Robust Sequential Algorithms For Nonlinear Signal Processing Under Impulse Noise

Robust nonlinear filters are robust against outliers in applications in which the underlying processes are non-Gaussian and impulsive. Among the classes of robust nonlinear filters, the sample myriad which is a maximum likelihood estimator of location derived for symmetric α-stable (SαS) distribution, has gained popularity in recent years due to availability of a tuneable parameter that controls the robustness of the filter. However, the high computational cost incurred for implementing sample myriad and its related frameworks renders it impractical for certain applications such as wireless communications which require very efficient algorithms. This motivates the development of new algorithms and techniques that improves the computational efficiency of the myriad-based robust nonlinear filters. First, the sample myriad and the weighted myriad filters are commonly computed using the batch processing fixed-point algorithm. Since a block of input samples has to be gathered first before the algorithm can perform estimation, significant delay may arise if the block size is large. To address this issue, a sequential sample myriad filter and a sequential weighted myriad filter are derived to compute the estimate in real-time by updating the current estimate whenever a new input sample becomes available. The result showed that the proposed sequential techniques which have a lower computational complexity, achieve almost the same convergence speed and accuracy as the classical batch processing algorithm