Estimation for Nonlinear Systems
The optimal estimation problem for nonlinear systems is in general very complicated, and only in a few special cases do algorithms exist that are easy to implement or understand. This chapter focuses on the time and measurement updates for the entire hyper-state. It explores how to find update equations for the estimate and error covariance that are in general not computationally realizable. The chapter presents general equations for time and measurement updates of the hyperstate considering the discrete systems, and then continuous systems. Combining the time and measurement updates yields the desired recursion for the hyperstate. The chapter discusses the exact time and measurement updates for the mean and covariance of the nonlinear continuous system with discrete measurements. Higher-order approximations to the optimal nonlinear updates can also be derived by retaining higher-order terms in the Taylor series expansions.