Bayes Filter Algorithm

A Bayes Filter Algorithm is density estimation algorithm for estimating an unknown probability density function recursively over time using incoming measurements and a mathematical process model.

AKA: Recursive Bayesian Estimation.
See: Kalman Filter, Gabor Filter, Posterior Estimation, Spam Filtering Task.

References

(Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Recursive_Bayesian_estimation Retrieved:2014-9-23.
- 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.

http://en.wikipedia.org/wiki/Bayes_filter
- 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.

(Graham, 2003) ⇒ Paul Graham. (2003). “Better Bayesian Filtering.” http://www.paulgraham.com/better.html
(Patterson et al., 2003) ⇒ Donald J. Patterson, Lin Liao, Dieter Fox and Henry Kautz. (2003). “High-level Behavior from Low-level Sensors.” In: Proceedings of the 5th International Conference on Ubiquitous Computing (Ubicomp 2003). [http:/dx.doi.org/10.1007/b93949 doi:10.1007/b93949.
- We present a method of learning a Bayesian model of a traveler moving through an urban environment. This technique is novel in that it simultaneously learns a unified model of the travelerrsquos current mode of transportation as well as his most likely route, in an unsupervised manner. The model is implemented using particle filters and learned using Expectation-Maximization. The training data is drawn from a GPS sensor stream that was collected by th