HE Weikun ,SUN Jingbo ,ZHANG Xinyun ,and LIU Zhenming
1.College of Electronic Information and Automation,Civil Aviation University of China,Tianjin 300300,China;2.Cyber Intelligent Technology Co.,Ltd,Ji’nan 250100,China
Abstract:Micro-Doppler feature extraction of unmanned aerial vehicles (UAVs) is important for their identification and classification.Noise and the motion state of the UAV are the main factors that may affect feature extraction and estimation precision of the micro-motion parameters.The spectrum of UAV echoes is reconstructed to strengthen the micro-motion feature and reduce the influence of the noise on the condition of low signal to noise ratio (SNR).Then considering the rotor rate variance of UAV in the complex motion state,the cepstrum method is improved to extract the rotation rate of the UAV,and the blade length can be intensively estimated.The experiment results for the simulation data and measured data show that the reconstruction of the spectrum for the UAV echoes is helpful and the relative mean square root error of the rotating speed and blade length estimated by the proposed method can be improved.However,the computation complexity is higher and the heavier computation burden is required.
Keywords:micro-rotor unmanned aerial vehicle (UAV),low signal to noise ratio (SNR),micro-Doppler,feature extraction,parameter estimation.
In recent years,due to the advantages of portability,small size,and low cost,the unmanned aerial vehicle (UAV)industry has developed rapidly,and can provide great convenience for military and civilian applications [1].However,the rapid development of drones has led to an increased risk.With the presence of drones in civilian airspace,the interference with the operation of airports has also been caused.The monitoring and identification of micro-rotor UAV is of great significance.
Micro-Doppler features representing the micro-motion of the targets such as the blades rotation and wing flapping [2] are efficient and are widely used for target classification and recognition.However,in the actual flight environment of the UAV,the radar echoes are often affected by strong noise and the amplitudes of echoes are relatively weak,which may result in the difficulty with the extraction of the micro-motion features [3,4].The analysis and extraction of micro-Doppler features for rotor UAVs in a strong noisy environment is important and significant.
For micro-Doppler feature extraction of UAV,autocorrelation function,singular value decomposition (SVD)and empirical mode decomposition (EMD) methods have been used [5-10],but due to the influence of the random initial phases and noise,these methods are not easy to extract robustly the micro-motion parameters (rotation rate,blade length,etc.).A regularized 2D complex-log spectral method is proposed to realize the feature extraction and the classification for birds and UAVs [11].The cadence frequency diagram (CFD) method is used to classify the UAVs and estimate the corresponding micromotion parameters of the drones in the hover state[12-14].However,it is not efficient for the UAVs in motion because of the non-uniqueness rotation rate and random initial phase.The cepstrum is often exploited and used,but it is more sensitive to noise and the performance may be effected [15-17].The micro-motion feature extraction and parameter estimation of the moving UAVs on the condition of low signal to noise ratio (SNR)are mainly focused in this paper.
In the environment of low SNR,the above methods are unreliable to extract the corresponding parameters due to the weak scattering characteristics and the initial phase randomness of the rotor.The spectrum reconstruction of the UAV echoes in motion is reviewed in which an iterative optimization algorithm is described to solve L1-norm penalized least squares problem [18].By reconstructing the spectrum of the UAV,the micro-motion feature can be strengthened and the influence of noise on the feature extraction and parameter estimation can be reduced.Based on the instantaneous energy distribution in the timefrequency domain,the estimation of the maximum Doppler frequency for the rotor UAV can be achieved by using the maximum value parameter estimation method.The rotation rate of UAV rotor is estimated based on the improved 2D cepstrum method,and finally the blade length is also estimated by using the estimation of the maximum Doppler frequency and the rotation rate.It can be shown that the reconstruction of the spectrum for the UAV echoes is helpful and the relative mean square root error of the rotating speed and blade length estimated by the proposed method can be improved.
The remainder of the paper is organized as follows.Section 2 gives the signal model of the UAV echoes.The impact of noise on time-frequency spectrum of the UAV echoes is explored in Section 3.Section 4 introduces the denoising method for UAV echoes and the spectrum reconstruction method for UAV echoes on the environment of low SNR is proposed.The feature extraction and parameter estimation based on the maximum value parameter estimation and the improved 2D cepstrum method are focused in Section 5.In Section 6,the experimental results and the performance of the proposed method are presented.Section 7 concludes the paper.
