A state decoupling approach to estimate unobservable tracking systems

If a system is unobservable, the error covariance associated with a Kalman filter will be nearly singular. As a consequence, an optimum estimation in the sense of minimum error covariance does not exist. In this paper, we show that this (unobservable) system can be transformed into a nonlinear system with a linear measurement equation. In addition to other useful features, this transformation also serves to decouple the state in such a way that an observable part can be extracted and estimated while no information can be gained and processed for the unobservable part.