基于粒子滤波和优化TVAR模型的时频分析算法

A New and Better Time-Frequency Estimation Algorithm that Combines Particle Filter with Optimal Time-Varying Auto-Regressive(TVAR) Model

传统的卡尔曼滤波(KF)或时变参数自回归(TVAR)模型对非高斯和强非平稳信号处理无能为力,其算法往往跟踪不上频率的变化。粒子滤波能够处理非线性/非平稳问题,并与TVAR模型结合可获得较好的时频跟踪性能。然而,巨大的计算量是粒子滤波的主要问题。由于粒子滤波通常依赖于大量的粒子数目,尤其是估计量维数较高时,会产生较大的计算负荷。文章提出了一种基于优化TVAR模型结合粒子滤波的时频分析算法,实现了对非平稳、非高斯信号时频谱的准确估计,通过优化的TVAR模型跨过时变参数而直接以频率为估计量,并动态检测频率成分个数,降低估计量维数,从而比传统方法减低了一半以上的计算复杂度。通过仿真信号实验证明,文中算法时频分析精准度明显优于传统算法,并较大幅度地改善了计算性能。

The traditional Kalman Filter （KF） or TVAR model works, in our opinion, unsatisfactorily for the non- Gaussian and non-stationary signals, especially its slow response to the quickly shifting frequencies. So we propose what we believe to be a new and better algorithm, which is explained in sections 1, 2 and 3. Section 1 points out that the particle filter relies on too large a number of particles, thus causing heavy computational load. Section 2 u- ses the optimal TVAR model instead of time-varying parameters to directly estimate the frequencies of the non- Gaussian and non-stationary signals. To dynamically detect the number of frequencies and reduce the number of estimation dimensions, section 3 proposes our time-frequency estimation algorithm that combines the particle filter with the optimal TVAR model. Section 4 generates the non-stationary signal that has multiple spectral components and then simulates our algorithm. The simulation results, given in Figs. 4 and 5, demonstrate preliminarily that, compared with the traditional methods, our algorithm can reduce more than one half of computational and achieve better estimation accuracy. complexity