SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2023-2049, January 2020.
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.

中文翻译：

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非线性随机系统一类滤波器的稳定性

SIAM控制与优化杂志，第58卷，第4期，第2023-2049页，2020年1月。
本文开发了一个综合框架，用于对在某些强假设下具有非线性状态动力学和线性测量的随机动态系统的一类常用的连续和离散时间滤波器进行稳定性分析。滤波器的类别包括扩展的和无味的卡尔曼滤波器以及大多数其他高斯假设的密度滤波器及其数值积分近似值。稳定性结果的形式为时间均匀的均方边界和过滤误差的指数浓度不等式。与现有结果相反，该模型不一定总是指数稳定或完全观测的。我们回顾了三类模型，可以严格地证明它们满足稳定性定理的严格假设。