This paper is concerned with a systematic discussion on the problem of state estimation for a class of systems with multiple uncertain dynamics and multiple measurement biases. Instead of the traditional observability definition only for system state vector, we consider the generalized observability for the combinations of system state vector, uncertain dynamics and measurement bias. Firstly, a necessary and sufficient condition for the observability of system state vector is developed. Moreover, the set of all the observable combinations of system state vector, uncertain dynamics and measurement bias is presented. Correspondingly, an observer is constructed for estimating a special observable combination which is an approximation of system state vector. More importantly, the bound of the resulting estimation error for the system state vector is quantitatively discussed. Finally, the simulation study on a two-mass–spring system illustrates our theoretical results.

本文涉及对一类具有多个不确定动力学和多个测量偏差的系统的状态估计问题的系统讨论。代替仅针对系统状态向量的传统可观察性定义，我们考虑系统状态向量，不确定的动力学和测量偏差的组合的广义可观察性。首先，开发了系统状态向量可观性的充要条件。此外，提出了系统状态向量，不确定动力学和测量偏差的所有可观察组合的集合。相应地，构造观察器以估计特殊的可观察组合，该组合是系统状态向量的近似值。更重要的是，定量讨论了系统状态向量的估计误差范围。最后，在两质量弹簧系统上的仿真研究说明了我们的理论结果。