Convergence of Bayesian Histogram Filters for Location Estimation
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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. For more information: Kod*Lab
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BibTeX entry @inproceedings{paper:de_histogram_2013, 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} } This work was supported by AFOSR MURI FA9550–10–1−0567. Copyright 2013 IEEE. Reprinted from Proceedings of the 2013 IEEE Intl. Conference on Decision and Control. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.