带有相关噪声离散线性系统改进的卡尔曼滤波

Modified Kalman Filtering for Linear Discrete-Time Systems with Correlated Noise

研究在系统噪声和观测噪声相关情况下带有控制输入离散线性系统的估计问题,基于卡尔曼滤波和卡尔曼滤波的哈密尔顿方法,提出了一个改进的卡尔曼滤波算法.与经典卡尔曼滤波相比,此算法不需要计算卡尔曼增益矩阵和观测序列的条件均值,并在需要更少回归方程且回归方程易于计算的情况下,取得了最优性能.因此,此算法易于应用.仿真结果表明,此算法能够有效地估计系统状态.

The state estimation problem of linear discrete-time systems was studied in case the system noises and observation noises are both correlated. A modified Kalman filtering which is in combination with the Hamiltonian approach of Kalman filter was proposed. Compared with the classic Kalman filtering,the proposed algorithm needn＇t calculate the Kalman gain matrix and conditional mean of observation sequence,and it obtains the optimal performance under conditions that less regression equations are needed and they are easily calculated. Thus,the algorithm is easy to use. Simulation results demonstrated that the algorithm can effectively estimate the system states.