Performance Evaluation of Adaptive Polynomial Filtering Algorithms for Time-Varying Parameter Estimation

ii ACKNOWLEDGEMENT No volume of words is enough to express my gratitude towards my guide, Thapar University, who has been very concerned and has aided for all the material essential for the preparation of this thesis report. He has helped me to explore this vast topic in an organized manner and provided me with all the ideas on how to work towards a research-oriented venture. for the motivation and inspiration that triggered me for the thesis work. I would also like to thank the staff members and my colleagues who were always there in the need of the hour and provided with all the help and facilities, which I required, for the completion of my thesis. Most importantly, I would like to thank my parents and the Almighty for showing me the right direction out of the blue, to help me stay calm in the oddest of the times and keep moving even at times when there was no hope. ABSTRACT The current trend in the telecommunication systems design is the identification and compensation of unwanted nonlinearities. It is known that unwanted nonlinearities in the system will have a determinant effect on its performance. The use of nonlinear models considered in this thesis is to characterize and compensate harmful nonlinearities offer a possible solution. There are many applications in communication system where time varying nature of Volterra system is required therefore Gauss Morkol model is used to represent time varying systems. The time varying Volterra system has been widely applied as nonlinear system modeling technique with considerable success. When the nonlinear system is unknown, adaptive methods and algorithms are widely used for the Volterra kernel estimation. The accuracy of the Volterra kernels will determine the accuracy of the system model and the accuracy of the inverse system used for compensation. Parameter estimation of Volterra systems is a very important part of the adaptive algorithm when it comes to controlling noisy systems. This thesis proposes some adaptive algorithms, which is used to track and estimate the time varying nonlinear systems. Parameter estimation is used in tracking of objects like face, missiles, hand, head etc. Firstly we proposes Kalman filter which is used to recursively estimate and track the time variation of the first and second order Volterra kernels. It produces estimates of the true values of measurements and their associated calculated values by predicting a value, estimating the uncertainty of the …