Adaptative high-gain extended Kalman filter and applications

tel-00559107, version 1 - 24 Jan 2011
2.6 On Adaptive High-gain Observers
in such a way that at any moment at least one of the observers has θ large and at least one
observer has θ close to 1. The state of the observer having the shortest output error 26 is then
selected. As shown in [38], this observer performs well in our applications. It is successfully
applied for identification purposes in [40]. Nevertheless this procedure is not very reasonable
since:
− Even if the overall construction gives a persistent observer, it is a time-dependant
observer,
− It can be time consuming since it requires at least five (empirical value) observers in
parallel,
− The parameter λ has to be chosen sufficiently small, which means that after a perturbation,
we can not return as quickly as we would like to a classical extended Kalman
filter, even if the observer performs well,
− The choice of the criteria used to select the best prediction between our observers, is
not theoretically justified.
This second chapter, which focused on the theoretical framework that encompasses our
work, ends with the analysis of this last observer. In this chapter, we also provided insight
into several adaptation strategies. In the next chapter we introduce the adaptive high-gain
extended Kalman filter and develop the full proof of convergence.
26 The output error (Cz − y) is the equivalent of innovation for continuous time systems.
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