A Reorganized Innovation Approach to Linear Estimation

Abstract

REFERENCES[1] H. Al-Duwaish, M. N. Karim, and V. Chandrasekar, "Use of multilayer feedforward neural networks in identification and control of Wiener model,"Abstract-This note will address a linear minimum variance estimation of discrete-time systems with instantaneous and delayed measurements. Although the problem may be approached via system augmentation and standard Kalman filtering, the computation of filter may be expensive when the dimension of the system is high and the measurement lag is significant. In this note, a new tool, termed as reorganized innovation sequence, is presented for deriving the optimal filter. The optimal filter is given by two Riccati difference equations (RDEs) with the same dimension as that of the original system. The approach is shown to induce saving of computational cost as compared to the system augmentation approach, especially when the delay is large. Further, it can be extended to solving the more complicated fixed-lag smoothing in Krein space.

Optimal Filtering in Discrete-Time Systems With Time Delays and Markovian Jump Parameters

“…When 0 ≤ k ≤ d, the optimal estimatorx(k|k) is indeed the projection of x(k) onto the linear space of {y(s)| 0≤s≤k }. Note that the observation sequence y(s) is delay-free, and thus the estimation problem is reduced to a linear mean-square estimator for Systems (2.1) and (2.2), which has been considered in [18].…”

“…When the systems have delays in their dynamics, the filtering and control problems become difficult to solve. For the class of deterministic linear time-delay systems, there exist many papers in the literature; see [3,4,17,18] and the references therein. For the case of MJLSs with delay terms, robust filtering and robust H ∞ filtering methods have been designed in [8,15,16] by using the linear matrix inequality tool.…”

“…To the best of the authors' knowledge, the problem of state estimation for MJLSs with observation delays has not received much attention in the past. The purpose of this paper is to extend some results on the state estimation of the class of linear time-delay systems [18] to the MJLS with delayed observations.…”

Multisensor Out of Sequence Data Fusion for Estimating the State of Discrete Control Systems

“…We skip [12], optimal for any delay too, because it restarts the fusion process from the time stamp of the incoming £ s t We also consider [13]-A1, although its degree of suboptimality is a few percent of MSE and is less general because (Fk,i, Qk,i, k < I) has to be available for arbitrary k and I. Table I compares the algorithms (column 1) according to their optimality (column 2), the algorithm they are based on (column 3) and their supporting assumptions (columns 4, 5 and 6).…”

“…The first, designed for linear systems and originally proposed in [17], [18], finds the same solutions as the KF or Information Filter (IF) when the measurements are not delayed. It is computationally more efficient, simple to implement and general in scope than [5]- [12]. The second, for nonlinear systems, is a novel approach inside the EKF and Extended IF (EIF), significantly different to the OOS PF [14]- [16] or the use of linear OOS algorithms for linearized systems [19].…”