The geometric relationship model of radar and multi-rotor UAV is shown in Fig.1 [19].The initial distance from the rotor center to the radar isR0,the azimuth angle and the pitch angle are denoted as α and β respectively.For a scattering pointPwith a distance oflpfrom the rotation center,its rotational angular velocity and initial phase angle are ω and θ0,and the radial velocity relative to the radar can be written asv.
Fig.1 Geometric relationship of radar and multi-rotor UAV
The distance from pointPto the radar at timetcan be expressed as
After removing the carrier,the echoes of the scattering pointPreceived by the radar is shown as follows:
where σPis the scattering coefficient and λ is the wavelength of the emitted signal.Using the principle of the scattering point superposition,the observed data of the multi-rotor UAV [20] can be described as
where cosh(·) is the hyperbolic cosine function,σ is the scattering coefficient of the blade,σdis the scattering coefficient of the fuselage,Nis the number of rotors,Lis the length of the blade,Sa is the samping function,θiis the initial phase of the blade,wiis the rotational angular velocity of the blade,andnis noise.The ground clutter is included in the clutter componentc.
The micro-Doppler characteristics of the quadcopter in the motion state on the condition of low SNR is demonstrated in this section and the influence of noise on the time-frequency spectrum is also analyzed.The C-band chirp radar is used in the experiment,and parameters related with radar and UAV are shown in Tables 1-2 (the UAV parameters refer to DJI Phantom 4 Pro).The noise is Gaussian white noise,and the SNR is set to 5 dB.The initial phase of the quadcopter rotor is uniformly distributed on [-π,π].
Table 1 Radar parameters
Table 2 UAV parameters
The micro-motion characteristics of the quadcopter in the motion state can be shown in Fig.2.The length of Gaussian window is 64 and the sliding length is 1.From Fig.2,it can be seen that it is the superposition of multiple blade flash components in the time-frequency domain.In low SNR environment,due to the influence of noise,blade flashes cannot be clearly observed by the time-frequency spectrum obtained by short-time Fourier transform (STFT) [21-23],Wigner Viller distribution(WVD) [24] and smooth pseudo WVD (SPWVD) [25].Compared with the above three methods,the time-frequency resolution obtained by reassigned spectrogram(RSP) is higher [26-28].However,it is not easy to estimate the micro-motion parameters precisely,so noise reduction is essential for the micro-motion characteristics extraction of UAVs.
Fig.2 Micro-Doppler characteristics of quadcopter in motion
In this section,the spectrum reconstruction method of the UAV echoes on the condition of low SNR will be introduced on the purpose of noise reduction,and then the micro-motion parameters of the UAV can be intensively estimated by combining with the feature extraction method.
4.1 Problem description
Given the observed vectoryand the corresponding transform domain (frequency domain) matrixA,the problem of reconstructing the spectrum of UAV echoes can be considered as that of finding a sparse vectorxsuch thaty≈Ax.Using the L1-norm as a measure of sparsity,the problem [18] can be formulated as
4.2 Algorithm design
First,an auxiliary variableuis introduced,and the optimization problem in (4) [18] is equivalent to
The augmented Lagrangian method (ALM) is used to solve the optimization problem shown in (5) [29],then the corresponding iterative algorithm can be obtained.
The vectordis usually initialized to the zero vector,and µ is the step size.The minimization problem in (6) is solved by the soft-thresholding rule.The minimization problem in (7) is the constrained least squares problem,hence its solution is available in explicit form (in terms of a matrix inverse).Utilizing the explicit forms for the above optimization problems,Algorithm 2 can be obtained.
The operator (·)His the complex conjugate transpose,the matrixAusually satisfies the Parseval form [29]:
wherepis the Parseval constant,and is usually set to 1.Iis the identity matrix.Let
then (9) can be simplified as
According to (10) and (11),Algorithm 2 is simplified to avoid the inversion operation,and Algorithm 3 can be intensively obtained.
The flow chart of the reconstruction method for the spectrum of UAV echoes is shown in Fig.3.
