Professor, Department of Surveying and Geomatics Eng., Center of Excellence in Geomatics Eng. and Disaster Prevention, Faculty of Eng., University of Tehran, Iran
Associate Professor, Space Physics Department, Institute of Geophysics, University of Tehran, Iran
M.Sc. in hydrographic Eng., Department of Surveying and Geomatics Eng., Center of Excellence in Geomatics Eng. and Disaster Prevention, Faculty of Eng., University of Tehran, Iran
*نگارنده رابط: تلفن: 61114383-021 دورنگار: 88337642-021 E-mail:email@example.com
Attitude determination of the moving platforms which is derivation of roll, pitch and yaw angles, is one of the challenging topics of modern geodesy. Commonly, the attitude parameters are obtained by inertial sensors, comprised of accelerometers, gyroscopes, and gyro-compasses. On the other hand nowadays, thanks to the availability of Global Navigation Satellite Systems (GNSS), like GPS, determination of the attitude parameters of the platforms by multiple onboard GNSS antennae has been among the studied topics in the different environments. The main idea behind the mentioned approaches is application of at least three onboard GNSS antennae and the use of double difference carrier phase observations for high-accuracy. From the theoretical point of view, the attitude determination requires establishment of the body frame (BF) and local level (LL) coordinate systems onboard the platform, while assuming the platform is a rigid body and the locations of the onboard antennae are unchanged throughout the experiment. Practically, the BF coordinate system is realized at the phase center of one of the onboard GNSS antennae, hereafter Ant. 1, the x- and y-axes along the transverse and longitudinal axes of the platform respectively, and the z-axis is perpendicular to the x-y plane, positive upward. The LL coordinate system is defined by its origin at the Ant. 1, the x- and y-axes along the geodetic east and north, and the z-axis is perpendicular to the horizontal plane, positive upward.
The multiple GNSS antennae for attitude determination can generally be categorized into dedicated systems, i.e. by using several onboard antennae and one receiver, and non-dedicated systems, i.e. by using several receivers with their corresponding onboard antennae. According to the current studies both systems lead to the same level of accuracy, though the dedicated systems may result in more cost effectiveness. From the computational point of view, the GNSS attitude determination algorithms can be based on either direct method or least squares. Within the direct algorithms the attitudes are determined by using the coordinates of the onboard GNSS Ant. 2 and Ant. 3 with respect to the LL coordinate system centered at the phase center of the Ant. 1. However, in the latter approach, the Euler angles are obtained by transforming the position vectors of the onboard antennae from the BF to LL coordinate systems through the rotation matrices containing the rotation angles. It is worth mentioning that the least square methods in their linearization process require some approximate values for the attitudes, which are commonly provided by the direct methods. Owing to the rigidity assumption of the platform, the BF-coordinates of the onboard antennae need to be determined once. The LL-coordinates can be obtained by using the relative coordinates of the onboard antennae in the Earth-Centered Earth-Fixed (ECEF) coordinate frame with respect to the Ant. 1.
The goal of this study, besides the representation of the GNSS-based attitude determination methods, is assessment of their obtainable accuracies by using different onboard antennae configurations. More specifically, we have compared two configurations based on three and four onboard GNSS antennae. For this purpose, we have started presenting the mathematical setup of attitude determination in details and then have organized a case study based on field operation. Considering the fact that one of the common application fields of the attitude determination is hydrographic surveying, e.g. for dredging, pipe-laying, and rig installations; we have selected a 27-meter long hydrographic survey vessel belonging to the National Geographic Organization (NGO) of Iran as the test platform. The vessel was equipped with four dual-frequency Javad GNSS receivers with choke-ring antennae mounted on a 15 m rectangular frame. Furthermore, a Leica GPS receiver antenna was established at the wharf as the base station for relative dynamic positioning. The marine experiment was performed in the surrounding waters of Kish harbor at different cruise ground speeds ranging from 5 to 12 knots, while the GNSS observations were continued with update rate of 1 Hz. The BF coordinates of the onboard GNSS antennae were determined by surveying measurements, when the vessel was on dry dock for some repair jobs. The GPS-derived ECEF coordinates of the onboard antennae were used to derive the LL coordinates of all the antennae with respect to LL-frame centered at the Ant. 1. The number of instantaneous visible satellites during the field operations reached up to 15. By considering the derived attitudes based on four GNSS antennae as the benchmark, the RMS’s of the attitudes obtained by three antennae configuration were computed. According to the results, the RMS values of the roll, pitch, and yaw angles are 2' 43", 4' 46", and 21’ 26", respectively. This clearly indicates that application of four GNSS antennae has significant improvement in the accuracies of the yaw and pitch angles, while the improvement in the roll accuracy is only marginal. Having done this experiment, we recommend implementation of four GNSS antennae configuration for delicate applications.