Single Range Localization in 3-D: Observability and Robustness Issues

The problem of estimating the position of a 3-D vehicle subject to a constant unknown velocity disturbance is addressed: the only available model output is assumed to be the distance (range) to a reference point. The vehicle's nominal velocity is also assumed to be known. An observability analysis is performed and an observer is designed. The proposed approach departs from alternative ones and leads to the definition of a linear time-invariant state equation with a linear time-varying output. The localization problem is solved using a novel outlier robust predictor-corrector state estimator. Numerical simulation examples are described to illustrate the performance of the method compared with a standard Kalman filter.