ABSTRACT

This chapter discusses the methods by which the state estimates are obtained from a finite structure estimator which is defined in terms of pre-assignable known functions and the filter’s gains. The discrete time nonlinear filter reduces to the discrete linear filter when the certain special choice of the structural functions is made and the linear system is considered. The chapter shows that some interconnections and differences of the conditionally optimal filtering structures with other existing methods. It describes some filters for special structure and models linear in noise. The systems matrices can be time varying and have appropriate dimensions. Such systems occur in practice, where the states and/or measurements have time delays in their dynamics, for example, and wireless sensor networks. The conditionally optimal filtering solutions for nonlinear systems can also be obtained when state noise and measurement noise are correlated or only the measurement noise is correlated.