A computationally efficient fixed-lag smoother using recent finite measurements

A Finite Memory Structure Smoother with Recursive Form Using Forgetting Factor

“…Using finite measurements ( ) on the most recent window [ − , ], FMS smoothers [6][7][8][9][10] as well as FMS filters [12][13][14][15] have been developed.…”

“…As shown in [6][7][8][9][10], the fixedlagged system state means there is a fixed delay between the measurement and the availability of its estimate. The delay length is the positive integer with 0 ≤ < .…”

“…Recently, to overcome the resulting problems of existing fixed-lag Kalman smoother with the infinite memory structure (IMS) in [1][2][3][4][5], the fixed-lag smoother with the finite memory structure (FMS) has been developed for state estimation in discrete time-invariant systems [6][7][8][9] and discrete time-varying systems [10]. This FMS smoother has been known to have some good properties such as unbiasedness and deadbeat, which cannot be obtained by the IMS smoother.…”

“…However, existing FMS smoothers in [6][7][8][9][10] have some limitations. Firstly, information about noise covariances to obtain the optimal estimate should be also assumed to be exactly known as the IMS smoother, which may be somewhat restrictive.…”

“…The proposed FMS smoother is represented in a recursive form as well as a matrix form. It is noted that the recursive form has not been developed by the existing FMS smoother in [6][7][8][9][10]. The forgetting factor is shown to be considered as useful parameter to make the estimation performance of the proposed FMS smoother as good as possible.…”