An Elementary Introduction to Kalman Filtering

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