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Undid revision 1036941046 by 14.207.10.177 (talk) seems to be made in error. PP might refer to percentage point, but that doesn't really make sense. Having it approach another known estimation method *does* |
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{{Short description|Process for estimating a probability density function}}
{{About|Bayes filter, a general probabilistic approach|the spam filter with a similar name|Naive Bayes spam filtering}}
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==In robotics==
A Bayes filter is an algorithm used in [[computer science]] for calculating the probabilities of multiple beliefs to allow a [[robot]] to infer its position and orientation.
In a simple example, a robot moving throughout a grid may have several different sensors that provide it with information about its surroundings.
== Model ==
The
[[Image:HMM Kalman Filter Derivation.svg|Hidden Markov model|center]]
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:<math>p(\textbf{z}_k|\textbf{x}_k,\textbf{x}_{k-1},\dots,\textbf{x}_{0}) = p(\textbf{z}_k|\textbf{x}_{k} )</math>
Using these assumptions the probability distribution over all states of the HMM can be written simply as
:<math>p(\textbf{x}_0,\dots,\textbf{x}_k,\textbf{z}_1,\dots,\textbf{z}_k) = p(\textbf{x}_0)\prod_{i=1}^k p(\textbf{z}_i|\textbf{x}_i)p(\textbf{x}_i|\textbf{x}_{i-1}).</math>
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Sequential Bayesian filtering is the extension of the Bayesian estimation for the case when the observed value changes in time. It is a method to estimate the real value of an observed variable that evolves in time.
There are several variations:
;filtering: when estimating the ''current'' value given past and current observations,
;[[smoothing problem|smoothing]]: when estimating ''past'' values given past and current observations, and
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The notion of Sequential Bayesian filtering is extensively used in [[control theory|control]] and [[robotics]].
==
*{{cite journal |first1=M. Sanjeev |last1=Arulampalam |first2=Simon |last2=Maskell |first3=Neil |last3=Gordon |title=A Tutorial on Particle Filters for On-line Non-linear/Non-Gaussian Bayesian Tracking |journal=IEEE Transactions on Signal Processing |volume=50 |issue= 2|pages=174–188 |year=2002 |doi= 10.1109/78.978374|bibcode=2002ITSP...50..174A |citeseerx=10.1.1.117.1144 }}
*{{cite book |last1=Burkhart |first1=Michael C. |title=A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding |date=2019 |publisher=Brown University |___location=Providence, RI, USA |chapter=Chapter 1. An Overview of Bayesian Filtering|doi=10.26300/nhfp-xv22 }}
*{{cite journal |last1=Chen |first1=Zhe Sage |title=Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond |journal=Statistics: A Journal of Theoretical and Applied Statistics |date=2003 |volume=182 |issue=1 |pages=1–69}}
*{{cite web |first1=Julien |last1=Diard |first2=Pierre |last2=Bessière |first3=Emmanuel |last3=Mazer |title=A survey of probabilistic models, using the Bayesian Programming methodology as a unifying framework |date=2003 |publisher=cogprints.org |url=http://cogprints.org/3755/1/Diard03a.pdf }}
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[[Category:Bayesian estimation]]
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