Adaptive state observer development using recursive extended least-squares method

This paper presents a recursive algorithm for adaptive observation of linear single-input single-output (SISO) time-invariant discrete systems. The problem of state observation is of main importance in automatic control, especially for designing modal state controllers when the state variables of the system are unknown. The proposed algorithm is based on the recursive extended least-squares (RELS) method. The adaptive state observer estimates system parameters, initial and current state vector by using the measured input and output system signals. In order to verify the algorithm performance, simulation experiments in the Matlab environment are carried out and provided.