  Due to the declining birthrate and aging population, the shortage of labor in
the construction industry has become a serious problem, and increasing
attention has been paid to automation of construction equipment. We focus on
the automatic operation of articulated six-wheel dump trucks at construction
sites. For the automatic operation of the dump trucks, it is important to
estimate the position and the articulated angle of the dump trucks with high
accuracy. In this study, we propose a method for estimating the state of a dump
truck by using four global navigation satellite systems (GNSSs) installed on an
articulated dump truck and a graph optimization method that utilizes the
redundancy of multiple GNSSs. By adding real-time kinematic (RTK)-GNSS
constraints and geometric constraints between the four antennas, the proposed
method can robustly estimate the position and articulation angle even in
environments where GNSS satellites are partially blocked. As a result of
evaluating the accuracy of the proposed method through field tests, it was
confirmed that the articulated angle could be estimated with an accuracy of
0.1$^\circ$ in an open-sky environment and 0.7$^\circ$ in a mountainous area
simulating an elevation angle of 45$^\circ$ where GNSS satellites are blocked.
