Consistency of three Kalman filter extensions in hybrid navigation

A filter is consistent if predicted errors are at least as large as actual errors. In this paper, we evaluate the consistency of three filters and illustrate what could happen if filters are inconsistent. Our application is hybrid positioning which is based on signals from satellites and from mobile phone network base stations. Examples show that the consistency of a filter is very important. We evaluate three filters: EKF, EKF2 and PKF. Extended Kalman Filter (EKF) solves the filtering problem by linearizing functions. EKF is very commonly used in satellite-based positioning and it has also been applied in hybrid positioning. We show that nonlinearities are insignificant in satellite measurements but often significant in base station measurements. Because of this, we also apply Second Order Extended Kalman Filter (EKF2) in hybrid positioning. EKF2 is an elaboration of EKF that takes into consideration the nonlinearity of the measurement models. The third filter is called Position Kalman Filter (PKF), which filters a sequence of static positions and velocities. We also check what kind of measurement combinations satisfy CGALIES and FCC requirements for location.

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