Kalman filter

The process model or the system model, is what is used for the prediction step. For the rest of the document, we will assume that we are measuring a one dimensional value. The process model provides a means of predicting this value. But we will not be working with the value itself, but with a Gaussian that represents it. If our process model predicts as the prediction, but has a high degree of uncertainty, we will represent the prior (the prediction) as a Gaussian centered at having high variance.

The bar "" is used to denote that the value being talked about is a prior.

The measurement from the sensors is also taken as a Gaussian, centered around the reported value with the variance representing the inaccuracies in the sensor. This is called the likelihood function. The product of the likelihood function and the prior (normalized) yields us the posterior, or the filter's output.