Application of Network RTK Positions and Geometric Constraints to the Problem of Attitude Determination Using the GPS Carrier Phase Measurements

Nowadays, navigation is an unavoidable fact in military and civil aerial transportations. The Global Positioning System (GPS) is commonly used for computing the orientation or attitude of a moving platform. The relative positions of the GPS antennas are computed using the GPS code and/or phase measurements. To achieve a precise attitude determination, Carrier phase observations of GPS requiring the phase ambiguity resolution has been utilized. The more accurate the coordinates, the more accurate the attitude parameters will be. Attitude parameters are derived from the computed coordinates. Here, attitude parameters are computed by carrier beat phases of four single frequency GPS receivers. The problem of GPS attitude determination is an ill-posed problem if only GPS carrier phases are used. This is because the number of unknown parameters is always larger than the number of observations when the relative positions of the GPS antennas are computed. In this research, carrier beat phases of four single frequency GPS receivers are used to determine the orientation of a platform whose attitude parameters are already known. Observations are made for 10 minutes. In this research, two sets of constraints are used to fix the rank deficiency of the problem. The first consists of the Real Time Kinematic (RTK) coordinates of the GPS antennas. Fixed antennas to the moving body help add five additional constraints (second set) to the problem. These constraints increase the redundancy and make the least-squares estimation of the attitude parameters possible. Since the application of regularization methods contaminates the solution with regularization errors, application of the proposed constraints is superior to regularization techniques. This is practically shown through the comparison of the computed attitude parameters, a similar set of results which is derived using the Moore-Penrose algorithm as a regularization technique, and the reference values of these parameters which are provided through an independent research. According to the obtained results, 59 seconds is required to fix the ambiguity parameters. In other words, to reduces the accuracy of the float ambiguities to less than 1.0 cycle, their initial estimate should be updated by the next 58 measurement epochs. Then the ambiguity parameters are rounded to their nearest integer number. On average, the least squares estimate of the yaw parameter is 51.7000 with the standard deviation of ±0.01710. The average estimate of pitch is 39.1680 with the standard deviation of ±0.01540. Finally, on average, the least squares estimate of the roll is 26.1530 with the standard deviation of ±0.01370. Computed attitudes have been compared to their known values. By the new definition of the body frame given in this study, least-squares estimation of the attitude parameters would be possible even if only three GPS antennas are used. Computing the transformation parameters between the new and conventional body frames, attitude angles can be transformed to any conventional frame. The proposed method of this research is superior to the others. The computed biases represent the integrity of determination and corroborate usage of inner constraints and weighted parameters to resolve the rank deficiency of the problem.