TOTAL CONSTRAINED Q–R´ENYI ADAPTIVE KERNEL FUNCTIONED ALGORITHM FOR SYSTEM IDENTIFICATION

Abstract

System identification aims at creating a system model from the input and output measurements of the system. An adaptive filter can use these input and output measurements to determine the mathematical model of an unknown system. Modelling of time varying systems in presence of noise is challenging due to the inherent time varying nature of the weights of the System. A limited number of solutions have been proposed in literature for modelling time varying systems in presence of noise in input as well as desired signals. Constrained q-R´enyi kernel functioned (CqRKF) adaptive algorithm is one of the state-of-the-art solutions proposed in literature for time variant systems. In comparison to traditional methods, the CqRKF algorithm performs better in presence of non-Gaussian noise in desired signal. However, the performance of CqRKF algorithm decreases severely when it is used for modelling time variant systems in presence of noise in input as well as desired signals. To overcome this Challenge, this thesis proposes a new algorithm called total constrained q-R´enyi kernel functioned (TCqRKF) algorithm which is implemented by solving a constraint optimization problem using the weighted error. To enhance the performance of the proposed TCqRKF algorithm, the kernel width parameter is made adaptive using the KL-divergence measure. The performance of the proposed total constrained q-R´enyi adaptive kernel functioned (TCqRAKF) algorithm is compared with that of CqRKF, and constrained adaptive filtering (CAF) algorithms like CLMS, CAP, Recursive CMCC. Theoretical investigation of the steady-state mean square deviation (MSD) of the proposed TCqRAKF algorithm is conducted and its performance is examined in presence of Gaussian, impulse, Laplacian and binary noise. The simulation study shows that the proposed TCqRAKF algorithm provides better performance in presence of non-Gaussian noise.