Feature Extraction Method of Helicopter Target Based on Flicker Phenomenon Combined with Phase Compensation

For the typical multi-component periodic micro-Doppler signal parameter estimation, a helicopter rotor feature extraction method based on flicker phenomenon and phase compensation is proposed in this paper. The method firstly analyzes the formation mechanism of helicopter rotor flicker phenomenon in time domain and time-frequency domain through the integral model. Then the demodulation operator of the micro-Doppler signal is constructed for the phase compensation of the echoes with respect to the time-frequency flicker characteristics and the phase information of the slow time dimension of the target echoes. The parameter combination of the possible number of blades and rotational speed is predicted using the time domain flicker interval, and the phase compensation process is evaluated and optimized to significantly reduce the amount of computation. Finally, the parameter estimation of rotor blade number, blade length and rotational speed is acquired by calculating whether the center frequency of each flicker after phase compensation is periodically focused to zero frequency. The simulation results show that the method can effectively estimate the main parameters of helicopter rotor blades, and the processing results of the measured data show that the proposed method has more stable performance compared with OMP algorithm and Hough transform, which provides a new technical way for helicopter rotor blade feature extraction.


I. INTRODUCTION
Apart from the center-of-mass transitional motion of the aerial vehicles, some micro-motion, such as vibration or rotation of components, also can be detected, which will result in periodic modulation of the phase of radar echoes and further generate an additional frequency modulation band near the target transitional Doppler shift. This additional modulation band is called the micro-Doppler signal, and the modulation phenomenon caused by micro-motion is called the Micro-Doppler effect (MDE) [1][2]. The MDE can reflect the geometric composition and motion characteristics of the target, which can be used to determine the properties of the target and innovate means to target identification [3]. Nowadays, the application of the MDE for target identification has been a research hotspot. There are three main types of aircraft in the modern battlefield: rotor helicopters, propeller aircraft and jet aircraft.
Among them, helicopters are typical "low, slow and small" targets with fetures such as flexibility and maneuverability, which has posed a great threat to air defense security. In order to enhance the situational awareness of the battlefield, it is imperative to extract and analyse the features of helicopter target to achieve automatic target identification. Currently, scholars have conducted indepth research on the modeling and feature extraction methods of helicopter. There are three main modeling methods: (1) RCS model [4][5], which obtains echoes by calculating the target backward scattering field and can fully consider the scattering characteristics of the target, and the model is the most accurate, but the calculation is too complicated; (2) Scattering point model [6][7], which is the most traditional and applied modeling method, analyzes the target by equating it into a number of scattering points. This method can be applied into complex scenes with non-uniform distribution and different scattering intensity, but the amount of computation increases with the increase of the number of scattering points; (3) Integral model [8][9][10][11], which equates the target as a rigid, uniform line, with simple mathematical calculation, can reflect the structural differences of the target as a whole. It should be noticed that the scattering point model can be equated to the integral model when the scattering points in the scattering point model are uniformly distributed and spaced less than half of the radar wavelength. Based on the MDE in the echo, the feature extraction of helicopter rotor blade can be transformed into a parameter estimation of multicomponent periodic micro-Doppler signals.
In general, the most common practice is to estimate the target parameters by using the flicker period and the maximum instantaneous micro-Doppler frequency, where the flicker period is determined by the number of blades and rotational speed, and the maximum instantaneous micro-Doppler frequency is determined by the blade length and rotational speed. Obviously, this is an underdetermined equation. Therefore, more effective information from the target echo is needed to avoid the problem of solving the undeterminated equation. The solutions to the parameter estimation of multicomponent periodic micro-Doppler signals can be classified into four main categories [12]: (1) Methods based on signal decomposition.
