On-the-fly ambiguity resolution involving only carrier phase measurements for stand-alone ground-based positioning systems

Despite the wide use of the global navigation satellite system (GNSS), its performance can be severely degraded due to blockage and vulnerability to interference. Stand-alone ground-based positioning systems can provide positioning services in the absence of GNSS signals and have tremendous application potential. For precise point positioning in ground-based systems, ambiguity resolution (AR) is a key issue. On-the-fly (OTF) AR methods are desirable for reasons of convenience. The existing methods usually linearize a nonlinear problem approximately by a series expansion that is based on an initial position estimation obtained by code measurements or measuring instruments. However, if the initial position estimation contains relatively large errors, the convergence of existing methods cannot be ensured. We present a new OTF-AR method based on the double difference square (DDS) observation model for ground-based precise point positioning, which involves only carrier phase measurements. The initial solution obtained from the DDS model is sufficiently accurate to obtain a float solution by linearization, and this step only requires the frequency synchronization of base stations. Further, if the clock differences of the base stations are accurately calibrated, a fixed solution can be obtained by employing the LAMBDA algorithm. Numerical simulations and a real-world experiment are conducted to validate the proposed method. Both the simulations and the experimental results show that the proposed method can achieve high-accuracy positioning. These results enable precise point positioning to be applied in situations where no reliable code measurements or other measuring instruments are available for stand-alone ground-based positioning systems.