Part I
A new approach to identification of time varying systems is presented, and evaluated using computer simulations. The new approach is built upon the similarities between recursive least squares identification and Kalman filtering.
The parameter variations are modelled as process noise in a state space model and then 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. This improvement is however gained at the price of a signification increase in computational complexity.
Part II
In this part we apply parameter estimation to the problem of transmission line protection.
One approach based on recursive least squares identification is presented. The method has ben tested using simulated data generated by the program EMTP.
Another approach based on the theory of travelling waves is also discussed.
Part III
In this part a method for input estimation or deconvolution is presented. The basis of the method is to use a parametrized model the input signal. To use the method we should thus be able to express the input signal as a function of some unknown parameters and time. The algorithms simultaneously estimates the parameters of the input signal and the parameters of the system transfer function. The presentation here is restricted to transfer functions of all pole type, i.e. ARX-models. The method can be extended to handle zeros in the transfer function. The computational burden would however increase significantly. The algorithm uses efficient numerical methods, as for instance QR-factorization thorugh Householder transformation.
The algorithm is in this paper applied to a problem in speech coding. It has been observed that the quality of synthesized speech can be improved, if a more detailed model than an impulse train is used for the pitch pulses, see Fant (1980). It is here shown how the method presented in this paper can be used to estimate the system parameters of the speech production and the parameters of the glottal pulse simultaneously.