Short baseline GPS multi-frequency single-epoch precise positioning: utilizing a new carrier phase combination method

Traditional carrier phase combinations are linear functions of the original carrier phases. We develop a new way of carrier phase combination that regards carrier phases of different frequencies as the basis of the carrier phase space. The combined carrier phase is a point of this space. Then, this point, i.e., the combined carrier phase, is mapped back to a single-dimensional carrier phase by a bidirectional mapping. The new single-dimensional carrier phase is called mapped carrier phase. The advantages of this combination approach are a long wavelength and small noise of the mapped carrier phase, which make ambiguity resolution easy. Unfortunately, the mapped carrier phase value is not well determined due to the noise in the observed phases. On the contrary, a set of possible mapped carrier phase values are attained; however, only one value is correct. To reduce the number of candidates and fix the correct value of the mapped carrier phase, the following steps are discussed: (1) The integer nature of the original carrier ambiguity is used to attain an initial set of possible mapped carrier phase values; (2) the distribution of the mapped carrier phase ambiguity is included to reduce the possible values; and (3) the Gaussian least-squares objective function is introduced to fix the correct value. As a result of these steps, a single-epoch positioning algorithm is established. Two experiments are carried out to preliminarily compare the new algorithm with LAMBDA. The results show that the new algorithm is slightly below LAMBDA in resolution success rate, but computationally more efficient than LAMBDA.