Recursive state and parameter estimation of SISO singular systems

Recursive algorithms are presented for the online state and parameter estimation of a linear time invariant single-input single-output discrete-time singular system. The model considered is in the canonical observable form. The approach is based on the generalised Kalman filter and can be developed in two steps. First, the parameters are estimated by recursive least squares method. These parameters are then used to estimate the state by the generalised Kalman filter in the second step. The results are illustrated by a numerical example.