摘要翻译：
最小均方(LMS)滤波器通常是通过维纳滤波器解导出的。对于系统辨识方案，这样的推导使得很难结合系统脉冲响应的先验信息。我们提出了一种基于最大后验概率解的替代方法，该方法允许开发一种知识辅助的Kaczmarz算法。基于这种知识辅助Kaczmarz，我们构造了一种知识辅助LMS滤波器。这两种算法都允许在待估计参数上结合先验均值和协方差矩阵。这些算法除了梯度中的测量信息之外，还使用这些先验信息来迭代更新它们的估计。我们分析了算法的收敛性，并给出了性能的仿真结果。正如预期的那样，可靠的先验信息允许改进算法在低信噪比(SNR)场景下的性能。结果表明，所提出的算法几乎可以达到最优的最大后验概率(MAP)性能。
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英文标题：
《Knowledge-Aided Kaczmarz and LMS Algorithms》
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作者：
Michael Lunglmayr, Oliver Lang, Mario Huemer
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最新提交年份：
2017
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  The least mean squares (LMS) filter is often derived via the Wiener filter solution. For a system identification scenario, such a derivation makes it hard to incorporate prior information on the system's impulse response. We present an alternative way based on the maximum a posteriori solution, which allows developing a Knowledge-Aided Kaczmarz algorithm. Based on this Knowledge-Aided Kaczmarz we formulate a Knowledge-Aided LMS filter. Both algorithms allow incorporating the prior mean and covariance matrix on the parameter to be estimated. The algorithms use this prior information in addition to the measurement information in the gradient for the iterative update of their estimates. We analyze the convergence of the algorithms and show simulation results on their performance. As expected, reliable prior information allows improving the performance of the algorithms for low signal-to-noise (SNR) scenarios. The results show that the presented algorithms can nearly achieve the optimal maximum a posteriori (MAP) performance.
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PDF链接：
https://arxiv.org/pdf/1712.02146