一个网络参数估计的增量式RLS算法

An Incremental RLS Algorithm for Network Parameter Estimation

摘要

针对现有增量式最小均方算法仅利用各节点的局部数据进行局部估计,在信息交互受限条件下估计精度较低的问题,提出一种循环网络估计的增量式递归最小二乘算法.该算法在循环网络中逐节点对局部损失函数进行指数加权求和,仅利用前一节点参数的局部估计值和中间过程矩阵的估计值,递归求解每个节点处的局部估计,具有信息交互需求低、估计精度高的特点.通过对该估计方法的均值和均方误差理论分析可知,仿真实验结果与理论分析高度吻合.在不同应用场景下,该算法估计精度均优于目前对比增量式最小均方算法,为分布式循环网络中的参数估计提供了一种高效可行的解决方案.

Abstract

Aiming at the problem that existing incremental least mean square algorithms, which relied solely on the local data at each node to perform local estimation, suffered from low estimation accuracy under limited information exchange, we proposed an incremental recursive least squares algorithm based on cyclic network estimation. The algorithm performed exponentially weighted summation of local loss functions node by node in the cyclic network, and recursively solved the local estimate at each node by using only the local estimate of parameter and intermediate process matrix estimate from the immediately preceding node. It featured low demand for information exchange and high estimation accuracy. Through theoretical analysis of the mean and mean-square error of proposed estimation method, the simulation experimental results are highly consistent with the theoretical analysis. In different application scenarios, the estimation accuracy of proposed algorithm is superior to the current comparative incremental least mean square algorithms, providing an efficient and practical solution for parameter estimation in distributed cyclic networks.

关键词

自适应算法 / 增量形式 / 递归最小二乘

Key words

adaptive algorithm / incremental form / recursive least squares

参考文献

[1] SAYED A H. Adaptive Networks[J]. Proceedings of the IEEE, 2014, 102(4): 460-497.

[2] LOPES C G, SAYED A H. Incremental Adaptive Strategies over Distributed Networks[J]. IEEE Transactions on Signal Processing, 2007, 55(8): 4064-4077.

[3] LOPES C G, SAYED A H. Diffusion Least-Mean Squares over Adaptive Networks: Formulation and Performance Analysis[J]. IEEE Transactions on Signal Processing, 2008, 56(7): 3122-3136.

[4] LOPES C G, SAYED A H. Distributed Adaptive Incremental Strategies: Formulation and Performance Analysis[C]// International Conference on Acoustics, Speech, and Signal Processing. Piscataway, NJ: IEEE, 2006: 584-587.

[5] SCHIZAS I D, MATEOS G, GIANNAKIS G B. Distributed LMS for Consensus-Based in-Network Adaptive Processing[J]. IEEE Transactions on Signal Processing, 2009, 57(6): 2365-2382.

[6] YU Y, ZHAO H. Robust Incremental Normalized Least Mean Square Algorithm with Variable Step Sizes over Distributed Networks[J]. Signal Processing, 2018, 144: 1-6.

[7] ALI ABADI A, CHEHELA M, GHOBADI C. Theoretical Performance Analysis of Sparse System Identification Using Incremental and Diffusion Strategies over Adaptive Networks[J]. Wireless Personal Communications, 2019, 109(2): 1181-1193.

[8] SAEED M O B, ZERGUINE A. An Incremental Variable Step-Size LMS Algorithm for Adaptive Networks[J]. IEEE Transactions on Circuits and Systems Ⅱ: Express Briefs, 2019, 67(10): 2264-2268.

[9] SAEED M O B, PASHA S A, ZERGUINE A. A Variable Step-Size Incremental LMS Solution for Low SNR Applications[J]. Signal Processing, 2021, 178: 107730-1-107730-8.

[10] SAEED M O B, ZERGUINE A, HAMEED U, et al. An Incremental Noise Constrained LMS Algorithm[J]. Signal Processing, 2023, 213: 109187-1-109187-9.

[11] DINIZ P S R. Adaptive Filtering: Algorithms and Practical Implementation[M]. 5th ed. New York: Springer, 2020: 156-187.

[12] SAYED A H, LOPES C G. Distributed Recursive Least-Squares Strategies over Adaptive Networks[C]// Asilomar Conference on Signals, Systems and Computers. Piscataway, NJ: IEEE, 2006: 233-237.

[13] CATTIVELLI F S, LOPES C G, SAYED A H. A Diffusion RLS Scheme for Distributed Estimation over Adaptive Networks[C]// Signal Processing Advances in Wireless Communications. Piscataway, NJ: IEEE, 2007: 1-5.

[14] CATTIVELLI F S, LOPES C G, SAYED A H. Diffusion Recursive Least-Squares for Distributed Estimation over Adaptive Networks[J]. IEEE Transactions on Signal Processing, 2008, 56(5): 1865-1877.

[15] LEUNG S H, SO C F. Gradient-Based Variable Forgetting Factor RLS Algorithm in Time-Varying Environments[J]. IEEE Transactions on Signal Processing, 2005, 53(8): 3141-3150.

基金资助

国家自然科学基金(12571329)