A new variable step-size strategy for the least mean square (LMS) algorithm is presented for distributed estimation in adaptive networks using the diffusion scheme. This approach utilizes the ratio of filtered and windowed versions of the squared instantaneous error for iteratively updating the step-size. The result is that the dependence of the update on the power of the error is reduced. The performance of the algorithm improves even though it is at the cost of added computational complexity. However, the increase in computational complexity can be minimized by careful manipulation of the update equation, resulting in an excellent performance-complexity trade-off. Complete theoretical analysis is presented for the proposed algorithm including stability, transient and steady-state analyses. Extensive experimental analysis is then done to show the performance of the proposed algorithm under various scenarios.

提出了一种新的最小均方（LMS）算法的可变步长策略，用于使用扩散方案的自适应网络中的分布式估计。该方法利用平方和的平方和瞬时误差的比率来迭代更新步长。结果是减少了更新对误差的影响。即使以增加的计算复杂度为代价，算法的性能也会提高。但是，通过谨慎地操作更新公式可以将计算复杂性的增加减到最小，从而实现出色的性能-复杂性折衷。对所提出的算法进行了完整的理论分析，包括稳定性，瞬态和稳态分析。