Single-frequency GNSS cycle slip estimation with positional polynomial constraint

Single-frequency GNSS RTK is a promising technology in the popularization application due to its relative low expense compared to multi-frequency RTK. Owing to the incapability of forming between-frequency combination and the relatively poor quality of single-frequency receivers, particularly for low-cost receivers, the cycle slip estimation in single frequency is a significant challenge. We propose a new efficient method for real-time single-frequency cycle slip estimation by imposing position-based polynomial constraint based on a fact that the motion of vehicle often obeys a low-order polynomial over a short period. The key is to precisely model the motion kinematics by means of a low-order polynomial fitting of several historical epochs. With the constraint of positional polynomial, the estimation of cycle slips can be significantly improved. To evaluate the feasibility and reliability of this method, a variety of cycle slip situations are tested by comparing with two traditional methods, i.e., the measurement-based polynomial fitting and the triple-differenced residual-based method. The results show that the new method can achieve better results than two traditional methods.