Single range localization in 3D: observability and robustness issues

The issue of single range based observability analysis and observer design for the kinematics model of a 3D vehicle eventually subject to a constant unknown drift velocity is addressed. The proposed method departs from alternative solutions to the problem and leads to the definition of a linear time invariant state equation with a linear time varying output. Simple necessary and sufficient observability conditions are derived. The localization problem is finally solved using a novel outlier robust predictor - corrector state estimator. Numerical simulation examples are described to illustrate the performance of the method as compared to a standard Kalman filter.