Recursive Bayesian estimation
Recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.
The Bayes filter should not be confused with Bayes spam filtering, which is also often referred to as Bayesian filtering. In this article, filtering is the process of sequentially estimating the states of a dynamic system (see Sequential Bayesian filtering below). In Bayes spam filtering, the term filter denotes the separation of spam and non-spam content.
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 normally 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 farther and farther 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.
The true state is assumed to be an unobserved Markov process, and the measurements are the observed states of a Hidden Markov model (HMM). The following picture presents a Bayesian Network of a HMM.
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