A pre-filter for recursive continuous-time-model parameter estimation : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Technology at Massey University
This thesis reports the development of a prefiltering technique for estimating the parameters of continuous-time models given by differential equations. This technique is based on some special integrals, named the Fixed Interval Integrals (FII), which result from multiple integrations over intervals of fixed length. An estimation method using this prefiltering technique has several significant features: - it is capable of estimating both system delay and the parameters of a second order dynamical model. - it is able to be implemented on discrete-time digital devices. - it is independent of initial conditions, hence these do not need to be known. - it uses well-established discrete-time estimation algorithms. This development starts with the definition of a new operator notation system. It then studies in detail the properties of the fixed interval integration and its relationship to traditional calculus operations. Several possible methods to realize the FII operation using analog and digital filters are also given. Using these results and some simulation examples, the use of FII in parameter and delay estimation of continuous-time models is demonstrated. Since the FII is likely to be useful in engineering and mathematics beyond parameter estimation, some other possible applications of the FII are outlined.