Overbounding position errors in the presence of carrier phase multipath error model uncertainty

In this paper, a methodology is developed to overbound the error in position estimation for carrier phase navigation systems subject to multipath error mis-modeling. In high accuracy and high integrity applications, carrier phase positioning systems with cycle resolution usually rely on time-filtering, in many cases using Kalman filters. Naturally, for a computed integrity risk to be meaningful, it must be guaranteed that the predicted state estimation error covariance always bounds the true covariance. The Kalman filter ensures state error covariance bounding provided that the measurement errors and system dynamics are accurately modeled. However, uncertainties in the dynamic model of the multipath error states always exist. In response, the focus of this work is to quantify and bound position estimate errors subject to uncertainties associated with the time correlation of multipath error.