A state estimation problem can be dealt with by set‐membership approaches, where both the uncertainties on the model and the measurements errors are known. The solution set may even be made of several connected subsets or include holes. The chapter illustrates different methods to represent a set, namely zonotopes or polyhedral enclosures, ellipsoids, intervals or subpavings. These latter two have been proven to be efficient when dealing with nonlinear systems or complex solution shapes. This chapter presents their theoretical basis that will be used then throughout this book. It first focuses on interval analysis, and then presents tools named contractors that aim at reliably reducing bounds of interval sets. The chapter shows that intervals can even be used to represent strong temporal uncertainties. It also introduces subpavings for set‐inversion, and provides discussions about implementation and concrete use of intervals.
Static Set‐membership State Estimation
Reliable Robot Localization ; 5-39
2019-12-16
35 pages
Article/Chapter (Book)
Electronic Resource
English
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