A stochastic average gradient (SAG) algorithm is proposed for multirate (MR) finite impulse response (FIR) models with varying time delays in this article. The time delays at each sampling instant are computed through the self‐organizing maps technique, and then the parameters are estimated by using the SAG algorithm. Considering that the SAG algorithm updates the parameters using all the directions up to and including the current sampling instant, but only compute one gradient at each sampling instant, thus it has less computational efforts and quicker convergence rates. Furthermore, some modified SAG algorithms are also developed. Two simulation examples show that these algorithms identify MR FIR models with varying time delays correctly.

中文翻译：

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使用自组织映射的具有可变时延的多速率FIR模型的随机平均梯度算法

本文针对具有变化时间延迟的多速率（MR）有限冲激响应（FIR）模型，提出了一种随机平均梯度（SAG）算法。通过自组织映射技术计算每个采样时刻的时间延迟，然后使用SAG算法估计参数。考虑到SAG算法使用直到当前采样时刻（包括当前采样时刻）的所有方向更新参数，但是在每个采样时刻仅计算一个梯度，因此其计算工作量较小，收敛速度更快。此外，还开发了一些改进的SAG算法。两个仿真示例表明，这些算法可以正确识别具有不同时延的MR FIR模型。