Quantile Tracking Filters for Robust Fencing in Intermittently Nonlinear Filtering

Abstract

Robust fencing is an essential component of intermittently nonlinear filtering for mitigation of outlier interference. In such filtering, the upper and the lower fences establish a robust range that excludes noise outliers while including the signal of interest and the non-outlier noise. Then, the outlier values are replaced with those in mid-range. To increase the effectiveness of outlier noise identification, and to minimize the false negatives, the fences need to be both tight and robust to outlier noise. On the other hand, to minimize the false positives and to avoid the detrimental effects, such as instabilities and excessive distortions, often associated with nonlinear filtering, the fences need to be inclusive, so that the signal of interest and the non-outlier noise remain within the fences. Quantile Tracking Filters (QTFs) are an appealing choice for such robust fencing in intermittently nonlinear filtering, as QTFs are analog filters suitable for wideband real-time processing of continuous-time signals and are easily implemented in analog circuitry. Further, their numerical computations are O(1) per output value in both time and storage, which also enables their high-rate digital implementations in real time. In this paper, we first provide a brief general discussion of the outlier noise and its mitigation by intermittently nonlinear filters. We then focus on the basic properties of the QTF-based fencing, discuss the approaches to choosing its parameters, and illustrate the use of the QTF fencing for various types of the signal+noise mixtures. We also demonstrate how the Complementary Intermittently Nonlinear Filtering (CINF) arrangements allow us to increase the tightness and robustness of the QTF fencing, while preserving its inclusivity, and to enable the mitigation of outlier noise obscured by high-amplitude non-outlier signals such as the signal of interest itself.