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{{mergefrom|Bayes filter|discuss=Talk:Recursive Bayesian estimation#Merger proposal|date=January 2008}}
'''Recursive Bayesian estimation''', also known as a '''Bayes filter''', is a general probabilistic approach for [[density estimation|estimating]] an unknown [[probability density function]] recursively over time using incoming measurements and a mathematical process model.
==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. Essentially, Bayes filters allow robots to continuously update their most likely position within a coordinate system, based on the most recently acquired sensor data. This is a recursive algorithm. It consists of two parts: prediction and innovation. If the variables are linear and gauss-distributed the Bayes filter becomes equal to the [[Kalman filter]].
In a simple example, a robot moving throughout a grid may have several different sensors that provide it with information about its surroundings. The robot may start out with certainty that it is at position (0,0). However, as it moves further and further from its original position, the robot has continuously less certainty about its position; using a Bayes filter, a probability can be assigned to the robot's belief about its current position, and that probability can be continuously updated from additional sensor information.
== Model ==
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