On-the-fly GPS-based attitude determination using single- and double-differenced carrier phase measurements

Carrier phase measurements are primary observations for GPS attitude determination. Although the satellite-related errors can be virtually eliminated by forming single differences, the baseline-related errors such as line biases are still present in the single-differenced carrier phase measurements. It is, therefore, difficult to resolve the single-differenced integer ambiguities due to the line biases. By forming double differences, the line biases of the single-differenced carrier phase measurements can be effectively removed. However, the main disadvantages of this method lie in the fact that the double-differenced measurements are mathematically correlated and consequently the attitude obtained from the double differences is noisy. This paper presents a new algorithm through which both single and double differences are used simultaneously to resolve these problems in realtime. The solution of the integer ambiguities can be obtained by searching for the most likely grid point in the attitude domain that is independent of the correlation with the double differences. Next, the line biases and corresponding single difference integer ambiguities can be resolved on the fly by using the noisy attitude solution obtained from the previous double difference procedure. In addition, the relationship between the physical signal path difference and the line bias is formed. A new method is also applied to derive the attitude angles through finding the optimal solution of the attitude matrix element. The proposed new procedure is validated using ground and flight tests. Results have demonstrated that the new algorithm is effective and can satisfy the requirement of real-time applications.