These methods can decompose multicomponent signals into single component signals, such as separating micro-Doppler components from echoes by chirplet transform [13], variational mode decomposition (VMD) [14] and empirical mode decomposition (EMD) [15], but due to the serious overlap of each micro-Doppler component in echoes, it is difficult to perform effective separation and micro-motion parameter extraction when the frequencies of two components are close to each other; (2) Transform domain-based method. The micro-Doppler signals caused by target vibration and rotation are in the form of Sinusoidal Frequency Modulation (SFM) signals, so the micro-Doppler spectrum of the echoes can be obtained by constructing a matching calculation to establish a sinusoidal frequency modulation signal domain with a unique operational definition and decomposing the echoes in an orthogonal triangular function basis [16]. This method have better estimation accuracy and anti-noise performance, but the cross terms are serious when there are more than three signal components, and it is difficult to extract micro-motion features based on the micro-Doppler spectrum; (3) Image domain-based methods. This type of method is widely used. Firstly, the time-frequency image is obtained by timefrequency analysis through short time Fourier transform (STFT) or short time fractional order Fourier transformation (STFRST) [17]. Then the curve detection in the image space is transformed into the peak detection in the parameter space to extract the micro-motion features of the target by using Hough transform [18][19], iRadon transform [20] and other image processing methods. The advantage is that the extraction of target micro-motion features can be achieved as long as the curve equation of the target micro-motion in the time-frequency domain can be derived. However, such methods rely heavily on the performance of time-frequency analysis methods, and when there are multiple micro-motion signal components in the echo, the time-frequency aggregation is poor, and the computational complexity increases exponentially with the increase of the parameter space dimension; (4) Sparse reconstruction-based methods. Since the target echoes naturally have sparse characteristics, the micro-Doppler signal can be analyzed by sparse reconstruction methods. These methods based on the sinusoidal modulation property of the micro-Doppler signal, construct the corresponding sparse dictionary, and invert the micro-Doppler components by algorithms such as Orthogonal Matching Pursuit (OMP) [6,21], which obtains a good estimation under subsampling conditions but is not robust when the search grid mismatched. For the helicopter rotor blade feature extraction in narrowband radar, this paper proposes a helicopter rotor blade feature extraction method based on flicker phenomenon and phase compensation, which optimizes the extraction process and greatly reduces the amount of computation. The specific work are as follows: (1) Use the integral model of helicopter rotor to obtain the echo under the flicker condition; (2) Predict the possible target blade number and rotational speed parameter combinations through the time-domain flicker interval to reduce the parameter search space dimension; (3) Analyze the mechanism of the generation of echo time domain flicker and time-frequency domain flicker; (4) The feasibility of phase compensation is demonstrated. Also the number of blades, the rotational speed and blade length of the target are estimated based on the periodicity of time-frequency flicker after phase compensation. The greatest advantage of the proposed method is that it can obtain the specific number of target rotor blades directly from the time-frequency diagram of the phase compensation result. The simulation results show that this method can effectively estimate the main parameters of helicopter rotor, and the measured data processing results show that compared with OMP algorithm and Hough transform, its performance is more stable, which means a new technical way for helicopter rotor feature extraction.

II. ROTOR BLADE MICRO-MOTION MODEL
The relative position of the rotor target and the radar is shown in Fig. 1, the distance between the radar and the rotor center is R0, the radar beam elevation angle is  , and the wavelength is  . Let the rotor blade rotation speed be r f and the corresponding rotation angular velocity be w .
where j is an imaginary unit, N is the number of rotor blades, L is the blade length,  n is the initial phase of the nth blade, and n=1,2,...,N-1. Then, the micro-Doppler frequency caused by the rotational motion of the nth blade is Equation (2) shows that the micro-Doppler frequency of target echo is modulated by the sinusoidal function ( ) sin  + n wt , which means that the micro-Doppler frequency is time-varying and nonlinear. In addition, (2) shows that the maximum value of the micro-Doppler frequency is determined by the length of the target rotor, the rotational speed, the wavelength, and the position of the target. When =  + n wt satisfies (3), the instantaneous micro-Doppler frequency of this rotor target takes the maximum value, as shown in (4). In addition, combining the characteristics of (3) and sinc function, the extreme value of the sinc function appears at this time, that is, the flicker phenomenon occurs. The physical essence of the flicker phenomenon is that when a blade on the target rotor is rotated to be perpendicular to the radar LOS direction, the echo intensity is maximum, and when deviating from that position the echo intensity drops steeply, resulting in periodic peaks in the time domain echoes [11]. r r r Considering the physical structure of the rotor blade, when the number of blades is even, the flicker phenomenon caused by the relative symmetry of the blades is simultaneous, then the phase difference between two adjacent flickers appears as 2 N , but when the number of blades is odd, the phase difference between two adjacent flickers appears as only  N [22]. Combined with (3), it can be seen that the time interval between two adjacent flickers satisfies 1 , Equation (5) proves that the time domain flicker interval is inversely proportional to the true rotational speed of the target and is related to the parity of the number of blades.

