Multimodal Kalman Filtering
Résumé
A difficult aspect of multimodal estimation is the possible discrepancy
between the sampling rates and/or the noise levels of the
considered data. Many algorithms cope with these dissimilarities
empirically. In this paper, we propose a conceptual analysis of
multimodality where we try to find the “optimal” way of combining
modalities. More specifically, we consider a simple Kalman filtering
framework where several noisy sensors with different sampling
frequences and noise variances regularly observe a hidden state.
We experimentally underline some relationships between the sampling
grids and the asymptotic variance of the maximum a posteriori
(MAP) estimator. However, the explicit study of the asymptotic
variance seems intractable even in the simplest cases. We describe a
promising idea to circumvent this difficulty: exploiting a stochastic
measurement model for which one can more easily study the average
asymptotic behavior.
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