Accelerated gradient techniques and adaptive signal processing
The main objective of this thesis is to demonstrate the application of the accelerated gradient techniques to various fields of adaptive signal processing. A variety of adaptive algorithms based on the accelerated gradient techniques are developed and analysed in terms of the convergence speed, computational complexity and numerical stability. Extensive simulation results are presented to demonstrate the performance of the proposed algorithms when applied to the fields of adaptive noise cancelling, broad band adaptive array processing and narrow band adaptive spectral estimation. These results are very encouraging in terms of convergence speed and numerical stability of the developed algorithms. The proposed algorithms appear to be attractive alternatives to the conventional recursive least squares algorithms. In addition, the thesis includes a review chapter in which the conventional approaches (ranging from the least mean squares algorithm to the computationally demanding recursive least squares algorithm) to three types of minimization problems (namely unconstrained, linearly constrained and quadratically constrained) are discussed.