This paper develops a framework for the design of diffusion adaptive algorithms, where a network of nodes aim to estimate system parameters from the collected distinct local data stream. We explore the time and spatial knowledge of system responses and model their evolution in both time and spatial domain. A weighted maximum a posteriori probability (MAP) is used to derive an adaptive estimator, where recent data has more influence on statistics via weighting factors. The resulting recursive least squares (RLS) local estimate can be implemented by the QR decomposition (QRD). To mediate the distinct spatial information incorporation within neighboring estimates, a variable spatial regularization (VSR) parameter is introduced. The estimation bias and variance of the proposed algorithm are analyzed. A new diffusion VSR QRRLS (Diff-VSR-QRRLS) algorithm is derived that balances the bias and variance terms. Simulations are carried out to illustrate the effectiveness of the theoretical analysis and evaluate the performance of the proposed algorithm.

中文翻译：

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一种新的扩散变量空间正则化QRRLS算法


本文开发了一个用于扩散自适应算法设计的框架，其中节点网络旨在从收集的不同本地数据流中估计系统参数。我们探索系统响应的时间和空间知识，并对其在时间和空间域中的演化进行建模。加权最大后验概率（MAP）用于导出自适应估计器，其中最近的数据通过加权因子对统计数据有更大的影响。由此产生的递归最小二乘 (RLS) 局部估计可以通过 QR 分解 (QRD) 来实现。为了调节相邻估计中的不同空间信息合并，引入了可变空间正则化（VSR）参数。分析了该算法的估计偏差和方差。推导了一种新的扩散 VSR QRRLS (Diff-VSR-QRRLS) 算法来平衡偏差和方差项。进行仿真来说明理论分析的有效性并评估所提出算法的性能。