固定区间Wiener平滑器及其实用稳定性

Fixed-interval Wiener smoother and its practical stability

中文关键词  固定区间Wiener平滑器  固定区间Kalman平滑器  实用稳定性  Kalman滤波方法

英文关键词  fixed-interval Wiener smoother  fixed-interval Kalman smoother  practical stability  Kalman filtering method

中文摘要

      应用稳态Kalman滤波理论,提出了一种固定区间Wiener平滑器,由稳态最优非递推固定区间Kalman平滑器的递推变形引出固定区间Wiener平滑器.该平滑器具有一种在有限区间上的实用稳定性,即当原系统Kalman滤波器的所有特征值远离单位圆周时,对任意选取的平滑初值该平滑器能快速消除其影响而具有快速收敛性.当有接近单位圆周的特征值时,为消除其不良影响,给出了平滑初值的选取方法.仿真例子说明了其有效性.

英文摘要

       Using steady-state Kalman filtering theory, a fixed-interval Wiener smoother was presented, the recursive version of non-recursive steady-state optimal fixed-interval Kalman smoother yielded the fixed-interval Wiener smoother. The smoother has a practical stability in finite interval, i.e. when all eigenvalues of Kalman filter for original system are far from the unit circle, to arbitrary initial values of smoother, the smoother can quickly eliminate their effects to have the quick convergence. When there were eigenvalues near to the unit circle, the choosing method of smoothing initial values was given to eliminate their bad effects. A simulation example showed its effectiveness.