Covariance matrix estimation is a crucial task in adaptive signal processing applied to several surveillance systems, including radar and sonar. In this paper we propose a dynamic learning strategy to track both the covariance matrix of data and its structure (class). We assume that, given the class, the posterior distribution of the covariance is described through a mixture of inverse Wishart distributions, while the class evolves according to a Markov chain. Hence, we devise a novel and general filtering strategy, called multi-class inverse Wishart mixture filter, able to capitalize on previous observations so as to accurately track and estimate the covariance. Some case studies are provided to highlight the effectiveness of the proposed technique, which is shown to outperform alternative methods in terms of both covariance estimation accuracy and probability of correct model selection. Specifically, the proposed filter is compared with class-clairvoyant covariance estimators, e.g., the maximum likelihood and the knowledge-based recursive least square filter, and with the model order selection method based on the Bayesian information criterion.

中文翻译：

---

自适应学习的多类随机矩阵滤波

协方差矩阵估计是应用于多种监视系统（包括雷达和声纳）的自适应信号处理中的一项关键任务。在本文中，我们提出了一种动态学习策略来跟踪数据的协方差矩阵及其结构（类）。我们假设，给定类，协方差的后验分布是通过逆 Wishart 分布的混合来描述的，而类是根据马尔可夫链演化的。因此，我们设计了一种新颖且通用的过滤策略，称为多类逆 Wishart 混合过滤器，能够利用先前的观察结果准确跟踪和估计协方差。提供了一些案例研究以强调所提出技术的有效性，它在协方差估计精度和正确模型选择的概率方面均优于替代方法。具体而言，将所提出的滤波器与类透视协方差估计器（例如，最大似然和基于知识的递归最小二乘滤波器）以及基于贝叶斯信息准则的模型顺序选择方法进行比较。