Adaptive Filtering Approaches In α-Stable Noise Environments

As the ideal mathematical model for non-Gaussian impulsive noise, a -stable distribution has been the focus of intensive research in signal processing fields. This dissertation aims at the development of adaptive filtering approaches in a -stable noise environments. The main work can be summarized as follows.We start our discussion with the introduction of the basic theory such as the definition, algebraic properties and theorems of the a -stable distribution. Then we presents an overview in a unified perspective for the adaptive techniques for FIR system identifying. With the a -stable assumption of the output noise, two novel adaptive algorithms for FIR filtering are introduced based on least -norm estimation. Considering both the input and the output are corrupted with a -stable disturbances, we introduce the idea of a new total least L~ -norm estimation algorithm based on least -norm and total least squares estimation algorithm. The geometric interpretation of the new estimation has also been studied. Applying the total least L~ -norm estimation to the FIR filtering, we introduce a total least mean -norm adaptive algorithm.