This article provides an extension of the observability rank condition to time-varying nonlinear systems. Previous conditions to check the state observability only hold for nonlinear systems that do not explicitly depend on time, or, for time-varying systems, they only account for the linear case. In this article, a general analytic condition is provided. The new condition reduces to the well-known observability rank condition in the two simpler cases of time-varying linear systems and time-invariant nonlinear systems. The proposed condition is applied to aerospace robotics to study the observability of a lunar-module-type system equipped with monocular vision and inertial sensors.

中文翻译：

---

可观测等级条件对时变非线性系统的推广

本文将可观察性等级条件扩展到时变非线性系统。检查状态可观测性的先前条件仅适用于不明确依赖于时间的非线性系统，或者，对于时变系统，它们仅适用于线性情况。在本文中，提供了一般分析条件。在时变线性系统和时不变非线性系统这两种更简单的情况下，新条件简化为众所周知的可观测性等级条件。提出的条件应用于航空航天机器人，以研究配备单目视觉和惯性传感器的登月舱型系统的可观测性。