A. TIME-FREQUENCY FLICKER MECHANISM
Examining (1) carefully and neglecting the effect of echo amplitude, the echo of a single blade is mainly the product of the sinc function (profile) and the exponential function (phase). Without loss of generality, the echo of the first blade can be abbreviated as Under the condition that the wavelength and target properties are determined, this term can be considered as a constant value. As seen from (6), the echo of a single blade is presented as the form of multiplication of sinc function and exponential function, and the micro-Doppler frequency is time-varying, so the short time Fourier transform (STFT) is considered here to analyze the micro-Doppler frequency of the echo in the slow time dimension. From the properties of the Fourier transform, it is known that FT wt (7) where FT{ } denotes the Fourier transform and  is the sign of the convolution operation. Given that sinc(t) and rect(f) are a pair of Fourier transform pairs, then the Fourier transform of the time domain echo envelope is a rectangular strip function occupying a certain bandwidth, which is expressed as a flicker strip in the time-frequency diagram, as shown in Fig. 2(a). The Fourier transform of the exponential function is easy to solve as a sinusoidal function, as shown in Fig. 2  As a result, the completed phase compensated flicker can be identified and extracted from the multiple flickers. Given that the flicker focused to zero frequency must belong to the same blade, the number of blades of the whole rotor can be estimated according to the number of flickers between the two zero frequency flickers.

B. ECHO PHASE COMPENSATION
Since the rotational speed and length of each blade on the rotor are the same, and only different in the initial phase, which means obtaining one of the blade parameters can obtain the relevant parameters of the whole rotor, this paper considers using the phase compensation of a single blade to extract the feature of the whole rotor target. According to (6), the phase compensation operator is established to compensate the phase of the echo, and the rotor blade feature extraction can be converted into the optimal solution of parameter estimation.
where ,,    is the amplitude, angular velocity and initial phase factor, respectively. According to section 3.1, the timefrequency distribution of single blade echoes after phase compensation is a series of flickers with zero center frequency, and the feasibility of phase compensation is mathematically analyzed below. When the target rotor contains an odd number of blades (asymmetrical structure), the time-frequency flicker alternates between positive and negative frequencies due to the asymmetry of the blades, and the time-frequency distribution is similar to Fig. 2 A further study of the phase term reveals that it is positively correlated with the difference of two sinusoidal functions, and the trend of the difference is related to the parameter  . This can be discussed in three specific cases as , the phase of this blade echo is fully compensated, and the phase term is annotated.
, the residual phase is the difference between two sinusoidal signals of the same frequency but with unequal initial phases, varying with the same trend as the sinusoidal signal.
 is a constant that does not vary with time.
3) When , the residual phase is the difference between two cosine signals of different frequencies and different amplitudes, presented as an oscillation of both amplitude and frequency with time.
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.
