LAUSR

Employing observability analysis of a dynamic system is necessary to determine the efficiency of a Kalman filter designed to estimate the state of dynamic system, and the system state is a set of variables which can describe the motion state of the dynamic system. The observability sets a lower limit for the estimation error, and the lower the limit, the better the likelihood of obtaining an accurate estimate of the system state. In other words, if the system is not observable, it is not possible to accurately estimate the system state, even if the noise level is negligible. While the observability analysis of a constant linear system is simple, analyzing a time-varying nonlinear system is quite complicated. Goshen-Meskin and Bar-Itzhack [1] modeled the time-varying nonlinear system as the piece-wise constant system (PWCS) to analyze its observability, which is presented as a step-by-step procedure. Chen [2] introduced a concept of the local observability for the time-varying linear system, and Bartosiewicz [3] extended this concept to the nonlinear system. For the observability of the system state, singular value decomposition (SVD) [4] has been widely used to analyze the observable degree. However, this method had a theoretical limitation, namely, the dimensions of singular values corresponding to different system states are different; therefore it is unreasonable to directly compare the singular values. However, to the best of our knowledge, little research has been conducted on the observability analysis of the time-varying nonlinear system.