带乘性噪声系统在加性噪声相关时的最优固定域平滑及反褶积算法

Optimal Fixed-Interval Smoothing and Deconvolution for Systems with Multiplicative Noise and Correlated Additive Noises

最优平滑及最优反褶积在石油地震勘探、通讯工程、语音处理等应用领域都具有十分重要的意义。以往的带乘性噪声系统的平滑及反褶积大都对系统模型的噪声特性有着较强的限制条件 ,要求动态噪声及观测噪声互相独立或只能在同时刻相关。该文给出了一种在动态噪声为有色噪声及动态噪声和量测噪声在有限时间段上相关的情形下带乘性噪声系统的固定域平滑及反褶积算法 ,该算法在线性最小方差意义下是最优的。通过仿真计算 ,说明了该算法的有效性。

As to the most existing, smoothing and deconvolution algorithms for the systems with multiplicative noise, there is an assumption that the state and the observation noises are uncorrelated or correlated just at the same time. In this paper, an optimal fixed interval state smoothing and deconvolution for systems with multiplicative noise are developed in the sense of linear minimum variance under the assumption that the state and the observation noises of the system are correlated on a finite time interval. Satisfactory simulation results are obtained and validate the algorithm.