Tianniu group optimization algorithm, so that the signals after rotating and translating tend to be stable, and the energy concentration of a time-frequency spectrogram can be effectively improved. Because the invention is based on the matching degree of the GLCT-GPTF transformed signal stability measurement transformation kernel parameter vector and the multi-rotor target radar echo signal, the problem of rotor parameter estimation is converted into the problem of maximum signal stability after rotary translation, the maximum Doppler frequency of the rotor in the transformation kernel parameter vector is determined by the rotating speed of the rotor and the blade length of the rotor, the estimation of the rotating speed and the blade length of the rotor can be directly realized by transforming the mapping relation between the kernel parameter vector and the rotor physical parameters, thereby the estimation of the maximum Doppler frequency is not required to be obtained by the time-frequency spectrogram quantization, and the problem that the estimation precision of the rotor physical parameters is influenced by the preset quantization threshold is avoided.
The specific steps for realizing the purpose of the invention are as follows:
step 1, calculating the rotating speed of each rotor wing target:
(1a) calculating the third-order instantaneous moment of the radar echo signal at each moment and each delay time;
(1b) calculating a third-order fuzzy value of the radar echo signal at each frequency and each delay time;
(1c) according to the following formula, calculating the third-order fuzzy entropy of the radar echo signal at each delay time:
wherein epsilon (tau) represents the third-order fuzzy entropy of the radar echo signal in the time of delaying tau, tau is more than 0 and less than or equal to N, N represents the total time of the radar echo signal, N is more than or equal to 2000, | | represents the modulus operation, C (f, tau) represents the third-order fuzzy value of the radar echo signal in the f-th frequency and the time of delaying tau, f is more than or equal to 1 and less than or equal to N, ln () represents the logarithmic operation with the natural constant e as the base;
(1d) the rotor speed is calculated according to the following formula:
wherein, omega represents the rotating speed of the rotor wing, pi represents the circumferential rate, prf represents the pulse repetition frequency of the radar echo signal, prf is more than or equal to 10000Hz, NLRepresenting the total number of rotor blades, S representing a sign factor, when NLWhen the number is even, S is 1, and when N isLWhen the number is odd, S is 2, and T represents the delay time corresponding to the maximum value of the fuzzy entropy at all the delay times;
step 2, calculating the stability of the signal after the rotation translation by utilizing the generalized linear frequency modulation wavelet transform-generalized parametric time frequency analysis GLCT-GPTF transform:
(2a) constructing a sine-form transformation kernel matched with the multi-rotor radar echo signals according to the following formula:
wherein, κP(t) represents a transformation kernel in a sine form obtained based on a transformation kernel parameter vector P consisting of the maximum Doppler frequency of the rotor, the rotating speed of the rotor and the initial phase of the rotor at the tth moment, wherein P (1), P (2) and P (3) respectively represent a first element, a second element and a third element in the transformation kernel parameter vector P;
(2b) calculating the module value of each pixel in the three-dimensional time-frequency spectrogram according to the following formula:
wherein S (t, f, c, P) represents the three-dimensional time-frequency spectrogram obtained based on the transformation kernel parameter vector P at the t moment, the f frequency and the c frequency modulation rateC is more than or equal to 1 and less than or equal to 5, s (tau) represents radar echo signals at the tau-th moment in the radar echo signal vector,
represents the signal rotation operator obtained by transforming the kernel parameter vector P at the time instant t,
exp denotes the exponential operation with the natural constant e as base, j denotes the imaginary symbol, κP(τ) denotes the transformation kernel in sine form from the transformation kernel parameter vector P at the τ -th instant, sin denotes the sine operation,
represents the signal translation operator resulting from the transformation of the kernel parameter vector P at the instant t,
κP(t) represents a sine-form transform kernel derived from the transform kernel parameter vector P at time t, tan represents a tangent operation;
(2c) the flatness of the rotationally translated signal is calculated as follows:
wherein F represents the smoothness of the signal after the rotation translation, and E represents a two-dimensional time-frequency spectrogram S of a curve fitted by a transformation kernelc(t, f, P) the sum of the modulus values of the corresponding pixels,
the optimal tuning frequency at the t moment and the f frequency on the three-dimensional time-frequency spectrogram is represented, and C represents the sum of the number of points of which the optimal tuning frequency is not equal to 3 at the corresponding pixel position on the three-dimensional time-frequency spectrogram by a curve fitted by a transformation kernel;
step 3, obtaining a transformation kernel parameter vector matched with the multi-rotor target radar echo signal by using a longicorn swarm optimization algorithm:
iteratively updating the maximum Doppler frequency of the rotor wing and the initial phase of the rotor wing in the transformation kernel parameter vector P by using a space-borne radar group optimization algorithm until the signal stability is not changed any more, and taking the transformation kernel parameter vector corresponding to the maximum signal stability of all space-borne radars in the space-borne radar group when the iteration is terminated as the transformation kernel parameter vector matched with the multi-rotor-wing target radar echo signals;
and 4, calculating the length of the blade of the rotor.
