A New Diffusion Variable Spatial Regularized QRRLS Algorithm

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.