Recursive Bayesian estimation

In probability theory, statistics, and machine learning, recursive Bayesian estimation, also known as a Bayes filter, is a general probabilistic approach for estimating an unknown probability density function (PDF) recursively over time using incoming measurements and a mathematical process model.

The process relies heavily upon mathematical concepts and models that are theorized within a study of prior and posterior probabilities known as Bayesian statistics.

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.

are the manifestations of a hidden Markov model (HMM), which means the true state

(This is achieved by marginalising out the previous states and dividing by the probability of the measurement set.)

This leads to the predict and update steps of the Kalman filter written probabilistically.

The probability distribution of update is proportional to the product of the measurement likelihood and the predicted state.