Implementation of Kalman Filter for Localization

In general, an estimation algorithm predicts the values of quantities of interest from indirect, inaccurate, and uncertain observations. Numerous applications implement estimation algorithms. This chapter investigates the implementation of the linear and nonlinear Kalman filters (KFs) for localization problems. It first formulates the positioning problem in the estimation context. Next, the chapter presents a deterministic derivation for the KF. It also presents examples on the use of KF in localization. The chapter describes the extended Kalman filter (EKF) for nonlinear dynamic systems estimation, and presents an example on its implementation in positioning of a nonlinear system. The basic idea of the EKF is to linearize the nonlinear equations around the current estimate, and then apply a linear KF to the linearized model