Abstract
In this paper the consistent estimation problem of single-input-single-output continuous time systems is considered. For a given continuous-time system an algebraic equation containing parameters of the given system can be obtained via Block Pulse Functions (BPF). Thus these parameters can be estimated using the well known Least Squares (LS) method if there is no any measurement noise or the noise level is very low. But in the case that system input-output measurements are contaminated by noises, even if white noises, satisfied parameter estimates cannot be got by the LS method.
In this paper the reason of the above problem is analyzed. To solve this problem the idea of Extended Least Squares (ELS) method in discrete-time system estimation problem is applied to a new kind of discrete-time model, which is derived using one of the properties of BPF transfermation, to get a recursive estimation algorithm. Provided some weak conditions are satisfied, fairly good estimation results can be obtained by this method. The asymptotic property of the newly developed method is analyzed, numerical examples are also given to show the efficiency of the proposed method.
