Accuracy Assessment of Single and Double Difference Models for the Single Epoch GPS Compass

The single epoch GPS compass is an important field of study, since it is a valuable technique for the orientation estimation of vehicles and it can guarantee a total independence from carrier phase slips in practical applications. To achieve highly accurate angular estimates, the unknown integer ambiguities of the carrier phase observables need to be resolved. Past researches focus on the ambiguity resolution for single epoch; however, accuracy is another significant problem for many challenging applications. In this contribution, the accuracy is evaluated for the non-common clock scheme of the receivers and the common clock scheme of the receivers, respectively, we focus on three scenarios for either scheme: single difference model vs. double difference model, single frequency model vs. multiple frequency model and optimal linear combinations vs. traditional triple-frequency least square. We deduce the short baseline precision for a number of different available model and analyse the difference in accuracy for these models. Compared with the single or double difference model of the non-common clock scheme, the single difference model of the common clock scheme can greatly reduce the vertical component error of baseline vector, which results in higher elevation accuracy. The least squares estimators can also reduce the error of fixed baseline vector with the aid of the multi-frequency observation, thereby improving the attitude accuracy. In essence, the “accuracy improvement” is attributed to the difference in accuracy for different models, not a real improvement for any specific model. If all noise levels of GPS triple frequency carrier phase are assumed the same in unit of cycles, it can be proved that the optimal linear combination approach is equivalent to the traditional triple-frequency least squares, no matter which scheme is utilized. Both simulations and actual experiment have been performed to verify the correctness of theoretical analysis.