Compared with the prior art, the invention has the following advantages:
firstly, the method utilizes the generalized linear frequency modulation wavelet transform-generalized parametric time frequency analysis GLCT-GPTF transform to calculate the stability of the signal after the rotation translation, overcomes the defect of low time-frequency spectrum energy concentration in the rotor physical parameter estimation method based on the short-time Fourier transform time-frequency spectrum in the prior art, and has the advantage of more accurately depicting the time-frequency characteristics of the multi-rotor target radar echo signal.
Secondly, the invention utilizes a longicorn swarm optimization algorithm to obtain a transformation kernel parameter vector matched with the multi-rotor target radar echo signal, overcomes the problem that the prior art needs to preset a time-frequency spectrogram quantization threshold to influence the estimation precision of the physical parameters of the rotor, and improves the estimation precision of the rotating speed and the blade length of the rotor.
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FIG. 1 is a flow chart of the present invention.
Detailed Description
The specific steps of the present invention will be further described with reference to fig. 1.
Step 1, calculating the rotating speed of each rotor wing target.
Calculating the third moment of the radar echo signal at each moment and each delay time according to the following formula:
c(t,τ)＝s(t)[s(t+τ)]*[s(t+τ)]*s(t+2τ)
c (t, tau) represents the tth moment in the radar echo signal and the third-order moment delayed by tau time, t is more than or equal to 1 and less than or equal to N, s (t) represents the radar echo signal at the tth moment in the radar echo signal vector, s represents the radar echo signal vector, s (t + tau) represents the radar echo signal at the tth + tau moment in the radar echo signal vector, a represents conjugate operation, and s (t +2 tau) represents the radar echo signal at the tth +2 tau moment in the radar echo signal vector.
Calculating the third-order fuzzy value of the radar echo signal at each frequency and each delay time according to the following formula:
C(f,τ)＝∫c(t,τ)exp(-j2πft)dt
wherein, C (f, tau) represents the third-order fuzzy value of the radar echo signal at the f-th frequency and delayed tau time.
According to the following formula, calculating the third-order fuzzy entropy of the radar echo signal at each delay time:
wherein epsilon (tau) represents the third-order fuzzy entropy of the radar echo signal in the time of delaying tau, tau is more than 0 and less than or equal to N, N represents the total time in the radar echo signal, N is more than or equal to 2000, | | represents the modulus operation, C (f, tau) represents the third-order fuzzy value of the radar echo signal in the f-th frequency and the time of delaying tau, f is more than or equal to 1 and less than or equal to N, ln () represents the logarithmic operation with the natural constant e as the base.
The rotor speed is calculated according to the following formula:
wherein, omega represents the rotating speed of the rotor wing, pi represents the circumferential rate, prf represents the pulse repetition frequency of the radar echo signal, prf is more than or equal to 10000Hz, NLRepresenting the total number of rotor blades, S representing a sign factor, when NLWhen the number is even, S is 1, and when N isLWhen the number is odd, S is 2, and T represents a delay time corresponding to the maximum value of the blur entropy at all delay times.
And 2, calculating the stability of the signal after the rotation translation by utilizing the generalized linear frequency modulation wavelet transform-generalized parametric time frequency analysis GLCT-GPTF transform.
Constructing a sine-form transformation kernel matched with the multi-rotor radar echo signals according to the following formula:
wherein, κP(t) represents a sine-shaped transformation kernel obtained based on a transformation kernel parameter vector P composed of the maximum Doppler frequency of the rotor, the rotation speed of the rotor, and the initial phase of the rotor at the tth time, and P (1), P (2), and P (3) represent the first element, the second element, and the third element in the transformation kernel parameter vector P, respectively.
