State Estimation using Shifted Legendre Polynomials

A new recursive algorithm is presented for estimating state variables of observable linear time-invariant continuous-time dynamical systems from the system input-output information using shifted Legendre polynomials (SLP). The principle of Luenberger observer is utilized for estimating the state variables. The proposed approach has the distinct advantage that the smoothing effect of integration reduces the influence of zero-mean observation noise on estimation. Results of simulation study on two examples indicate that the proposed recursive algorithm works quite well.