The Development of a Median Adaptive Filter

这项工作是关于分析和发展一类 鲁棒的自适应滤波算法， 在脉冲噪声的环境中有效地。 自适应信号 处理和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强有力的方法。 的 自适应算法在先验受限时的操作能力 信息是可用的，使他们理想地匹配到许多实际的 应用. 然而，线性自适应滤波器的性能是， 当滤波器输入中存在脉冲噪声时，性能严重下降。 这种脉冲干扰在许多应用中经常发生。 本文的工作是研究一类非线性的 自适应滤波器，其对这样的存在不敏感， 干扰 这是通过一个建议的中位数最小均值- 平方（MLMS）算法。 该算法通过替换 均方误差梯度的瞬时估计 性能表面（如由众所周知的LMS自适应滤波器所使用的）， 该数量的样本中位数。 在这项工作中，MLMS的可行性建立和理论 的MLMS，无论是随机和确定性的输入，开发。 一类基于阶数的鲁棒自适应滤波方法 统计（MLMS是其中的一个成员）。 的 包括第k阶的关键阶统计自适应滤波器的特性 秩和修剪平均值的建立，和算法设计， 促进适应以优化顺序统计滤波器， 与输入的统计数据的关系。

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.