Direct Determination of Angular Velocity Using GPS

Abstract

Controlling a ship in a berthing operation is carried out mainly by the change of state, such as velocity and yaw rate (turn rate), although the value of the change of state is very small at berthing. Very high precision is, therefore, required to determine the velocity and angular velocity. A sensor that has an accuracy of ±0.02°/s (1 σ) is sought for determination of turn rate in a berthing system. Three-dimensional angular velocity can directly be determined, with 2 independent baselines of 3 GPS antennas, using instantaneous Doppler measurements or phase rate (temporal difference of phase) observations. This paper discusses the mathematical model for direct determination of angular velocity using GPS, and the comparison of the results of the angular velocity determination using the Doppler and phase rate. The precision of angular velocity determination is estimated using temporal difference of the attitude sensors (TSS and gyrocompass) on board a hydrographic sounding ship. The RMS values of the difference of yaw rate determination between the two systems were: ±0.16°/s using phase rate and ±0.31°/s using Doppler measurements with the separation of onboard antennas of ca. 1·34 m. 10 m baselines could satisfy the sensor requirements for angular velocity determination during berthing maneuvers.