The Development of a Median Adaptive Filter

本工作致力于分析和开发一类能够在脉冲噪声环境中有效运行的鲁棒自适应滤波算法。自适应信号处理，特别是涉及线性滤波器的自适应滤波为许多信号处理问题提供了一种强有力的方法。当有限的先验信息可用时，自适应算法的运行能力使它们与许多实际应用相匹配。然而，当滤波器输入中存在脉冲噪声时，线性自适应滤波器的性能会严重下降。这种脉冲干扰在许多应用中经常出现。本文的工作是发展一类对这种干扰不敏感的非线性自适应滤波器。这是通过提出的中值最小均方(MLMS)算法来实现的。该算法通过将均方误差性能面(如众所周知的LMS自适应滤波器所使用的)的梯度的瞬时估计替换为该量的样本中值。在这项工作中，建立了MLMS的可行性，并发展了MLMS的理论，包括随机输入和确定性输入。发展了一类基于顺序统计量(MLMS是其单个成员)的鲁棒自适应滤波过程。建立了包括第k阶和修剪均值在内的关键阶统计自适应滤波器的性质，并提出了便于自适应的算法，以便于相对于输入的统计量来优化阶统计滤波器。

This work is concerned with the analysis and development of a class of robust adaptive filtering algorithms which are capable of operating effectively in an environment of impulsive noise. Adaptive signal processing and particularly adaptive filtering involving linear filters provides a powerful approach to many signal processing problems. The capacity of adaptive algorithms to operate when limited a priori information is available makes them ideally matched to many practical applications. The performance of linear adaptive filters is, however, severely degraded when impulsive noise is present in the filter inputs. Such impulsive interference occurs frequently in many applications. The work here is concerned with the development of a class of nonlinear adaptive filters which are insensitive to the presence of such interference. This is achieved through a proposed Median Least-Mean- Squares (MLMS) algorithm. This algorithm operates by replacing the instantaneous estimate of the gradient of the mean-squared error performance surface (as used by the well-known LMS adaptive filter) by the sample median of that quantity. In this work, the feasibility of the MLMS is established and a theory for the MLMS, both for random and deterministic inputs, is developed. A general class of robust adaptive filtering procedures based on order statistics (of which the MLMS is a single member) is developed. The properties of key order statistical adaptive filters including the kth rank and trimmed mean are established, and algorithms designed to facilitate adaptation to optimize the order statistical filter in relation to the statistics of the input are developed.