一类相关噪声下离散线性系统的递推状态估计

Discrete-time linear estimation with correlated noises

已有的相关噪声情况下,离散线性系统的递推状态估计算法大多假定系统噪声和量测噪声在同一时刻相关,通过对系统噪声和量测噪声相互独立的连续线性系统的采样离散化,发现离散化后的系统相邻时刻的系统噪声和量测噪声相关。在线性无偏最小方差估计准则下,推导出了该离散化后所得系统的全局最优递推状态估计算法。通过Monte Carlo仿真,与假定系统噪声和量测噪声互不相关的Kalman滤波算法进行了比较,进一步表明了新算法的有效性。

Most of the existing recursive state estimation algorithms for discrete-time linear system with correlated noises assume that process and measurement noises are correlated at the same instant. Via sampling discretization to the continuous-time linear system with uncorrelated process and measurement noises, it is shown that the neighbouring process and measurement noises are correlated in its discretized counterpart. In the sense of linear unbiased minimum variance estimation, a global optimal recursive state estimation algorithm for this discretized linear system is proposed. Monte-Carlo simulation results are provided to compare the new algorithm with the Kalman filter with uncorrelated process and measurement noises, which demonstrates the validity of the new algorithm.