Ellipsoid bounding estimation for kinematic geodetic positioning

In kinematic position estimation, a Kalman filter procedure is often used to provide improved solution benefiting from the history information. However, the optimal Kalman filtering solutions are subject to precise function models and statistic knowledge of noises, which may be difficult to obtain in advance. As a result, Kalman filter does not necessarily provide better performance for kinematic positioning solutions. In real world situations, a bound of the noise distribution would be easily and more reasonably determined than noise statistics. This paper studies ellipsoid bounding estimation for kinematic position estimation. In this estimation, neither process nor measurement noise characteristics are necessary, as long as the noises at each sample points can be confined in a bound (ellipsoid). A general trace criteria is adopted to choose the optimal estimator. For a the special case that only scalar measurement is available, e.g., a position measurement, we designed a modified intersection approach to reduce the estimation conservatism. Numerical results are given in each estimation step to illustrate the algorithm. A flight trajectory data is processed and the estimation results are compared under three different measurement noise cases: Gaussian white noise, uniformly noise (non-Gaussian) and the real measurement noise. Kalman filter results are also given for comparison. Results demonstrate the ellipsoid estimation indeed offers improved kinematic position solution in the sense of robustness for non-Gaussian noises, and retains nearly the same estimation error variance.