Degree Name

Doctor of Philosophy


Department of Electrical, Computer and Telecommunications Engineering


This thesis deals with infinite impulse response adaptive notch filtering and its application to the industrial problem of roll eccentricity signal estimation and retrieval.

A minimal notch filter parametization is examined and a number of modifications are proposed which serve to enhance the notch filter characteristics and hence its usefulness. Firstly, a special constraint is introduced which allows the notch filter to be converted into a line enhancer without requiring structural changes. A further advantage associated with this modification is that the notch filter becomes a minimum phase filter. Secondly, a normalizing gain factor is introduced which ensures unity gain everywhere except at the notch frequency even for wide bandwidths. Thirdly, a design procedure together with design graphs are developed to assist in the design of notch filters.

Estimation accuracy of the modified adaptive notch filter is analysed by deriving the Cramer-Rao Lower Bound for the multiple cascaded notch filter model. Theoretical values are obtained for the Cramer-Rao Lower Bound and verified by extensive simulation results. A performance comparison of three adaptive algorithms (proposed by previous researchers) is carried out under the same conditions to establish the merits of each algorithm.

The thesis then considers a simpler class of adaptive algorithms and applies these to notch filtering for the first time. The algorithms of interest are in fact gradient-based algorithms. Two novel notch filter model structures are synthesized which have special applicability to the roll eccentricity problem.

The error surfaces associated with these model structures are analysed and Monte Carlo simulations are carried out to ascertain their performance. Results show that gradient-based adaptive notch filtering offers a number of distinct advantages including simplicity and robustness over other methods.

Finally, the roll eccentricity problem is examined in detail and a new software sensor is proposed as a solution. The sensor is made up of a gradient-based adaptive comb filter which is constructed from 2nd order notch filter modules. The comb filter estimates and tracks the harmonic series characterizing the roll eccentricity phenomenon. Once the harmonic series is retrieved a standard recursive least squares algorithm is implemented to estimate the amplitude and phase of each harmonic component. The sensor is subjected to extensive simulation trials with typical data being obtained from an operational plant. Results are conclusive and indicate that the proposed sensor offers an excellent solution to the problem of roll eccentricity signal retrieval.