ABSTRACT
This chapter considers block-pulse functions (BPF) and shifted Legendre polynomials (SLP), and presents two recursive algorithms for state estimation. Compared to the recursive algorithms in, the algorithms in are computationally more elegant. The chapter deals with the inherent filtering property of orthogonal functions (OF). It also deals with state estimation via BPFs and SLPs. The chapter demonstrates and compares the performance of recursive algorithms. Two recursive algorithms are presented for estimating state variables of observable linear time-invariant continuous-time dynamical systems from the input-output information using two classes of OFs, namely BPFs and SLPs. The OF approach has an inherent filtering property as it involves an integration process which has the smoothing effect. As it appears from the literature, two attempts have been made on the state estimation problem by using two different classes of OFs. The recursive algorithm is applicable to single-input single-output systems whose dynamical equations are available in observable canonical form.
