Observability quantification for linear stochastic system and its application in state estimation

This paper presents a method for quantitatively evaluating the observability of linear stochastic systems and pre-evaluating the accuracy of state estimations. In this method, according to the relation among the current state vector, measurement sequence and noise sequence, the observability degree for the state variables of linear stochastic systems is defined. And it is further proved that, the proposed observability degree can be used to examine the existence of unbiased estimated states and measure the estimation error lower bound. In addition, the necessary and sufficient condition for the state variable to be observable is also given according to the proposed observability degree. Finally, a numerical simulation example on target tracking problem is presented to validate the efficiency of the proposed observability degree.