动态时频谱分析、探测和跟踪的随机有限集法
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摘要
动态出现和消失多分量信号的时频分析问题一直是非平稳信号处理的难点之一。为此,提出了一种分析、探测和跟踪多分量信号的随机有限集法。该算法利用时频变换,如短时傅里叶变换或自适应谱估计法,以及多项式预测模型,将多分量信号的时频分析问题归纳成可利用随机有限集进行多目标追踪的问题。分析表明:借助于提出的初始权重赋值算法,以及谱分量幅度和频率的联合似然函数,就可利用高斯混合概率假设密度滤波器来实现对动态时频谱的分析、探测和跟踪。在仿真实验中,所提算法有效提升了动态时频谱的跟踪精度,其对微弱时频谱分量的探测能力,以及对载频差异的分析能力均优于文献报道的算法。
Time-frequency analysis of multi-component signal with dynamic births and deaths has always been one of the difficulties in non-stationary signal processing.In this paper,a random finite set approach to analyzing,detecting,and tracking multi-component signal is proposed.By means of time-frequency transform,such as short-time Fourier transform or iterative adaptive approach,and polynomial prediction models,time-frequency analysis of multi-component signal can be formulated as multi-target tracking with random finite sets.The analyses show that,by adopting the given initial weight assignment algorithm and the provided joint likelihood function of the amplitudes and frequencies of the time-frequency spectra,the Gaussian mixture probability hypothesis density filter can be used to achieve the analysis,detection and tracking of dynamic timefrequency spectra.Simulation results show that the proposed method effectively improves the tracking accuracy of dynamic time-frequency spectra,and its performances of weak component detection and close modes analytical capabilities are much better than the ones reported in the literature.
Time-frequency analysis of multi-component signal with dynamic births and deaths has always been one of the difficulties in non-stationary signal processing.In this paper,a random finite set approach to analyzing,detecting,and tracking multi-component signal is proposed.By means of time-frequency transform,such as short-time Fourier transform or iterative adaptive approach,and polynomial prediction models,time-frequency analysis of multi-component signal can be formulated as multi-target tracking with random finite sets.The analyses show that,by adopting the given initial weight assignment algorithm and the provided joint likelihood function of the amplitudes and frequencies of the time-frequency spectra,the Gaussian mixture probability hypothesis density filter can be used to achieve the analysis,detection and tracking of dynamic timefrequency spectra.Simulation results show that the proposed method effectively improves the tracking accuracy of dynamic time-frequency spectra,and its performances of weak component detection and close modes analytical capabilities are much better than the ones reported in the literature.
引文
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[2] TANTIBUNDHIT C,PERNKOPF F,KUBIN G.Joint time-frequency segmentation algorithm for transient speech decomposition and speech enhancement[J].IEEE Transactions on Audio,Speech,and Language Processing,2010,18(6):1417-1428.
[3] BOASHASH B,AZEMI G,O’TOOLE J M.Time-frequency processing of nonstationary signals:Advanced TFD design to aid diagnosis with highlights from medical applications[J].IEEE Signal Processing Magazine,2013,30(6):108-119.
[4]王殿伟,李言俊,张科.基于S变换的时频特征提取与目标识别[J].航空学报,2009,30(2):305-310.WANG D W,LI Y J,ZHANG K.Time-frequency signature extraction and recognition of target based on S-transform[J].Acta Aeronautica et Astronautica Sinica,2009,30(2):305-310(in Chinese).
[5] CAREVIC D,DAVEY S.Two algorithms for modeling and tracking of dynamic time-frequency spectra[J].IEEE Transactions on Signal Processing,2016,64(22):6030-6045.
[6] PAPANDREOUSUPPAPPOLA A.Applications in timefrequency signal processing[J].Journal of Research in Childhood Education,2013,27(2):127-152.
[7] DJUROVI′CI,SEJDI′CE,JIANG J.Frequency-based window width optimization for S-transform[J].AEU-International Journal of Electronics and Communications,2008,62(4):245-250.
[8]李淑雅,施明,张建秋.时频分析的卡尔曼滤波匹配解调变换法[J].电子学报,2018,46(4):769-774.LI S Y,SHI M,ZHANG J Q.Matching demodulation transform with a Kalman filter for time-frequency analyses[J].Acta Electronica Sinica,2018,46(4):769-774(in Chinese).
[9] ZHONG J,HUANG Y.Time-frequency representation based on an adaptive short-time Fourier transform[J].IEEE Transactions on Signal Processing,2010,58(10):5118-5128.
[10] WANG S,CHEN X,CAI G,et al.Matching demodulation transform and synchrosqueezing in time-frequency analysis[J].IEEE Transactions on Signal Processing,2014,62(1):69-84.
[11] CHEN S,DONG X,PENG Z,et al.Nonlinear chirp mode decomposition:A variational method[J].IEEE Transactions on Signal Processing,2017,65(22):6024-6037.
[12] LI Z,MARTIN N.A time-frequency based method for the detection and tracking of multiple non-linearly modulated components with births and deaths[J].IEEE Transactions on Signal Processing,2016,64(5):1132-1146.
[13] HEINONEN P,NEUVO Y.FIR-median hybrid filters with predictive FIR substructures[J].IEEE Transactions on Acoustics Speech&Signal Processing,2002,36(6):892-899.
[14] VO B N,MA W K.The gaussian mixture probability hypothesis density filter[J].IEEE Transactions on Signal Processing,2006,54(11):4091-4104.
[15] STANKOVIC L,STANKOVIC S,DAKOVIC M.From the STFT to the Wigner distribution[J].IEEE Signal Processing Magazine,2014,31(3):163-174.
[16] MAHLER R P S.Multitarget Bayes filtering via first-order multitarget moments[J].IEEE Transactions on Aerospace&Electronic Systems,2004,39(4):1152-1178.
[17]瑚成祥,刘贵喜,董亮,等.区域杂波估计的多目标跟踪方法[J].航空学报,2014,35(4):1091-1101.HU C X,LIU G X,DONG L,et al.Region clutter estimation method for multi-target tracking[J].Acta Aeronautica et Astronautica Sinica,2014,35(4):1091-1101(in Chinese).
[18] STONE M H.The generalized weierstrass approximation theorem[J]. Mathematics Magazine,1948,21(4):167-184.
[19] MIYAKAWA T,TSUTSUI H,OCHI H,et al.Realization of frequency-domain circuit analysis through random walk[C]∥Design Automation Conference.Piscataway,NJ:IEEE Press,2013:169-174.
[20] VO B N,SINGH S,DOUCET A.Sequential Monte Carlo methods for multitarget filtering with random finite sets[J].IEEE Transactions on Aerospace&Electronic Systems,2005,41(4):1224-1245.
[21] ZHANG J Q.An eigenvalue residuum-based criterion for detection of the number of sinusoids in white Gaussian noise[J]. Digital Signal Processing,2003,13(2):275-283.
[22] LEE J,YOUM H W,LEE J R,et al.Joint multi-target detection and tracking using conditional joint decision and estimation with OSPA-like cost[C]∥International Conference on Information Fusion. Piscataway, NJ:IEEE Press,2015:1740-1747.
[23] STOICA P,LI J,HE H.Spectral analysis of nonuniformly sampled data:A new approach versus the periodogram[J].IEEE Transactions on Signal Processing,2009,57(3):843-858.