Calculating the module value of each pixel in the three-dimensional time-frequency spectrogram according to the following formula:
wherein S (t, f, c, P) represents the module value of a three-dimensional time-frequency spectrogram obtained based on the transformation kernel parameter vector P at the tth moment, the fth frequency and the kth frequency, c is more than or equal to 1 and less than or equal to 5, S (tau) represents the radar echo signal at the tth moment in the radar echo signal vector,
represents the signal rotation operator obtained by transforming the kernel parameter vector P at the time instant t,
exp denotes the exponential operation with the natural constant e as base, j denotes the imaginary symbol, κP(τ) denotes the transformation kernel in sine form from the transformation kernel parameter vector P at the τ -th instant, sin denotes the sine operation,
denotes the t-thA signal translation operator obtained at each instant by transforming the kernel parameter vector P,
κP(t) denotes a sine-shaped transform kernel derived from the transform kernel parameter vector P at time t, and tan denotes a tangent operation.
The optimal frequency modulation frequency at the t moment and the f frequency on the three-dimensional time-frequency spectrogram
Is obtained by the following formula:
wherein the content of the first and second substances,
and (3) representing the value of c when the module value S (t, f, c, P) of the three-dimensional time-frequency spectrogram at the f frequency obtains the maximum value at the t moment when the transformation kernel parameter P is given.
The flatness of the rotationally translated signal is calculated as follows:
wherein F represents the smoothness of the signal after the rotation translation, and E represents a two-dimensional time-frequency spectrogram S of a curve fitted by a transformation kernelc(t, f, P) the sum of the modulus values of the corresponding pixels,
and C, representing the optimal tuning frequency at the t moment and the f frequency on the three-dimensional time-frequency spectrogram, and representing the sum of the number of points of which the optimal tuning frequency is not equal to 3 at the corresponding pixel position on the three-dimensional time-frequency spectrogram by the curve fitted by the transformation kernel.
And 3, obtaining a transformation kernel parameter vector matched with the multi-rotor target radar echo signal by using a longicorn herd optimization algorithm.
And (3) iteratively updating the maximum Doppler frequency of the rotor wing and the initial phase of the rotor wing in the transformation kernel parameter vector P by using a space-borne radar group optimization algorithm until the signal stability is not changed any more, and taking the transformation kernel parameter vector corresponding to the maximum signal stability of all space-borne radars in the space-borne radar group when the iteration is terminated as the transformation kernel parameter vector matched with the multi-rotor wing target radar echo signals.
The longicorn swarm optimization algorithm is the combination of the particle swarm optimization algorithm and the longicorn beard algorithm, and can better avoid the problems of low stability, large calculation amount and easy falling into local optimization existing in the traditional particle swarm optimization algorithm. Each particle in the particle swarm optimization is replaced by a longicorn to search simultaneously, and the initialization of the position and the speed of the longicorn individual is obtained by the following formula:
wherein, XimRepresents the position vector of the mth longicorn in the ith iteration, wherein i is more than 0 and less than or equal to 300, m is more than 0 and less than or equal to 30,
the first element of the position vector representing the mth cow at the ith iteration corresponding to the maximum doppler frequency of the rotor,
slave interval
The method comprises the steps of (1) randomly selecting,
the second element of the position vector representing the mth longicorn at the ith iteration,
from the interval [0,2 π]In random selection, VimRepresenting the velocity vector of the m-th longicorn at the i-th iteration,
representing the velocity of the first dimension of the mth longicorn at the ith iteration,
representing the velocity of the second dimension of the mth longicorn at the ith iteration,
and
all from the interval [ -2,2 [)]The selection is carried out randomly.
In the iteration process, the updating rule of the position of each longicorn is combined with the optimal global positions of all the longicorn and the optimal position of the longicorn individual, a search mechanism of the antenna is introduced, signal stabilities corresponding to the antenna position vectors on the left side and the right side of the longicorn individual are compared in the iteration process, and the position with higher stability is used for updating the position of the longicorn individual. The precision and the speed of the transformation kernel parameter vector estimation can be effectively improved by utilizing the longicorn swarm optimization algorithm.
