奇异线性连续随机系统动态噪声统计特性未知时的最小阶滤波器

本文讨论了奇异线性定常连续随机系统最小阶滤波器的设计问题。在系统部分观测能量精确测量以及其有限导数存在的情况下,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,从而推导出动态噪声统计特性未知时的降阶线性最优滤波器,其阶数为n-m+r。当观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。

Minimal Order Filter for Singular Linear Continuous Stochastic System without Statistical Property of Dynamic Noise

In this paper, formulas are derived for the minimal order filter in a singular, linear time-invariant, continuous and stochastic system. The equations are derived for the reduced order (n - m + r th order), linear optimal filter without statistical property of dynamic noise, under the assumptions that some measurements are noiseless and that there is a finite number of derivatives for the exact measurements. By means of 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 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 in the end.