ABSTRACT
This chapter introduces Kalman filter algorithm for optimal state estimation. The review of statistical tools needed in the design of Kalman filter namely: Sample mean, sample standard deviation, sample variance, sample covariance and variance, covariance and cross-covariance of stochastic process are discussed. The introduction to Kalman filter design, Gaussian noise, advantages, disadvantages, applications of Kalman filter and assumptions used in Kalman filter design are initially explained. The Kalman filter design for continuous-time systems and time-invariant systems and discrete-time systems are also discussed in detail with the help of flowcharts and block diagrams. The estimation procedures are illustrated with the help of numerical examples. The Extended Kalman Filter (EKF) for multi-dimensional system is also explained briefly.
