Análise e implementação em circuito eletrônico de algoritmos adaptativos de gradiente estocástico baseado em função contínua, par e não linear

Abstract

Adaptive filters have solved many signal processing problems, in addition to being a fundamental part of machine learning. The study of adaptive filtering was boosted with the development of the Least Mean Square (LMS) algorithm in 1960. Since then, other adaptive algorithms have emerged with a superior performance to the LMS algo rithm in terms of misfit and convergence rate. Several algorithms have emerged in order to improve the performance of the LMS algorithm. Among them, adaptive algorithms based on stochastic gradient based on non-square mean error criteria, were developed and analyzed by Douglas and Meng, these algorithms provide superior performance over their stochastic gradient counterparts when analyzed against misfit and the speed of conver gence. These adaptive algorithms constitute an important family of algorithms. When implementing these algorithms in hardware devices such as DSPs, Microcontrollers and FPGAs, they are implemented in finite precision. Some effects in this implementation can affect its performance. Ultimately they can lead to divergence due to quantization errors. This important family of adaptive non-mean-square error algorithms was analyzed in 1994 by Douglas and Meng. The time constant and the maladjustment were analyzed. The results found from this analysis have presented divergences when compared with the experimental results. In this sense, this work aims to analyze this family of algorithms in finite precision, specifically we developed a new methodology for the misfit calculation, as well as an FPGA hardware implementation for problem solving and nanosatellite.