# Kalman Filter

A technique for estimating an unknown state of a linear dynamic system given observations of the system which have additive (Gaussian) noise. Can be used for non-linear systems by an approximate linear model. It creates an optimum solution to such a system by minimising the state error correlation matrix. It makes use of a recursive algorithm in which a non-linear difference equation represents the covariance matrix of the optimal estimate error. This equation can be solved recursively or iteratively. Widely used in industry for real-time applications such as control systems, seismology and radar tracking.

### Kalman Gain

The multiplier used for the correction term in the estimation part of the algorithm. This is multiplied by the measured error and subsequently added to the prediction. This gives the optimum estimate of the state.

**See also: **Electronic Filter, Recursive Filter.

**Subjects: ** Mathematics Signal Processing