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Convergence of Bayesian Histogram Filters for Location Estimation

Proceedings of the 2013 IEEE Intl. Conference on Decision and Control, December, 2013.

Avik De *, Alejandro Ribeiro * , William Moran † and D. E. Koditschek *
* Electrical and Systems Engineering, University of Pennsylvania
† Defence Sciences Institute, University of Melbourne

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Comparison of estimator MSE for an approximate algorithm to the ideal Bayes estimator presented in this paper
       We prove convergence of an approximate Bayesian estimator for the (scalar) location estimation problem by recourse to a histogram approximant. We exploit its tractability to present a simple strategy for managing the tradeoff between accuracy and complexity through the cardinality of the underlying partition. Our theoretical results provide explicit (conservative) sufficient conditions under which convergence is guaranteed. Numerical simulations reveal certain extreme cases in which the conditions may be tight, and suggest that this procedure has performance and computational efficiency favorably comparable to particle filters, while affording the aforementioned analytical benefits. We posit that more sophisticated algorithms can make such piecewise-constant representations similarly feasible for very high-dimensional problems.
This work was supported by AFOSR MURI FA9550–10–1−0567.
BibTeX entry
  author       = {Avik De, Alejandro Ribeiro, William Moran and Daniel E. Koditschek},
  title        = {Convergence of Bayesian Histogram Filters for Location Estimation},
  booktitle    = {Proceedings of the 2013 IEEE Intl. Conference on Decision and Control},
  month        = {December},
  year         = {2013}

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