Combined difference square observation-based ambiguity determination for ground-based positioning system

Abstract

In the absence of a global navigation satellite system, a ground-based positioning system can provide stand-alone positioning service and has advantages in layout flexibility of terrestrial base stations that broadcast ranging signals. To realize precise point positioning (PPP) in ground-based positioning systems, the carrier phase ambiguity must be determined for the receiver. On-the-fly (OTF) ambiguity determination methods are desirable for their convenience in practice. In most existing OTF methods based on the initial position estimate obtained from code measurements or other measuring instruments, the nonlinear term representing true distances are linearized by a series expansion. However, due to the severe nonlinear effects, if the accuracy of the initial position estimate is relatively poor, such linearization will result in large errors and convergence difficulties. Moreover, the more accurate initial estimate a method requires, the more inconvenient it will be. To avoid the dependence on the initial estimate, we proposed a combined difference square (CDS) observation and it provides a framework to eliminate the nonlinear terms in the difference square observations by linear combination. Based on this, a rotational-symmetry CDS (RS-CDS) observation-based ambiguity determination method is proposed, which needs no a priori information or reliable code measurements and is especially suitable for dynamic applications. In addition, it does not require accurate time synchronization of base stations, making the deployment of the overall system easier. The numerical simulations show that geometry diversity effectively improves the performance of ambiguity determination. Two real-world experiments indicate that the proposed method enables PPP for ground-based positioning systems without accurate time synchronization.