Summary
In this chapter, we explored the Kalman filter – the estimation and prediction algorithm utilized to solve problems in signal processing, navigation, and control systems. There are linear and univariate (one-dimensional) Kalman filters in which the system dynamics are assumed to be linear. Many dynamic processes, however, have more than one dimension, and in such cases, we utilize multivariate and mostly non-linear (or extended) Kalman filters. For example, the state vector that describes a moving object’s position and velocity in space is six-dimensional, and a non-linear Kalman filter is utilized to determine the displacement (and velocity) in space of such an object. Also, the Kalman filter consumes low computational power (leading to a shorter runtime) due to the usage of matrices in its operation that occupy less computer memory. The Kalman filter is arguably the best estimation algorithm with noisy data as it mitigates the uncertainty by combining the information...