连续最小阶奇异滤波器

 本文讨论了当动态噪声统计特性未知时,奇异线性定常连续随机系统最小阶滤波器的设计问题。在系统部分观测量能精确测量的情况下,利用广义逆阵方法选择L矩阵,以消除动态噪声对降阶系统的影响,从而推导出缺动态噪声统计特性时的降阶奇异最优滤波器,其阶数为n-m+r。当量测方程奇异假设条件成立及引理有解时,本文证明了最小阶奇异滤波器必定存在。文中举例说明了这一降阶滤波方法的可行性。

A CONTINUOUS MINIMAL ORDER SINGULAR FILTER

This paper is concerned with the minimal order filter for a singular linear time-invariant continuous stochastic system. The equations are derived for the reduced order(n-m+r order) linear optimal filter without knowing statistical property of dynamic noise, under the assumption that some measurements are noise-free and that there is a finite number of derivatives for the exact measurements. By means of using the simplest matrix generalized inverse,a matrix L is chosen in order to eliminate the impact of dynamic noise. When the observational equation is under the hypothesis on singularity and a solution of the lemma exists,we show that there exists a minimal order filter. The possibility of the reduced order filtering method is illustrated by a simple example at the end.