A Finite Memory Structure Smoother with Recursive Form Using Forgetting Factor

Abstract

This paper proposes an alternative finite memory structure (FMS) smoother with a recursive form under a least squares criterion using a forgetting factor strategy. The proposed FMS smoother does not require information of the noise covariances as well as the initial state. The proposed FMS smoother is shown to have good inherent properties such as time-invariance, unbiasedness, and deadbeat. 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. Through computer simulations for the F-404 engine system, it is shown that the proposed FMS smoother can be better than the existing FMS smoother for incorrect noise covariances and the IMS smoother for temporary uncertainties.

Finite Memory Structure Filtering and Smoothing for Target Tracking in Wireless Network Environments

“…Using (13) with (15) and (16), the proposed unified algorithm of a FMS filtering and smoothing-based target tracking scheme provides estimates for position as well as acceleration of moving target in real time, while eliminating unwanted noise effects and maintaining desired moving positions. Via extensive computer simulations, the performance of the proposed unified algorithm-based target tracking scheme is evaluated and compared with the existing IMS filtering-based scheme of [20][21][22].…”

“…Likewise the recursive Kalman filter in [1][2][3][4][5], the FMS filter in [6][7][8][9] is a causal filter that provides state estimates at given times based only on the relative past. Hence, as a noncausal filter, the FMS smoother has been also designed for estimation problems when there is a fixed delay d between the original state and the estimated state [13][14][15][16]. The FMS smoother has been shown to be much less computationally complex and more robust against temporary uncertainties than the recursive Kalman smoother.…”

Adaptive Fading-Memory Receding-Horizon Filters and Smoother for Linear Discrete Time-Varying Systems

“…RH estimation has good properties such as bounded-input bounded-output (BIBO) stability, dead-beat property, fast-tracking ability, and robustness against modeling uncertainties and numerical errors. Furthermore, the RH estimators in [7][8][9][10][11][12][13][14] do not require a priori knowledge of initial information. Thus, as an alternative to Kalman-filter-based methods, RH estimators have been extensively investigated recently [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…Furthermore, the RH estimators in [7][8][9][10][11][12][13][14] do not require a priori knowledge of initial information. Thus, as an alternative to Kalman-filter-based methods, RH estimators have been extensively investigated recently [7][8][9][10][11][12][13][14][15][16][17][18][19].…”

“…With a constant fading factor, the fadingmemory RH filters were proposed for linear continuous time-invariant and discrete timevarying state-space models in [17] and [10], respectively. For the RH smoothing problem, the fading-memory algorithm was applied to the fixed-lag RH smoother with a recursive form in [11]. The results in these approaches show that the combination of RH estimation and fading-memory strategy can provide faster tracking ability and better robustness concerning temporary modeling uncertainties than the fading Kalman filter and nonfadingmemory RH filter.…”