, the amplitude is taken to the maximum value of + ab ; when cos( ) 1  Similarly, when the target rotor contains an even number of blades (symmetrical structure), due to the symmetry between the blades, positive frequency flicker and negative frequency flicker will occur at the same time in the time-frequency domain, called flicker pairs. Among them, positive frequency flicker means that the center frequency of the flicker strip is positive, while the center frequency of negative frequency flicker is negative. Since the symmetrical two blades' initial phase difference is  , the phase compensation of the two blades can not be completed simultaneously, that is, the rotor echo flicker pair cannot be focused to zero frequencies simultaneously, and the flicker pair is independently analyzed. =4 + f f f , and the echo after phase compensation can be expressed as  (15) From (15), it can be seen that at the time of flicker generation, the two symmetrical blades produce zero frequency flicker and non-zero frequency flicker, respectively. Specifically the Doppler frequency of the latter is ( ) showing a sinusoidal trend with amplitude w , namely, the center frequency of the non-zero frequency flicker undulates as a sinusoidal function. The scene is characterized by the phase of one of the blades being fully compensated, and the echo of this blade is left with a slow time domain envelope. The flicker in the time-frequency pattern is focused near the zero frequency, and the phase of the other blade becomes the original negative quadratic, with its center frequency focused near max md  f . As with an odd number of blades, the flicker caused by a single blade in the blade pair can be focused to zero frequency by phase compensation. Overall, a uniform description of phase compensation for echoes with different numbers of rotor blades can be obtained by choosing a suitable reference standard, and (8) is rewritten as In (16), od bb = ff when the target has an odd number of blades; ev bb = ff when the target has an even number of blades, so the parameter space dimension is transformed (5), because the number of blades usually ranges from 2 to 7, the rotational speed search node does not need to be set iteratively in fact, only a small number of special nodes are needed. By this way, the amount of search process calculations can be significantly reduced.

C. PARAMETER ESTIMATION
For the above analysis, the phase of a single blade in the echo can be determined by calculating whether the center frequency position of the flicker is shifted to the zero frequency position after phase compensation which means the phase of the echo is completely compensated. Since it is not known which flicker belongs to the same blade at the beginning of phase compensation, and there may be multiple phase compensation operators that can focus the center frequency of a flicker to zero frequency, but only when the phase of a blade is fully compensated, the center of the

A. SIMULATION ANALYSIS
This subsection based on the AH-64 helicopter gunship and Mi-28N helicopter gunship rotor models, simulates and analyzes them by using a conventional narrowband system whose radar parameters of carrier frequency is 1GHz, repetition frequency is 4000 Hz, and bandwidth is 2MHz. The target simulation parameters are shown in Table 1. To fully illustrate the feasibility and comprehensive advantages of the proposed parameter estimation method, this subsection also analyzes the estimation accuracy and computational of the proposed algorithm.

1) EVEN NUMBERED BLADE TARGET
The target in this part of the simulation is AH-64, and the target rotor contains four blades. Fig. 4 shows the echoes and time-frequency distribution of the rotor target, where Fig. 4(a) shows the slow time dimensional echoes of the distance bin where the target is located. It can be seen that because of the continuous rotation of the target blades, the slow time dimensional echoes are mainly composed of a series of identically spaced spectral peaks called flickers, and the average flicker interval can be estimated to be 0.05206s. Fig.  4(b) shows the results of the STFT of the slow time dimensional echoes, and it is obvious that both positive and negative frequency flickers occur simultaneously, and the center frequency of a single flicker can be estimated to be 633.32Hz. The asymmetry of the flicker in the timefrequency domain is mainly caused by the asymmetry of the rotor structure, which can be determined by accumulating the pixel values of the time-frequency diagram, and the accumulation results are shown in Fig. 4(c). Then the cross correlation process is performed, and the time delays of the two curves are judged to be 0 in Fig. 4(d), so it can be figured out that the target rotor contains an even number of blades.   . The algorithm gives priority to the combination of the least number of search nodes to compensate for the phase of the echo, that is to say, the first search process is under the six blades case. At this time, it can be seen that the minimum value of the offset matrix recording the deviation of all flicker center frequencies from the reference frequency is 39.52Hz and that after the phase compensation the timefrequency flicker is not focused to zero frequency. So it can be judged that this search process did not get the true value. Update the blade search parameters, and the search results under four blades case as shown in Fig. 5(a) and Fig. 5(b). It can be seen that during this phase search process, the center frequency of the 3rd flicker was focused to zero frequency at the 16th phase node, and at the same time the 1st, 5th, 7th and 9th flickers were focused to zero frequency, showing an obvious periodicity, and the period is 2. After optimal phase compensation, the time-frequency result is shown in Fig. 5(c).  , it can be estimated that the target blade length is 7.274m. Compared with the parameter settings in Table 1, it can be seen that the estimation of blade number and rotational speed is absolutely accurate, and the estimation error of blade length is only 0.36%.