Fig.3 Flow chart of the reconstruction method of UAV echoes
5.1 Feature extraction
The CFD method is widely used in the feature extraction of UAVs and the definition [11] is as follows:
where RS(n,m) denotes the time-frequency spectrum of the echoes obtained by RSP method and F denotes the fast Fourier transform (FFT) operation along the time axis.In the CFD method,FFT is performed along the periodic blade flashes in the time-frequency spectrum,which represents the repetition frequency of each Doppler component,so the rotation speed of the rotor UAV can be obtained.
The multi-rotor UAV in the motion state usually has two different rotation speeds,and the initial phase of each rotor is random,the blade flashes in the time-frequency spectrum are seriously overlapped,which makes the CFD method unable to accurately obtain the rotation frequency of the UAV.
The cepstrum can be used and the definition [16] is as follows:
where F and F-1are denoted as FFT and inverse FFT(IFFT) operations respectively.By the logarithmic operation,the weak signal components can be enhanced and the spectrum energy is concentrated.For multi-rotor UAVs,the output obtained by the cepstrum can be equivalent to the linear superposition of multiple periodic impulse responses,which can solve the rotation frequency estimation problem of the UAV in the motion state.
While considering the variance of rotor rates with the time in complex motion state,the cepstrum analysis can be improved and it is performed on the basis of the timefrequency spectrum obtained by STFT,then the relationship of rotation speed with time can be obtained.The definition can be derived as follows:
whereS(n,m) is the time-frequency spectrum of the observed signal.By the sliding window,the cepstrum analysis is performed on the truncated signal obtained by the sliding window.Thus the variance of the rotation speed with the time can be accurately obtained.
5.2 Parameter estimation
To estimate the parameters of the UAV,it is necessary to find the mapping relationship between the micro-motion features and the corresponding parameters of the UAV.
For rotor UAVs,when the radar beam illuminates the blade vertically,the radial velocity of the blade tip is maximum,and the maximum Doppler frequency can be written as
where λ is the radar wavelength,β is the pitch angle of the radar line of sight (LOS) relative to the center of the UAV,Lis the blade length,andfrotis the rotation speed.The four rotors of the UAV have the same rotation speed when it is in hover.However,for the drones in the motion state,there are commonly two different rotation speeds,which correspond to two different maximum Doppler frequencies.
The estimation of the maximum Doppler frequency for the rotor UAV is a multi-component parameter estimation problem which can be achieved based on the instantaneous energy distribution in the time-frequency domain,and it is called the maximum value parameter estimation method [30].
Let R S(n,m) be theN×Mmatrix corresponding to the time-frequency spectrum obtained by RSP,andNandMcorrespond to the time and frequency dimensions respectively.The maximum value can be searched on each column of the above R S(n,m) [30].
The number of blades for each rotor of the UAV is two,and the blade flash frequency is twice of the rotation speed,which can be written as
5.3 Process of the proposed feature extraction and parameter estimation method for UAVs
The process of feature extraction and parameter estimation for UAVs is shown in Fig.4.First the UAV echoes are reconstructed to denoise the echoes,and RSP is performed to obtain the time-frequency spectrum.The maximum Doppler frequency can be estimated based on the maximum value parameter estimation method.At the same time,improved cepstrum is used to extract the rotation speed of the UAV,and then the blade length of the rotor can be intensively estimated.
Fig.4 Block diagram of UAV feature extraction
The implementation steps are as follows:
Step 1Reconstruct the UAV echoes to denoise the echoes；
Step 2Obtain the time-frequency spectrum by RSP;
Step 3Estimate the maximum Doppler frequency based on the maximum value parameter estimation method；
Step 4Extract the rotation speed of the UAV by using the improved cepstrum and then estimate the blade length of the rotor.
6.1 Estimation of micro-motion parameters for quadcopter in hover
The radar and the UAV parameters are shown in Tables 1-2.In the experiment,the UAV fuselage scattering is considered,and the initial phases of the four rotors are uniformly distributed.The SNR is 5 dB.Fig.5 shows the estimation results of the micro-motion parameters of the quadcopter in hover state.
Fig.5 Micro-motion parameter estimation results of quadcopter in hover state
The random initial phases of the four rotors result in the different time at which the flashing occurs for each rotor blade,but the flashing characteristics of the blades can still be seen in the RSP spectrum.The theoretical maximum Doppler value is 1 548.22 Hz.The estimated value before spectrum reconstruction is 1 652.01 Hz,and the estimated value after spectrum reconstruction is 1 516.3 Hz.It can be seen that the estimation precision has been greatly improved.The theoretical value of the blade flash frequency is 112 Hz.The estimated value before spectrum reconstruction is 114.16 Hz,and after spectrum reconstruction the estimated value is 111.86 Hz.
