Linear Estimation of Dynamic Systems
This chapter provides a concise review of the R. E. Kalman filter without delving into its theoretical development and properties and presents the most widely used discrete-time linear Kalman filter. The difficulties stem from the nonlinear dynamics and computation of statistics that involves integrals of large dimensionality with respect to arbitrary Probability Density Function. However, under the Gaussian and linearity assumptions, the estimation problems become tractable. The continuous-time Kalman filter was developed by Kalman and Bucy after the discrete-time Kalman filter. The chapter discusses the linear discrete Kalman filter is derived from minimizing the MSE and shows that the relationship between this filter and the Bayesian estimation in the prediction and update steps. The Kalman filter equations can be presented in many different forms by algebraic manipulations. One of the alternative forms is called the information filter.