统一的和通用的Kalman滤波理论

Unified and General Kalman Filtering Theory

用射影理论对一般线性离散时变随机系统提出了统一和通用的Kalman滤波理论,其中系统噪声在相邻时刻是相关的,且系统噪声和观测噪声在相同和相邻时刻是相关的。提出了最优和稳态Kalman滤波器、平滑器和预报器,推广了经典Kalman滤波理论。

Using the projection theory, a unified and general Kalman filtering theory is presented for general linear discrete time-varying stochastic systems, where the system noise is correlated at adjoining times, and the system noise and measurement noise are correlated at the same and adjoining times. The optimal and steady-state Kalman filter, smoother and predictor are presented. The classical Kalman filtering theory is extended.