We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family.

翻译：本文研究跟踪一个未知时变参数的问题，该参数决定了独立观测序列的概率演化。为此，我们提出一种基于随机梯度下降的递推方案，其中观测的对数似然函数充当时变增益函数。我们证明了在未知时变参数的适当邻域内均方误差的收敛性，并以数据来自指数族分布的情形为例，详细阐述了我们的发现。