ABSTRACT
This chapter discusses local approximations for nonlinear filtering/estimation for easy implementation of practical filters: first-order filtering and higher-order filters. It examines global approximations for discrete time nonlinear filters: orthogonal series expansion, Gaussian sums, point mass and splines. The chapter describes the unscented Kalman filter, extended information filter, and extended H-infinity filter. It explains the conditional pdf p is almost symmetric and concentrated near its mean, thus its odd-numbered central moments are negligible. The chapter reviews the system’s nonlinear functions f, h and g are expanded in Taylor’s series around the conditional mean up to the second-order terms. It utilizes the continuous time dynamic system’s model 1 and the discrete time measurement model. In many real-data fusion problems, as well as in other systems, the state of interest could evolve in a nonlinear manner, in which case simple linear models cannot adequately describe such a nonlinear behaviour, and sensor observations may not be linear functions of the states.