In order to verify the estimation performance of the rotation speed and blade length,100 Monte Carlo experiments are carried out.The results are shown in Table 3.The relative mean square root errors of rotation speed and blade length are 0.21% and 2.21%,respectively.The results show that the proposed method can estimate the micro-motion parameters of quadcopter more accurately in hover state.
Table 3 Result comparison of the micro-motion parameters estimation for the quadcopter in hover state (SNR=5 dB)
6.2 Estimation of micro-motion parameters for quadcopter in motion
The parameters of radar and the UAV remain unchanged.The UAV is assumed to be flying at a constant speed.The fuselage speed is 6 m/s,and SNR is 5 dB.The results are shown in Fig.6.
Fig.6 Micro-motion parameter estimation results of quadcopter in motion state
As shown in Fig.6,theoretical values of the maximum Doppler frequencies are 1 350.29 Hz and 1 728.37 Hz.The estimated values before spectrum reconstruction are 1 452.50 Hz and 1 821.60 Hz,and the estimated values after spectrum reconstruction are 1 308 Hz and 1 683.23 Hz.The quadcopter in the motion state has two different rotation speeds,and the theoretical values of the blade flash frequencies are 100 Hz and 128 Hz respectively.Sometimes,the cepstrum method cannot be accurately estimated before spectrum reconstruction,just as shown in Fig.6(c).However,just as shown in Fig.6(d),after the spectrum reconstruction,the estimated values of the flash frequency are 99.80 Hz and 128.21 Hz respectively.Similarly,100 Monte Carlo experiments are performed,and the results are shown in Table 4.The relative mean square root errors of the rotation speed and blade length are 0.45% and 3.51% for a rotation speed 50 r/s,and 0.33% and 2.89% for a rotation speed 64 r/s.
Table 4 Result comparisons of micro-motion parameters estimation for quadcopter in motionr state (SNR=5 dB)
The micro-Doppler feature extraction of rotor UAV in the complex motion state is also discussed.During the observation time,the acceleration movement is supposed and the rotation speeds change from 56.02 r/s and 64.09 r/s to 50.5 r/s and 70.28 r/s.The results are shown in Fig.7.Before spectrum reconstruction,the maximum Doppler frequency cannot be accurately extracted due to the complexity change of the rotation speed and the influence of noise.After spectrum reconstruction,the noise is effectively suppressed,and the theoretical values of the maximum Doppler frequency are 1 534.36 Hz and 1 755.67 Hz before 0.1 s,1 332.34 Hz and 1 854.19 Hz after 0.1 s.The estimated values are 1 464.41 Hz and 1 689.57 Hz before 0.1 s,and 1 256.11 Hz and 1 796.39 Hz after 0.1 s,which are consistent with the actual values.
Fig.7 Maximum Doppler frequency estimation results of quadcopter in complex motion state
The improved cepstrum method is used to extract the rotation speed of quadcopter in the above complex motion state,and the results are shown in Fig.8.Before spectrum reconstruction,the rotation speed of the UAV cannot be accurately estimated by the cepstrum method.After spectrum reconstruction,the estimated values of rotation speeds are 56.31 r/s and 64.1 r/s before 0.1 s,49.9 r/s and 70.62 r/s after 0.1 s,which are consistent with the actual value.
Fig.8 Rotation speed estimation results of quadcopter in complex motion state
6.3 Performance analysis
In this subsection the quadcopter in motion is taken as an example,and the estimation precision of the maximum Doppler frequency before and after spectrum reconstruction is compared for different SNRs.A total of 100 Monte Carlo experiments are performed,and the relative mean square root error is shown in Fig.9.It can be seen that the spectrum reconstruction helps to reduce the relative mean square root error.When the SNR is greater than 10 dB,the relative root mean square error before and after spectrum reconstruction does not vary much,but when the SNR is less than 5 dB,the estimation precision of the maximum Doppler frequency after spectrum reconstruction is improved by at least 1.65%.When the SNR is greater than 0 dB,the relative mean square root error after spectrum reconstruction is less than 4.8%.However,as far as before spectrum reconstruction is concerned,the required SNR is about 10 dB in order to achieve the above estimation performance.
