On System Identification in one and two Dimensions with Signal Processing Applications

Abstract: This thesis consists of four parts, with system identification as the common theme. The first part studies the asymptotic properties of two-dimensional identification methods. In the second part an approach to identification of time varying systems is presented. Part three applies system identification to the problem of transmission line protection. Finally part four deals with input estimation in speech coding.Part I is devoted to system identification in two dimensions. First we study the asymptotic properties of the estimates as the number of data tends to infinity. The main objective is to investigate what happens if the model order also tends to infinity. The focus is on frequency expressions of the extimation variance. The analysis covers both the least squares method for causal models, and the maximum likelihood method for noncausal models.In Part II we study one approach to identification of time varying sytems. The parameter variations are modelled as process noise in a state space model, and identified using adaptive Kalman filtering. A method for adaptive Kalman filtering is derived and analysed. The simulations indicate that this new approach is superior to previous methods based on adjusting the forgetting factor. The improvement is however gained at the price of a significant increase in computational complexity.Part III describes the use of recursive identification in protective relaying. The Fourier coefficients of voltage and current are estimated using recursive least squares identification. The estimates are then used to detect short circuits. The method is evaluated using data generated by the standard program EMTP.In Part IV a method for inverse glottal filtering is presented. The basis of the method is to use a parameterized model of the input signal, i.e. the glottal pulses. The algorithm simultaneously estimates the parameters of the input signal and the parameters of the system transfer function, the vocal tract model. The presentation is restricted to transfer functions of all-pole type.