Sampled-data observer error linearization

Abstract

An analysis of the effects of time-sampling on the obseroer error linearization design methodology shows that requiring the method to be applicable for an open set of sampling times trioializes the class of allowable systems.

Convergence Analysis of Extended Kalman Filter in a Noisy Environment Through Difference Equations

“…Filtering is a procedure of estimating hidden states based on observable data [4]. The Kalman filter equations for (2) are given as follows [5]. Now Consider the measurement and time update of a noisy environmented system of equations, Measurement Updatê…”

“…To obtain an error dynamics, let's rewrite the Kalman filter in terms of the priori variables [5]. From (3) and (4) we use y k instead of ξ k ,…”

Restricted dynamic observer error linearizability

“…Then, a simple Luenberger-like observer design is feasible for a NOCF, as in Remark 1. We call this problem observer error linearization or the state equivalence to a NOCF which has been studied by many researchers in Besancon (1999), Normand-Cyrot (2003, 2009), Chung and Grizzle (1990), Hou and Pugh (1999), Huijberts (1999), Keller (1987), Krener and Respondek (1985), Lee, Arapostathis, and Marcus (2008), Lee and Hong (2011), Lee and Nam (1991), Lin and Byrnes (1995), Xia and Gao (1988) and Xia and Gao (1989). The observer error linearization problem is a sort of dual concept of the feedback linearization problem.…”

Nonlinear discrete-time observer design with linearizable error dynamics

“…It is assumed, that β(y), T have been chosen such that A = T (F − T −1 BH)T −1 . Therefore, the known quantities are f, h, β, A and the unknown ones are the higher degree terms θ [2] , θ [3] , . .…”

“…The design of an observer for such a system is relatively easy since the error dynamics can be made linear in the transformed coordinates. This approach was extended to discrete time systems in [16] , [17], [3]. For more on discrete time observer design we refer the reader to [5] and its references.…”