Low-complexity approximations for the Kalman filter.

• Autor(a) principal: Claser, Raffaello
• Data de Publicação: 2021
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/3/3142/tde-27012022-145240/
• topic: Adaptive filter; Convex combination; Filtros de Kalman; Kalman filter; Processamento de sinais adaptativos; Processos estocásticos; Stochastic process

Adaptive filters are usually employed in situations where the environment is constantly changing, so that a fixed system would not have adequate performance to optimally perform the desired task. Examples include channel equalization, data prediction, echo cancellation and so on. A fundamental feature of adaptive filters is their ability to track variations in the signal statistics for nonstationary environments. However, as they are usually applied in real-time applications, they must be based on algorithms that require a small number of computations per input sample.The least mean squares (LMS) algorithm represents the simplest and most easily applied adaptive filter with linear complexity while the standard recursive least squares (RLS) algorithm is known for its high convergence rate, but requires a higher computational cost (O(M2) for a filter of size M). In time-varying scenarios, combination schemes oer improved tracking capabilities with respect to the component filters. When combining filters from dierent families,namely LMS and RLS, it is possible to take advantage of the tracking properties from each filter and obtain a structure with better performance than if each filter were implemented individually. On the other hand, despite the high computational complexity (O(M3) for general state-space models), the Kalman filter has long been shown to be the optimal solution to many tracking and data prediction tasks, in a wide variety of applications ranging from navigation to image processing. This filter is optimal in the sense it minimizes the mean square error of the estimated parameters when all noises involved are Gaussian and the parameter vector to be estimated changes according to a linear model. Unlike the adaptive filters, the Kalman filter requires prior knowledge of the mathematical model of the system and the statistical characteristics of noise in order to be designed. Other versions of this filter, such as extended Kalman filter and unscented Kalman filter, were develop in order to deal with nonlinear models.Based on this scenario, the present work seeks to compare the performance between the adaptive filters LMS and RLS as well as their convex combination with the optimum solution obtained via Kalman filter under dierent first order autoregressive models. In addition, this work also shows that there exist other models for the evolution of the optimum weight vector for which it is possible to derive fast (i.e., O(M)) versions of the Kalman filter, extending the RLS-DCD algorithm proposed in the literature