Fast Integer Ambiguity Resolution for Gps Attitude Determination

In this paper, a new algorithm for GPS integer ambiguity resolution is shown. The algorithm first incorporates an instantaneous (static) integer search to significantly reduce the search space using a geometric inequality. Then a batch-type loss function is used to check the remaining integers in order to determine the optimal integer. This batch function represents the GPS sightline vectors in the body frame as the sum of two vectors, one depending on the phase measurements and the other on the unknown integers. The new algorithm has several advantages: it does not require an a-priori estimate of the vehicle’s attitude; it provides an inherent integrity check using a covariance-type expression; and it can resolve the integers even when coplanar baselines exist. The performance of the new algorithm is tested on a dynamic hardware simulator. Introduction The use of phase difference measurements from Global Positioning System (GPS) receivers provides a novel approach for three-axis attitude determination and/or estimation. These measurements have been successfully used to determine the attitude of airbased, space-based, and sea-based vehicles. Since phase differences are used, the correct number of integer wavelengths between a given pair of antennas must be found. The integer ambiguities can be .Copyright © 1999 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. determined using either “instantaneous” (motionless) or “dynamic” (motion-based) techniques. The ambiguities essentially act as integer biases to the phase difference measurements. Once the integer ambiguities are resolved, then the attitude determination problem can be solved. Instantaneous methods find a solution that minimizes the error residual at a specific time by searching through an exhaustive list of all possible integers and rejecting candidate solutions when the residual becomes too large. Refinements can be made to the solution by restricting the search space with knowledge of a-priori information, such as the maximum tilt the baseline should encounter. Instantaneous methods generally rely on solving a set of Diophantine equations. The appeal of these methods is that they provide an “instantaneous” attitude solution, limited only by computation time, and are well suited to short baselines. However, the minimum residual does not guarantee a correct solution in the presence of noise. In fact, it is possible that instantaneous methods can report a wrong solution as valid. This lack of integrity can cause significant problems if the sensor output is used to control a high bandwidth actuator, such as gas jets on a spacecraft. Another consideration is that instantaneous methods sometime require that the antenna array must be within a defined angle (typically 30 degrees) of a reference attitude, which is often true for ground-based applications, but is less likely for space-based applications. All of the aforementioned limitations imply that instantaneous methods, while attractive AIAA-99-3967