## The discrete Kalman filter

The Kalman filter is a mathematical model that provides an accurate and recursive computation approach to estimate the previous states and predict the future states of a process for which some variables may be unknown. R.E. Kalman introduced it in the early 60s to model dynamics systems and predict a trajectory in aerospace [3:10]. Today, the Kalman filter is used to discover a relationship between two observed variables that may or may not be associated with other hidden variables. In this respect, the Kalman filter shares some similarities with the Hidden Markov models, as described in the *The hidden Markov model* section in Chapter 7, *Sequential Data Models* [3:11].

The Kalman filter is used as:

A predictor of the next data point from the current observation

A filter that weeds out noise by processing the last two observations

A smoothing model that identifies trends from a history of observations

### Note

**Smoothing versus filtering**

Smoothing is an operation that removes...