Density-ratio robustness in dynamic state estimation

Benavoli, Alessio and Zaffalon, Marco (2013) Density-ratio robustness in dynamic state estimation. Mechanical Systems and Signal Processing, 37 (1–2). 54 - 75. ISSN 0888-3270

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The ltering problem is addressed by taking into account imprecision in the knowledge about the probabilistic relationships involved. Imprecision is modelled in this paper by a particular closed convex set of probabilities that is known with the name ofdensity ratio class or constant odds-ratio (COR) model. The contributions of this paper are the following. First, we shall de ne an optimality criterion based on the squared-loss function for the estimates derived from a general closed convex set of distributions. Second, after revising the properties of the density ratio class in the context of parametric estimation, we shall extend these properties to state estimation accounting for system dynamics. Furthermore, for the case in which the nominal density of the COR model is a multivariate Gaussian, we shall derive closed-form solutions for the set of optimal estimates and for the credible region. Third, we discuss how to perform Monte Carlo integrations to compute lower and upper expectations from a COR set of densities. Then we shall derive a procedure that, employing Monte Carlo sampling techniques, allows us to propagate in time both the lower and upper state expectation functionals and, thus, to derive an efficient solution of the ltering problem. Finally, we empirically compare the proposed estimator with the Kalman lter. This shows that our solution is more robust to the presence of modelling errors in the system and that, hence, appears to be a more realistic approach than the Kalman flter in such a case.

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