Derivative-Free Observability Analysis of a Stochastic Dynamical System

This paper proposes a novel approach to analyze the observability of a stochastic linear or non-linear dynamical system. Unlike the traditional observability analysis approach, our approach is fully derivative-free, resulting in a low complexity and an easy implementation. Furthermore, it can not only analyze the observability of each system state, but also it can assess the effect of the observation and the system noise on the system observability, which is not considered by the traditional approach. Specifically, using the generalized polynomial chaos expansion, an observability-coefficient matrix is first calculated, which enables us to judge whether the system is observable or not. Then, the puny and brawny observability indexes are assessed to quantify the degree of observability. The equivalence between the conventional method and the proposed method for a continuous-time linear time-invariant system is proved in the appendix. The effectiveness of the proposed approach is mathematically proved and its good performance is demonstrated in several test cases.