[论文解读] Quantile Tracking Filters for Robust Fencing in Intermittently Nonlinear Filtering

Alexei V. Nikitin, Ruslan L. Davidchack|arXiv (Cornell University)|Nov 2, 2019

Advanced Adaptive Filtering Techniques参考文献 11被引用 12

一句话总结

本文提出分位数追踪滤波器（QTFs）作为间歇性非线性滤波（INF）中抑制异常值噪声的鲁棒、高效解决方案，实现对信号异常值的紧密、包容且实时的围堵。通过利用QTFs的O(1)计算复杂度和模拟友好设计，该方法能有效抑制脉冲性和瞬态噪声，同时保持信号完整性，而互补间歇性非线性滤波（CINF）进一步提升了在高动态范围场景下的性能。

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.

研究动机与目标

• 解决在通信和传感器系统中抑制脉冲性、瞬态性和突发性噪声的挑战，同时不降低感兴趣信号的质量。
• 克服非线性滤波中鲁棒性（紧密围栏）与包容性（避免误报）之间的权衡。
• 开发一种计算高效、适用于模拟和高速数字实现的实时滤波解决方案。
• 展示互补间歇性非线性滤波（CINF）如何在保持信号保真度的同时，提升围栏紧密度和鲁棒性。
• 通过基于CINF的信号恢复，实现对受异常值噪声污染的重叠宽带和窄带信号的有效分离。

提出的方法

• 将分位数追踪滤波器（QTFs）用作模拟或数字滤波器，实时跟踪输入信号的特定分位数（例如中位数、四分位数）。
• 利用QTFs在感兴趣信号周围建立上下围栏，定义一个能排除异常值的鲁棒范围。
• 将围栏外的异常值替换为中值范围的值，以抑制噪声，同时保持信号动态特性。
• 通过基于输入与跟踪分位数偏差的自适应更新规则，采用有限差分算法实现QTFs。
• 通过结合两个INF级联阶段实现互补INF（CINF）：一个用于滤除宽带噪声，另一个用于从滤波后的混合信号中恢复原始信号。
• 利用全通滤波在宽带信号中引入人工异常值，以测试CINF分离重叠波形的能力。

实验结果

研究问题

• RQ1 如何在间歇性非线性滤波中实现鲁棒围栏，以同时最小化异常值检测中的误报和漏报？
• RQ2 QTFs围栏的最佳参数设置是什么，以在实时信号处理中平衡紧密度、鲁棒性与包容性？
• RQ3 QTFs能否在不引入不稳定或失真情况下，有效抑制宽带信号中的脉冲性和瞬态噪声？
• RQ4 互补间歇性非线性滤波（CINF）在多大程度上改善了受异常值噪声污染的重叠宽带与窄带信号的分离？
• RQ5 QTFs的O(1)计算复杂度如何支持其在实时应用中的高速率数字实现？

主要发现

• QTFs在时间和存储空间上均实现每输出样本O(1)的计算复杂度，支持高速率实时数字滤波。
• 基于QTF的围栏能有效抑制宽带信号中的异常值噪声，如图4所示，显著降低了感兴趣频带的功率谱密度（PSD）。
• 基于CINF的信号分离相比线性互补带阻/带通滤波器，将信号恢复误差降低了高达8 dB，如图17所示。
• 该方法通过鲁棒围栏保持信号结构，成功缓解了‘蟑螂效应’——即因异常值去除导致的低频PSD增加问题。
• QTFs通过在输入偏差超过阈值时强制施加边界条件，防止数字实现中的过冲，确保数值稳定性。
• CINF即使在全通滤波导致人工异常值后，仍能有效恢复原始时域信号波形，实现最小失真恢复。