# The 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 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** (**HMM**) described in Chapter 6, *Regression and Regularization* [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 smoother that computes trends from a history of observations

### Note

**Smoothing versus filtering**

Smoothing is an operation that removes high-frequency fluctuations from a time series...