带随机参数线性系统参数和状态估计的两阶段卡尔曼滤波算法

A Two-Stage Kalman Filter Algorithm for State and Parameter Estimation of Linear Systems with Random Parameters

本文提出了一种带随机参数线性系统参数和状态估计的两阶段卡尔曼滤波算法.先利用卡尔曼滤波器和参数的观测信息作出参数的估计;然后把参数估计值代入状态方程得到原状态方程的近似,再次利用卡尔曼滤波器和观测信息作出状态的估计.优点是节省计算量,同时,估计的精度也有所提高.

When random parameters are correlated to states,linear systems withrandom parameters are,in fact,non-linear systems.The two-stage Kalman filteralgorithm proposed in this paper approaches parametetr and state estimation oflinear systems with random parameters in this way:first,random parameters areestimated by observed information and the Kalman filter;then theestimated pa-rameters are substituted into the state equations,which derives the approximat-ion of the original state equations;the state estimations are computed by apply-ing Kalman filter again for the approximate state equations.In comparison withthe extanded Kalman filter,the major advantage of this paper's algorithm is thatit reduces a lot of computation.At the same time,the precision of estimation isalso improved to some extent.