Step 4, calculating the length of the rotor blade according to the following formula:
wherein L represents the blade length of the rotor, λ represents the wavelength of the radar echo signal, PmaxRepresenting transformed kernel parameter vectors, P, matched to radar return signals of multiple rotor targetsmax(1) Representation and multi-rotor target radar echoThe first element in the wave signal matched transform kernel parameter vector.
The effect of the present invention will be further described with reference to simulation experiments.
1. Simulation experiment conditions are as follows:
the hardware platform of the simulation experiment of the invention is as follows: the processor is an Intel i 76700 k CPU, the main frequency is 4.0GHz, and the memory is 16 GB.
The software platform of the simulation experiment of the invention is as follows: windows 10 operating system and Matlab2020 a.
The radar echo data used in the simulation experiment of the invention is the high signal-to-noise ratio actual measurement radar data of the 'fortune eight' aircraft collected under the cooperation condition. The eight-purpose aircraft is a four-rotor propeller aircraft, the length L of the blade of the eight-purpose aircraft is 1.8m, and the rotating speed omega of the rotor wingr40 pi rad/s, the number of blades per rotor N is 4; the repetition frequency of the radar pulse is 12KHz, the dwell time is 1s, and the carrier frequency is 5 GHz.
2. Simulation content and result analysis thereof:
the simulation experiment of the invention is to respectively estimate the rotor rotation speed and the blade length of the measured radar data with high signal-to-noise ratio of the 'fortune eight' aircraft by adopting the method of the invention and two prior arts (RSP-CFD method and instantaneous frequency-FFT method).
In the simulation experiment, two prior arts are adopted:
the RSP-CFD method in the prior art is a multi-rotor unmanned aerial vehicle target rotor parameter estimation method which is provided by He, Wei and the like in 'small rotor unmanned aerial vehicle micro-motion feature extraction [ J ] based on the RSP-CFD method, 2021,37(3):399 and 408', and is called RSP-CFD method for short.
The instantaneous frequency-FFT method in the prior art refers to a multi-rotor unmanned aerial vehicle target rotor parameter estimation method which is provided by Majiao et al in 'micro Doppler characteristic analysis and feature extraction of multi-rotor unmanned aerial vehicle [ J ]. college of China academy of sciences, 2019,36(2): 235-plus 243', and is called the instantaneous frequency-FFT method for short.
The maximum doppler frequency of the rotor, the rotational speed of the rotor, and the blade length evaluation results of the rotor obtained from the simulation results of the present invention are shown in table 1. The parameter of the "maximum doppler frequency" of the present invention in table 1 is the first element in the transformation kernel parameter vector matched with the multi-rotor target radar echo signal obtained by the space and cow crowd optimization algorithm in step 3 of the present invention. The parameter of the "rotation speed" in the invention in table 1 is the rotation speed of the rotor wing estimated by using the third-order fuzzy entropy in step 1 of the invention. The "blade length" parameter of the present invention in table 1 is obtained using the calculation formula for the blade length of the rotor in step 4 of the present invention. The "maximum doppler frequency" parameter of the RSP-CFD method in table 1 is obtained by maximum search on the quantified RSP time-frequency spectrogram of the radar echo signal. The parameter of the RSP-CFD method 'rotating speed' in the table 1 is obtained by searching a maximum value on a CFD time-frequency spectrogram after the quantification of the radar echo signal. The parameter of the RSP-CFD method "blade length" in table 1 is calculated by using the mapping relationship between the maximum doppler frequency and the rotational speed and the blade length. The parameter of the "maximum doppler frequency" of the instantaneous frequency-FFT method in table 1 is obtained by maximum search on the short-time fourier transform time-frequency spectrogram after quantization of the radar echo signal. The parameter of the instantaneous frequency-FFT method 'rotating speed' in the table 1 is obtained by carrying out Fourier transform on a short-time Fourier transform time-frequency spectrogram after quantization of radar echo signals to search for a maximum value. The parameters of the instantaneous frequency-FFT method "blade length" in table 1 are calculated using the mapping relationship between the maximum doppler frequency and the rotational speed and the blade length. The actual values "speed" in table 1 and "blade length" were measured by the partner instrument. The actual parameter "maximum doppler frequency" in table 1 is calculated by using the mapping relationship between the maximum doppler frequency and the rotational speed and the blade length.