Fig.9 Performance comparison for estimation of the maximum Doppler frequency
Based on the cepstrum method,the performance curve for the rotation rate estimation before and after the spectrum reconstruction is shown in Fig.10.The estimation accuracy will increase as the increase of SNR.When the SNR is less than 0 dB,compared with that before spectrum reconstruction,the estimation accuracy of the rotation rate after the spectrum reconstruction is improved by at least 3.15%.When the SNR is greater than -5 dB,the relative mean square root error after spectrum reconstruction is less than 4.1%.
Fig.10 Performance comparison for estimation of rotation rate
The performance curve for the estimation of the blade length after spectrum reconstruction is shown in Fig.11.Because the estimation precision of the blade length is determined by that of the rotation speed and Doppler frequency,the relative mean square root error of the blade length is larger than those of the rotation speed and Doppler frequency.When SNR is -10 dB,the relative mean square root error reaches 11.63% and 14.72%respectively corresponding to the rotation speed of 50 r/s and 64 r/s.When SNR is greater than 0 dB,the relative mean square root error is less than 4.9%.When SNR is greater than 15 dB,the relative mean square root error tends to 2.45% and 1.85%.In addition,due to the random initial phases of the four rotors,the Doppler components in that spectrogram may overlap each other,which results in that estimation performance of the Doppler frequency corresponding to 50 r/s is not so good as that of Doppler frequency corresponding to 64 r/s.Therefore,the performance for the estimation of the blade length corresponding to 64 r/s is better than that corresponding to 50 r/s.
Fig.11 Performance for estimation of blade length
The computational complexity is also analyzed which is shown in Table 5.The computer CPU model is Intel(R)Core (TM) i5-5200U,and the main frequency is 2.2 GHz.For the estimation of the maximum Doppler frequency,the calculation time before and after the spectrum reconstruction is 22.01 s and 25.74 s respectively，and the calculation time for the rotation speed is 3.56 s and 5.77 s respectively.It can be seen that the spectrum reconstruction will increase the computational burden,but the estimation accuracy for the micro-motion parameters after the spectrum reconstruction is higher than that before the spectrum reconstruction.
Table 5 Analysis of computational complexity s
6.4 Results of the measured data
A surveillance radar in a linear frequency modulation(LFM) is considered,and measured data is processed.The UAV accelerates in the radial direction.Mountains,small buildings,trees,etc.are included in the observed data.The range-Doppler spectrum is obtained and the experimental results are shown in Fig.12.The ground clutter is near the zero frequency,and the coordinate point in Fig.12(b) indicates the UAV target.According to the Doppler frequency shift of the UAV fuselage,the fuselage velocity is calculated to be approximately 9.1 m/s.
Fig.12 Observed data
Notch filter is designed and used to suppress ground clutter.The filtered results are shown in Fig.13.It can be shown that the ground clutter has been filtered out and the UAV fuselage information can be clearly seen,but due to the long propagation distance and the interference of noise,the received blade echoes are relatively weak and their micro-Doppler is not obvious.
Fig.13 Results after ground clutter suppression
The spectrum of UAV echoes is firstly reconstructed,then the improved cepstrum method is used to obtain the variance of the rotation speeds with time,which can be shown in Fig.14.The estimated value of the rotation speed is 94.88 r/s at about 1 s,and the estimated values are 65.04 r/s,75.37 r/s and 88.62 r/s after 2 s.The proposed method can be used to estimate the rotation rate of the multi-rotor UAV under the low SNR.
Fig.14 Estimation result of rotation speed
The micro-Doppler characteristics of the quadcopter on the condition of low SNR is firstly analyzed in this paper,which shows that the influence of noise may make it difficult to observe clearly the micro-motion characteristics especially for that of the UAVs in motion.Aiming at the extraction of the micro-motion parameters of the rotor UAV,the spectrum is reconstructed to reduce the influence of the noise,and the Doppler frequency and the rotation speed can be intensively estimated.Experimental results show that the estimation accuracy for the micromotion parameters can be improved,and when SNR is greater than 0 dB,the relative mean square root error of the rotating speed and blade length can be controlled within 5% based on the proposed method.However,we would like to point out that the computational burden for the proposed method is increased compared with that before the spectrum reconstruction.
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