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Robust fencing is an essential component of intermittently nonlinearfiltering for mitigation of outlier interference. In such filtering, the upperand the lower fences establish a robust range that excludes noise outlierswhile including the signal of interest and the non-outlier noise. Then, theoutlier values are replaced with those in mid-range. To increase theeffectiveness of outlier noise identification, and to minimize the falsenegatives, the fences need to be both tight and robust to outlier noise. On theother hand, to minimize the false positives and to avoid the detrimentaleffects, such as instabilities and excessive distortions, often associated withnonlinear filtering, the fences need to be inclusive, so that the signal ofinterest and the non-outlier noise remain within the fences. Quantile TrackingFilters (QTFs) are an appealing choice for such robust fencing inintermittently nonlinear filtering, as QTFs are analog filters suitable forwideband real-time processing of continuous-time signals and are easilyimplemented in analog circuitry. Further, their numerical computations are O(1)per output value in both time and storage, which also enables their high-ratedigital implementations in real time. In this paper, we first provide a briefgeneral discussion of the outlier noise and its mitigation by intermittentlynonlinear filters. We then focus on the basic properties of the QTF-basedfencing, discuss the approaches to choosing its parameters, and illustrate theuse of the QTF fencing for various types of the signal+noise mixtures. We alsodemonstrate how the Complementary Intermittently Nonlinear Filtering (CINF)arrangements allow us to increase the tightness and robustness of the QTFfencing, while preserving its inclusivity, and to enable the mitigation ofoutlier noise obscured by high-amplitude non-outlier signals such as the signalof interest itself.

Quantile Tracking Filters for Robust Fencing in Intermittently Nonlinear Filtering