GNSS integrated displacement and attitude determination for structural health monitoring of long-span bridges

Accurate monitoring of bridge deformation under environmental and operational loads is critical for ensuring structural safety and serviceability. This paper presents an integrated displacement and attitude determination approach for bridge health monitoring, leveraging Global Navigation Satellite System (GNSS) technology to simultaneously capture displacement and attitude variations, such as pitch and heading angles. This method combines the GNSS observations at multiple antennas located on the bridge, utilizes a unit quaternion to express the attitude, and parameterizes the displacement, attitude, and carrier-phase ambiguities in one unified measurement model. Then, the unscented Kalman filter is adapted to achieve the optimal estimation of the quaternion-based nonlinear systems. Finally, the double-differenced ambiguities between the stations are resolved to integers to improve the accuracy of estimated displacement and attitude. The proposed method was evaluated using the data collected in the Forth Road Bridge, a long-span suspension bridge with a main span of 1.006 km and a total length exceeding 2.5 km. Using GNSS baselines ranging from 1.2 to 2.0 km, the method achieved horizontal and vertical displacement accuracies of 0.004-0.006 m and 0.008-0.010 m, respectively. For a 263 m baseline between the quarter- and mid-span points, pitch and heading accuracies reached 0.0013 degrees and 0.0004 degrees, respectively. Furthermore, the method is capable of determining the roll angle by utilizing monitoring stations located on the opposite side of the bridge. It reveals that this method can sensitively detect subtle attitude changes, offering insights into bridge behaviour from a new perspective beyond displacement data. This work establishes the full cross-correlation between displacement and attitude parameters, which is beneficial for developing tightly coupled GNSS and inertial measurement unit in terms of both displacement and attitude parameters for structural health monitoring. The findings underscore the potential of this approach in the establishment of the next-generation structure health monitoring systems, with a focus on robustness, reliability, and scalability for broader applications.