2) ODD NUMBERED BLADE TARGET
The aforementioned validates the feature extraction effect of the symmetric structure rotor target. Since the flicker generated by the symmetric structure rotor differs from the asymmetric structure, this part verifies the feature extraction effect of the proposed method for the asymmetric structure rotor target, with Mi-28N as the simulation target, and its rotor contains 5 blades. Fig. 6 shows the echo and time-frequency distribution of the rotor target. In Fig. 6(a) a total of 19 complete flickers occurred, and the average flicker interval can be estimated to be 0.0245s. In Fig. 6   ,and the search step of initial phase remains the same. The search process under the five blades case can complete the phase compensation of the echo, and the initial phase node corresponding to the minimum difference between all flicker center frequencies and the reference frequency is the 16th, as shown in Fig. 7(a). The offset of each flicker is shown in Fig.  7(b), and it can be seen that the center frequency of the 8th flicker is focused to zero frequency under the 16th phase node, while the 3rd, 13th and 18th flickers are all focused to zero frequency at the same time, showing an obvious periodicity with a period of 5. After optimal phase compensation, the time-frequency result is shown in Fig. 7(c). For the time-frequency flicker with an odd number of blades, the number of blades should be equal to the period of timefrequency flicker of the same blade, thus the estimated number of blades is 5, the corresponding rotational speed estimation is 4.02r/s and the initial phase estimate is 12 Taking the target elevation angle into consideration, it can be estimated that the target blade length is 8.534m. Compared with the parameter settings in Table 1, it can be seen that the estimation of blade number is absolutely accurate, the estimation error of rotational speed and blade length are 0.5% and 0.77% respectively.

B. ESTIMATION AND COMPUTATION ANALYSIS
The above section has verified the effectiveness of the proposed algorithm for feature extraction of targets with symmetric rotor structure and asymmetric rotor structure, and the following section further analyzes the parameter estimation accuracy of the proposed algorithm by taking Mi-28N as an example. In fact, for rotor target identification, the estimation of the initial phase of the blade does not gain due attention, and the main parameters of interest are the number of blades, rotational speed and blade length. In section 3, the conclusion has been drawn only when the initial phase and rotational speed are matched to complete the phase compensation, and the algorithm uses the flicker center frequency deviation in the time-frequency diagram and the periodicity of the minimum value to conduct parameter estimation, then the accuracy of the rotor blade number estimation directly determines the effectiveness of the algorithm, and the rotational speed is affected by the flicker interval and the number of blades. For blade length estimation, it is both affected by the flicker reference frequency estimation and the accuracy of rotational speed estimation. So the estimation accuracy of rotor blade number and blade length is mainly discussed in this section. Fig. 8(a) gives the successful estimation times of blade number after 100 Monte Carlo experiments under different signal-to-noise ratio (SNR) conditions. It can be seen that the algorithm in this paper fails when the SNR is less than 6dB after the pulse compression, because the time-frequency diagram is heavily contaminated by noise under the condition of low SNR, and the central frequency of each flicker cannot be estimated accurately. Fig. 8(b) shows the average estimation error of blade length for the premise that the number of blades can be successfully estimated (SNR>5dB), and it can be seen that as long as the number of blades can be successfully estimated, then the estimation error of blade length can also be kept at a low level, specifically, kept below 1.5%.
