Upper-bounding bias errors in satellite navigation

A satellite navigation system for a safety critical application is required to provide an integrity alert of any malfunction; the probability that a navigation positioning error exceeds a given alert limit without an integrity alert is required to be smaller than a given integrity risk. So far, a little number of applications provide integrity alerts, because signal propagation from a satellite to a receiver depends on diversified phenomena and makes probabilistic upper-bound of possible threats difficult. To widen application fields of satellite navigation, two methods to upper-bound wide classes of bias errors are shown in this paper. The worst bias error in a maximum likelihood estimate caused by an interference signal within a given small power is derived. A novel inequality condition with a clock bias error and magnification coefficients that upper-bounds a horizontal position error is presented. Robustness of the inequality condition is numerically shown based on actual configurations of satellites.