Parameters of the mathematical model describing many practical dynamical systems are prone to vary due to aging or renewal, wear and tear, as well as changes in environmental or service conditions. These variabilities will adversely affect the accuracy of state estimation. In this paper, we introduce SSUE: Simultaneous State and Uncertainty Estimation for quantifying parameter uncertainty while simultaneously estimating the internal state of a system. Our approach involves the development of a Bayesian framework that recursively updates the posterior joint density of the unknown state vector and parameter uncertainty. To execute the framework for practical implementation, we develop a computational algorithm based on maximum a posteriori estimation and the numerical Newton's method. Observability analysis is conducted for linear systems, and its relation with the consistency of the estimation of the uncertainty's location is unveiled. Additional simulation results are provided to demonstrate the effectiveness of the proposed SSUE approach.

中文翻译：

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SSUE：动态系统的同时状态和不确定性估计

由于老化或更新、磨损以及环境或服务条件的变化，描述许多实际动力系统的数学模型的参数容易发生变化。这些可变性将对状态估计的准确性产生不利影响。在本文中，我们介绍了 SSUE：同时状态和不确定性估计，用于量化参数不确定性，同时估计系统的内部状态。我们的方法涉及开发贝叶斯框架，该框架递归更新未知状态向量和参数不确定性的后关节密度。为了执行实际实施的框架，我们开发了一种基于最大后验估计和数值牛顿法的计算算法。对线性系统进行可观察性分析，并揭示了它与不确定性位置估计一致性的关系。提供了额外的模拟结果来证明所提出的 SSUE 方法的有效性。