(a) Success times (b) Average error From the Monte Carlo experimental results, we can see that the estimation accuracy of this algorithm is very high under the conventional SNR condition. In addition, the algorithm also has a large advantage in terms of computational complexity. If we take the number of time-frequency analysis as the measure of the operation quantity, and the existing iterative search method of time-frequency analysis calculation number is

C. EXPERIMENT AND PERFORMANCE COMPARISON
In this section, the effectiveness of the algorithm is tested by a group of measured data of non-cooperative helicopters, and the performance is compared with the existing OMP algorithm and Hough transform method. These two methods for comparison are the commonly used micro-motion feature extraction methods at present. OMP algorithm is a classical sparse reconstruction algorithm, which inverts the micro-Doppler signal by constructing a sparse dictionary, and Hough transform is an image processing method which extracts the micro-motion feature by detecting the sinusoidal curve in the image. Iradon transform is another commonly used micro-motion feature extraction method, whose mechanism is similar to Hough transform. However, its performance has been proved to be weaker than Hough transform, so it will not be compared in this paper. In the measured scene, the wavelength of the observation radar is 0.3093m; the repetition frequency is 3000Hz; the helicopter target flies back to the station; the elevation angle with the radar is about 0.024rad. And the ground clutter in the field environment is strong, clutter suppression and translational motion compensation is needed to carry out for the measured data. In this section, VMD [14,23] and principal component analysis (PCA) [24] are selected to complete this work. Fig. 9(a) shows the slow-time dimension echo after clutter suppression (900 pulses in total). As the radar adopts mechanical scanning, the strength of the echo will fluctuate with the rotation of the beam. At this time, the time-domain flicker with different amplitude can be observed in the echo. Among them, flicker with relatively strong amplitude occurs about 7 times, and the occurrence times are 0.06167s, 0.087s, 0.1133s, 0.1387s, 0.1647s, 0.1907s and 0.216s respectively. It is estimated that the average flicker interval is 0.0257s. The time domain echo is transformed to the time-frequency domain, as shown in Fig. 9(b). The maximum instantaneous micro-Doppler frequency is 1346.5Hz, and there is a modulation frequency band covering a wide range in the range of [-550Hz, -300Hz] and [370Hz, 550Hz], which is caused by the non-rigid motion of the fuselage and the rotation of the tail rotor. Its micro-Doppler frequency is low and there is no flicker occured, therefore, it will not affect the feature extraction of helicopter by proposed method. The pixel value accumulation and cross correlation processing of Fig. 9(b) can easily determine that the number of target blades is odd, and it can be calculated that the product of the blade number and rotational speed is This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  [3,6.49] . The initial phase search method is consistent with before.
(a) The echoes in time domain (b) The TFD of echoes FIGURE 9. The process of measured data.
The offset of the center frequencies of the flickers relative to the zero frequency after phase compensation is calculated, as shown in Fig. 10(a). At this time, it can be seen that the first flicker and the 6th flicker are focused near the zero frequency, with offsets of 8.343Hz and 3.991Hz respectively. Since the number of target rotor blades is odd, the estimated value of the algorithm for the number of blades is 5, which corresponds to an estimated speed of 3.89r/s. And from the experimental results in Fig. 10(a) and the simulation results in Fig. 8(b), we can see that the offset change pattern is highly similar. Fig. 10(b) shows the best phase compensation result, when the single blade initial phase is 6 . Combined with the elevation relationship between radar and target, using (18) to estimate the blade length is 8.5193m.
