用贝叶斯框架统一推导传统与鲁棒自适应滤波器，揭示其内在联系。
A Unified Bayesian Perspective for Conventional and Robust Adaptive Filters
- 基于状态空间模型的贝叶斯递归推断，统一推导各类自适应滤波器。
- 在拉普拉斯噪声假设下，导出新鲁棒滤波算法，包含已知的符号误差法。
- 框架简洁通用，适合信号处理、自适应系统研究者参考。
本文提出一种新的视角，阐释自适应滤波器的起源与解释。通过将贝叶斯递归推断应用于状态空间模型，并对解的结构进行一系列简化，我们在一个统一框架下推导出依赖于测量噪声概率模型的多种自适应滤波器。特别地，在高斯噪声假设下，可得到文献中熟知的解（如LMS、NLMS或卡尔曼滤波器）；而在非高斯噪声假设下，可导出新的自适应算法。值得注意的是，在拉普拉斯噪声假设下，我们得到一类鲁棒滤波器，其中符号误差算法是已知成员，而其他在该框架下轻松推导出的算法则是全新的。数值实验展示了所推导滤波器的性质，有助于深入理解其性能。
原文摘要 · Abstract (English)
In this work, we present a new perspective on the origin and interpretation of adaptive filters. By applying Bayesian principles of recursive inference from the state-space model and using a series of simplifications regarding the structure of the solution, we can present, in a unified framework, derivations of many adaptive filters that depend on the probabilistic model of the measurement noise. In particular, under a Gaussian model, we obtain solutions well-known in the literature (such as LMS, NLMS, or Kalman filter), while using non-Gaussian noise, we derive new adaptive algorithms. Notably, under the assumption of Laplacian noise, we obtain a family of robust filters of which the sign-error algorithm is a well-known member, while other algorithms, derived effortlessly in the proposed framework, are entirely new. Numerical examples are shown to illustrate the properties and provide a better insight into the performance of the derived adaptive filters.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。