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 time-frequency 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.
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