Table 1 simulation experiment table of estimated results of the parameters of the rotor of the present invention and of the various prior art
| True value | The method of the invention | RSP-CFD | Instantaneous frequency-FFT | |
| Maximum Doppler frequency (Hz) | 4484.85 | 4411.09 | 4210.20 | 4250.50 |
| Rotating speed (Pi rad/s) | 40.00 | 40.00 | 39.92 | 39.96 |
| Blade length (m) | 1.80 | 1.77 | 1.69 | 1.70 |
As can be seen from Table 1, the errors of the maximum Doppler frequency and the rotating speed of the rotor and the estimated value and the actual value of the blade length of the rotor of the method are lower than those of 2 methods in the prior art, and the method is proved to have higher rotor parameter estimation precision.
The above simulation experiments show that: the method of the invention realizes the accurate estimation of the rotor rotation speed by utilizing the third-order fuzzy entropy, converts the rotary translation multi-rotor target radar echo signal through GLCT-GPTF determined by the conversion kernel parameter vector, obtains the conversion kernel parameter vector matched with the multi-rotor target radar echo signal by utilizing the longicorn group optimization algorithm, the method has the advantages that the signals tend to be stable after the rotation and translation, the energy concentration of the time-frequency spectrogram can be effectively improved, the problem of rotor parameter estimation is converted into the problem of maximum stability of the signals after the rotation and translation by the time-frequency spectrogram obtained based on the GLCT-GPTF conversion, the estimation of the maximum Doppler frequency is not required to be obtained through the time-frequency spectrogram quantization, the problems that the energy concentration of the time-frequency spectrogram is not high in the prior art and the estimation precision of the physical parameters of the rotor is influenced by the need of presetting the time-frequency spectrogram quantization threshold are solved, and the method is a very practical multi-rotor target parameter estimation method.
Claims (5)
1. A multi-rotor target physical parameter estimation method based on GLCT-GPTF is characterized in that the rotation speed of a rotor is estimated by using third-order fuzzy entropy, and the matching degree of a transformation kernel parameter vector and multi-rotor target radar echo signals is measured based on the signal stability of GLCT-GPTF transformation; the steps of the estimation method include the following:
step 1, calculating the rotating speed of each rotor wing target:
(1a) calculating the third-order instantaneous moment of the radar echo signal at each moment and each delay time;
(1b) calculating a third-order fuzzy value of the radar echo signal at each frequency and each delay time;
(1c) according to the following formula, calculating the third-order fuzzy entropy of the radar echo signal at each delay time:
wherein epsilon (tau) represents the third-order fuzzy entropy of the radar echo signal in the time of delaying tau, tau is more than 0 and less than or equal to N, N represents the total time of the radar echo signal, N is more than or equal to 2000, | | represents the modulus operation, C (f, tau) represents the third-order fuzzy value of the radar echo signal in the f-th frequency and the time of delaying tau, f is more than or equal to 1 and less than or equal to N, ln () represents the logarithmic operation with the natural constant e as the base;
(1d) the rotor speed is calculated according to the following formula:
wherein, omega represents the rotating speed of the rotor wing, pi represents the circumferential rate, prf represents the pulse repetition frequency of the radar echo signal, prf is more than or equal to 10000Hz, NLRepresenting the total number of rotor blades, S representing a sign factor, when NLWhen the number is even, S is 1, and when N isLWhen the number is odd, S is 2, and T represents the delay time corresponding to the maximum value of the fuzzy entropy at all the delay times;
step 2, calculating the stability of the signal after the rotation translation by utilizing the generalized linear frequency modulation wavelet transform-generalized parametric time frequency analysis GLCT-GPTF transform:
(2a) constructing a sine-form transformation kernel matched with the multi-rotor radar echo signals according to the following formula:
wherein, κP(t) represents a transformation kernel in a sine form obtained based on a transformation kernel parameter vector P consisting of the maximum Doppler frequency of the rotor, the rotating speed of the rotor and the initial phase of the rotor at the tth moment, wherein P (1), P (2) and P (3) respectively represent a first element, a second element and a third element in the transformation kernel parameter vector P;
(2b) calculating the module value of each pixel in the three-dimensional time-frequency spectrogram according to the following formula:
wherein S (t, f, c, P) represents the module value of a three-dimensional time-frequency spectrogram obtained based on the transformation kernel parameter vector P at the tth moment, the fth frequency and the tth frequency modulation rate, c is more than or equal to 1 and less than or equal to 5, and S (tau) represents the radar echo signal at the tth moment in the radar echo signal vectorThe number of the mobile station is,
represents the signal rotation operator obtained by transforming the kernel parameter vector P at the time instant t,
exp denotes the exponential operation with the natural constant e as base, j denotes the imaginary symbol, κP(τ) denotes the transformation kernel in sine form from the transformation kernel parameter vector P at the τ -th instant, sin denotes the sine operation,
represents the signal translation operator resulting from the transformation of the kernel parameter vector P at the instant t,
κP(t) represents a sine-form transform kernel derived from the transform kernel parameter vector P at time t, tan represents a tangent operation;
(2c) the flatness of the rotationally translated signal is calculated as follows:
wherein F represents the smoothness of the signal after the rotation translation, and E represents a two-dimensional time-frequency spectrogram S of a curve fitted by a transformation kernelc(t, f, P) the sum of the modulus values of the corresponding pixels,
the optimal tuning frequency at the t moment and the f frequency on the three-dimensional time-frequency spectrogram is represented, and C represents the sum of the number of points of which the optimal tuning frequency is not equal to 3 at the corresponding pixel position on the three-dimensional time-frequency spectrogram by a curve fitted by a transformation kernel;
step 3, obtaining a transformation kernel parameter vector matched with the multi-rotor target radar echo signal by using a longicorn swarm optimization algorithm:
iteratively updating the maximum Doppler frequency of the rotor wing and the initial phase of the rotor wing in the transformation kernel parameter vector P by using a space-borne radar group optimization algorithm until the signal stability is not changed any more, and taking the transformation kernel parameter vector corresponding to the maximum signal stability of all space-borne radars in the space-borne radar group when the iteration is terminated as the transformation kernel parameter vector matched with the multi-rotor-wing target radar echo signals;
and 4, calculating the length of the blade of the rotor.
2. The GLCT-GPTF based multi-rotor target physical parameter estimation method according to claim 1, wherein the third moment of the radar echo signal at each time and each delay time in step (1a) is obtained by the following formula:
c(t,τ)＝s(t)[s(t+τ)]*[s(t+τ)]*s(t+2τ)
c (t, tau) represents the tth moment in the radar echo signal and the third-order moment delayed by tau time, t is more than or equal to 1 and less than or equal to N, s (t) represents the radar echo signal at the tth moment in the radar echo signal vector, s represents the radar echo signal vector, s (t + tau) represents the radar echo signal at the tth + tau moment in the radar echo signal vector, a represents conjugate operation, and s (t +2 tau) represents the radar echo signal at the tth +2 tau moment in the radar echo signal vector.
3. The GLCT-GPTF based multi-rotor target physical parameter estimation method according to claim 1, wherein the third-order ambiguity values of the radar echo signals at each frequency and each delay time in step (1b) are obtained by the following formula:
C(f,τ)＝∫c(t,τ)exp(-j2πft)dt
wherein, C (f, tau) represents the third-order fuzzy value of the radar echo signal at the f-th frequency and delayed tau time.
4. According to the claimsSolving 1 the GLCT-GPTF-based multi-rotor target physical parameter estimation method, wherein the optimal tuning frequency at the t moment and the f frequency on the three-dimensional time-frequency spectrogram in the step (2b)
Is obtained by the following formula:
wherein the content of the first and second substances,
and (3) representing the value of c when the module value S (t, f, c, P) of the three-dimensional time-frequency spectrogram at the f frequency obtains the maximum value at the t moment when the transformation kernel parameter P is given.
5. The GLCT-GPTF based multi-rotor target physical parameter estimation method according to claim 1, wherein the calculation of the rotor blade length in step 4 is obtained by the following formula:
wherein L represents the blade length of the rotor, λ represents the wavelength of the radar echo signal, PmaxRepresenting transformed kernel parameter vectors, P, matched to radar return signals of multiple rotor targetsmax(1) Representing a first element in a transformation kernel parameter vector that matches a multi-rotor target radar return signal.
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