Abstract

This paper looks at the problem of estimating the coefficients of a continuous time transfer function given samples of its input and output data. We first prove that any nth order continuous time transfer function can be written as a fraction of the form ∑_{k=0}^{n} b̄_{k}L_{k}(s)/ ∑_{k=0}^{n} ā_{k}L_{k}(s) where L_{k}(s) denotes the continuous time Laguerre basis functions. Based on this model, we derive an asymptotically consistent parameter estimation scheme which consists of the following two steps: 1) filter both the input and output data by L_{k}(s), 2) estimate {ā_{k}, b̄_{k}} and relate them to the coefficients of the transfer function. For practical implementation, one requires the discrete time approximation of L_{k}(s) since only sampled data is available. We shall prove that if Padé approximation schemes are used to approximate these filters, then the resulting discrete time filters are approximately orthogonal and it therefore gives rise to a well-conditioned numerical problem. Some other features of this new algorithm includes: the possibility to implement it as either an offline or a quasi-on-line algorithm; the incorporation of constraints on the transfer function coefficients. A simple example will be given to illustrate the properties of the proposed algorithm.

Keywords

System identification; continuous time systems; asymptotic consistency; Laguerre basis functions; Padé approximation; total least-squares; parameter estimation.