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Constrained Posterior Cramér-Rao Bound for Discrete-Time Systems

Andersson, Leif Erik; Brekke, Edmund Førland; Imsland, Lars Struen; Scibilia, Francesco
Journal article
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IFAC17_Constrained_CRB_IFAC_revised_A2.pdf (281.4Kb)
URI
http://hdl.handle.net/11250/2476532
Date
2017
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  • Institutt for teknisk kybernetikk [2240]
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Original version
IFAC-PapersOnLine. 2017, 50 (1), 3768-3773.   10.1016/j.ifacol.2017.08.479
Abstract
This article presents a Cramér-Rao lower bound for the discrete-time filtering problem under linear state constraints. A simple recursive algorithm is presented that extends the computation of the Cramér-Rao lower bound found in previous literature by one additional step in which the full-rank Fisher Information matrix is projected onto the tangent hyperplane of the constraint set. This makes it possible to compute the constrained Cramér-Rao lower bound for the discrete-time filtering problem without reparametrization of the original problem to remove redundancies in the state vector, which improves insights into the problem. It is shown that in case of a positive-definite Fisher Information Matrix the presented constrained Cramér-Rao bound is lower than the unconstrained Cramér-Rao bound. The bound is evaluated on an example.
Publisher
Elsevier
Journal
IFAC-PapersOnLine

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