  This paper proposes a highly accurate trajectory estimation method for
outdoor mobile robots using global navigation satellite system (GNSS) time
differences of carrier phase (TDCP) measurements. By using GNSS TDCP, the
relative 3D position can be estimated with millimeter precision. However, when
a phenomenon called cycle slip occurs, wherein the carrier phase measurement
jumps and becomes discontinuous, it is impossible to accurately estimate the
relative position using TDCP. Although previous studies have eliminated the
effect of cycle slip using a robust optimization technique, it was difficult to
completely eliminate the effect of outliers. In this paper, we propose a method
to detect GNSS carrier phase cycle slip, estimate the amount of cycle slip, and
modify the observed TDCP to calculate the relative position using the factor
graph optimization framework. The estimated relative position acts as a loop
closure in graph optimization and contributes to the reduction in the
integration error of the relative position. Experiments with an unmanned aerial
vehicle showed that by modifying the cycle slip using the proposed method, the
vehicle trajectory could be estimated with an accuracy of 5 to 30 cm using only
a single GNSS receiver, without using any other external data or sensors.
