Combinations of adaptive filters have attracted attention as a simple solution to improve filter performance, including tracking properties. In this paper, we consider combinations of LMS and RLS filters, and study their performance for tracking time-varying solutions. Modeling the variation of the parameter vector to be estimated as a first order autoregressive (AR) model, we show that a convex combination between one LMS and one RLS filters with their optimum settings may have a tracking performance close to the optimal excess mean-square error (EMSE) and mean-square deviation (MSD) obtained via Kalman filter, but with lower computational complexity (linear in the filter length instead of quadratic — in the case of diagonal matrices in the Kalman model — or cubic, for general Kalman models).

中文翻译：

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自适应滤波器及其组合的跟踪性能

自适应滤波器的组合作为提高滤波器性能（包括跟踪特性）的简单解决方案已经引起了人们的注意。在本文中，我们考虑 LMS 和 RLS 滤波器的组合，并研究它们在跟踪时变解决方案方面的性能。将要估计的参数向量的变化建模为一阶自回归 (AR) 模型，我们表明一个 LMS 和一个 RLS 滤波器之间的凸组合及其最佳设置可能具有接近最佳超均方的跟踪性能通过卡尔曼滤波器获得的误差 (EMSE) 和均方偏差 (MSD)，但计算复杂度较低（滤波器长度呈线性，而不是二次——对于卡尔曼模型中的对角矩阵——或三次，对于一般卡尔曼模型）。