(a) Blade number (b) The TFD after optimal phase compensation The same experimental environment is set up and three sets of possible parameter combinations are processed by using the OMP algorithm and the Hough transform. The Fig. 11 shows the processing result of OMP algorithm and the Fig.  12 shows the processing result of Hough transform, where Xaxis indicates the initial phase estimation, Y-axis indicates the rotor length estimation, and Z-axis indicates the normalized magnitude. The number of peaks is the estimate number of blades. Fig. 11 Similarly, as shown in Fig. 11(b) and Fig. 11(c), the OMP algorithm in both the 5 blades and 3 blades cases did not succeed in obtaining the target effective parameter estimations, and the algorithm failed. In the long-term experiments, it was found that the parameter search method based on the OMP algorithm tends to converge to the local extremes, but not stably to the global optimum, resulting in less reliable parameter estimation results. In addition, the degree of gridding of the parameter space can also seriously  However, the accumulated peaks cannot be observed in Fig.  12(a), thus it can be concluded that the Hough transform cannot obtain the target parameter estimation under seven blades case. The five blades case estimation results are shown in Fig. 12(b), where five peaks can be easily seen, that is, the estimated value of the number of blades by Hough transform under the condition of rotational speed of 3.89r/s is 5, and the initial phases of 5 blades are (1º , 73º , 149º , 226º , 289º ), which basically show the law of equal interval distribution, and this group of parameters can be considered as the target parameter estimation value. The corresponding blade length estimations are (8.0m, 7.9m, 7.9m, 8.2m, 8.3m), and the average value is taken as the target rotor blade length estimation of 8.06m. It is found that the feature extraction method based on Hough transform may be invalid in the measured data processing, and it is very easy to confuse the above valid estimates. As shown in Fig. 12(c), the sinusoid curve is detected at the rotational speed of 6.49r/s. Theoretically, there should be no peak at this time, but three peaks with poor sharpening are accumulated at the positions of initial phase (65º , 187º , 302º ) and corresponding blade lengths (8.7m, 8.4m, 8.2m). The reason for this is that the basis function constructed at 6.49r/s can partially fit the sinusoid curve of the target signal, thus forming the peaks, which is a very unfavorable coincidence. But thankfully, the peak in Fig. 12(b) is highly sharpened and no other peaks appear. On the contrary, there are not only the above three peaks in Fig. 12(c), but also many peaks with higher intensity near the blade length of 6.1m, which means the estimation is not valid. And the Hough transform as an image processing method is easily limited by the resolution of the timefrequency analysis tool, which further leads to a relatively low accuracy of the parameter estimation results.  The parameter estimation results of the three different methods are given in Table 2. It can be seen from the experimental results that the specific target type of the noncooperative helicopter may be Mi-28N with high probability. To sum up, it can be seen that the parameter estimation based on the OMP algorithm fails in this experiment, while the Hough transform successfully estimates two sets of target parameters with the interference of invalid estimation, and further discrimination is needed to obtain the final best estimation. Compared with the Hough transform whose best estimation error of blade length is 6.28%, the parameter This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/ACCESS.2022.3179395, IEEE Access VOLUME XX, 2017 9 estimation error of the proposed method in this paper is only 0.93%. In summary, the proposed method can accurately judge the parity of blade number by accumulating the pixel values of the positive and negative frequencies of the timefrequency diagram, and then combined with the flicker interval in the time domain, it can greatly reduce the parameter search range and the amount of computation. Specifically, it only needs to search for 3-4 groups of parameter combinations. Simulation and experimental results show that the proposed method can focus the center frequency of different flickers in the time-frequency diagram to the reference position through phase compensation, so as to determine which flickers are caused by the same blade, and judge the specific number of rotors through the periodicity between flickers. The experimental results show that the proposed algorithm can achieve more stable performance and more accurate parameter estimation than the OMP algorithm and the Hough transform, providing more ideas for further rotor target identification.

V. CONCLUSION
In this paper, we analyze the mathematical mechanism of flicker formation through the integral model of helicopter rotor blade, and propose a helicopter rotor feature extraction method based on flicker phenomenon and phase compensation by combining the time-frequency analysis and micro-motion signal characteristics. Firstly, the timefrequency analysis is used to obtain the time-frequency spectrum of the echoes, and then the phase compensation is applied to the echoes, and the blade number, blade length, rotational speed and initial phase of the target can be estimated according to the phase compensation results. During the execution of the algorithm, a small number of possible parameter combinations are firstly identified by the time domain flicker interval before the parameter estimation, which greatly reduces the amount of computations. In addition, by determining the periodicity of the flicker intervals that are all focused to zero frequency, the impact of individual flicker focus instability on the performance of the algorithm is effectively avoided. Simulation results show that the method can effectively estimate the main parameters of helicopter rotor, while the processing results of the measured data show that it has more stable performance compared with OMP algorithm and Hough transform, which provides a new technical way for helicopter rotor feature extraction.