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Title: Performance Evaluation of Adaptive Polynomial Filtering Algorithms for Time-Varying Parameter Estimation
Authors: Gupta, Ankur
Supervisor: Kohli, Amit Kumar
Keywords: Gauss Morkov model, DFFRLS, The Kalman filter, RLS algorithm, Volterra kernels
Issue Date: 14-Jul-2011
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 modelling 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 predicted value, and computing a weighted average of the predicted value and the measured value. The estimates produced by the method tend to be closer to the true values than the original measurements because the weighted average has a better estimated uncertainty than either of the values that went into the weighted average. Then there is another adaptive algorithm we propose which belongs kalman filter family that is Recursive least squares (RLS) algorithm which recursively finds the filter coefficients that minimize a weighted linear least squares cost function relating to the input signals. The tracking performance and convergence rate of RLS algorithm depends upon forgetting factor. RLS algorithm having fixed forgetting factor has to make some adjustment for previous performance. If the forgetting factor which is closed to unity RLS algorithm gives good stability but at the cost of low misadjustment and worse tracking performance. If forgetting factor is very low then it gives good tracking performance but with bad stability. So there is a need of an adaptive algorithm which is used to estimate and track the time varying volterra system having variable forgetting factor. Then we proposes Dynamic forgetting factor recursive least square (DffRLS) adaptive algorithm for first and second order volterra system. The DffRLS is adapted to a time varying signal by an extended prediction error criterion which accounts for the nonstationarity of the signal. This method has good adaptability in the nonstationary situation and low variance in the stationary situation.
Appears in Collections:Masters Theses@ECED

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