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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。
Optimal smoothing and optimal deconvolution are of great significance in the field of petroleum seismic exploration, communication engineering, voice processing and other applications. In the past, the smoothing and deconvolution of systems with multiplicative noise mostly have strong limitations on the noise characteristics of the system model. The dynamic noise and the observed noise are independent or only relevant at the same time. This paper presents a fixed-domain smoothing and deconvolution algorithm for the system with multiplicative noise in the case that the dynamic noise is colored noise and the correlation between the dynamic noise and the measured noise is limited for a certain period of time. The algorithm is based on the linear minimum variance In the sense of being the best. Simulation results show the effectiveness of the algorithm.