An Elementary Introduction to Kalman Filtering

Kalman filtering is a classic state estimation technique used in application areas such as signal processing and autonomous control of vehicles. It is now being used to solve problems in computer systems such as controlling the voltage and frequency of processors. Although there are many presentations of Kalman filtering in the literature, they usually deal with particular systems like autonomous robots or linear systems with Gaussian noise, which makes it difficult to understand the general principles behind Kalman filtering. In this paper, we first present the abstract ideas behind Kalman filtering at a level accessible to anyone with a basic knowledge of probability theory and calculus, and then show how these concepts can be applied to the particular problem of state estimation in linear systems. This separation of concepts from applications should make it easier to understand Kalman filtering and to apply it to other problems in computer systems.