Improved ARCE and Its Application to Rapid Positioning Using Single Frequency GPS Receivers

ARCE (ambiguity resolution using constraint equation) is a new method for resolving the integer ambiguities based on LSE (least-squares estimate) and null space. In this paper, ARCE is improved for the case that the observation time span is short and there are only a few epoch observations. The normal matrix is badly ill-conditioned in GPS rapid positioning if the observation epochs are fewer, which causes the result of LSE unreliable. In this instance, it is difficult to fix the integer ambiguities correctly using ARCE. On the basis of TIKHONOV regularization theorem, a new regularizer is designed to mitigate the ill-condition of the normal matrix. The accurate float ambiguity solutions are obtained and the search range of the integer ambiguities decreases greatly. Then, the integer ambiguities are fixed for reference of ARCE theorem and the success rate of fixing the integer ambiguities is high.