Weighted myriad filters: a robust filtering framework derived from alpha-stable distributions

In this paper we introlduce a robust and nonlinear filtering framework: Weighted Myriad Filtering. Much like the Gaussian assumption has motivated the development of linear filtering theory, the formulation of myriad filters is motivated by the statistical properties of a-stable processes. Weighted Myriad Fi1ter.s have a solid theoretical basis, are inherently more powerful than weighted median filters, and are very general subsuming traditional linear FIR filters. The foundation of the proposed filtering algorithms lies in the definition of the sample myriad as the location estimate for a class of a-stable distributions. In turn, the myriad has been discovered as the location parameter estimated by the sample myriad. This paper addresses some theoretical properties of myriad filters. The superior performance of myriad filters in impulsive environments is illustrated in the problem of robust synchronization by means of a “myriad phase lock loop”.