Conventional Nonlinear Filters
Most of the estimation problems in practice involve nonlinear models including nonlinear dynamics and nonlinear measurement functions of the states. This chapter presents some conventional nonlinear filters that have been well recognized and extensively applied. The extended Kalman filter (EKF) adapts the linear Kalman filter so that it can be applied to nonlinear problems. It is an analytical approximation based on the linearization of the nonlinear dynamics and the nonlinear measurement model. The marginalized particle filter utilizes the potential linear Gaussian structure of the system. The Zakai filtering method solves the Zakai equation to represent the Probability Density Function of the nonlinear filtering solution. The Kalman filter and EKF are the most widely used for real applications. For the general nonlinear estimation problem, the point-mass filter and the particle filter are reviewed. A variety of nonlinear filtering algorithms were derived and applied based on different approximation techniques.