Single Frequency GNSS Carrier Phase Cycle Slip Detection and Identification Using a Factor Graph Approach

Precise and robust GNSS positioning with low-cost receivers is a challenge, as these receivers will often be disturbed by biased observations due to a given environment, for example by code pseudoranges with multipath. One way to reach centimeter positioning accuracy is by using very precise observations, in particular by using GNSS carrier phase measurements. These carrier phase measurements can be very precise (under centimeter standard deviation) but they contain an unknown, the phase ambiguity. Throughout time, for a tracked satellite during multiple epochs, this phase ambiguity is supposed to remain constant. So by building an observation model containing observations from multiple epochs, we can take advantage of this information. This is what is usually done in a discrete-time Kalman filter: we estimate the ambiguity of each satellite, and we model this ambiguity to be constant in the state transition model. However, in practice, cycle slips happen. If we suppose that the ambiguity is constant, then the positioning algorithms solutions will be degraded when cycle slips happen. This work uses factor graph optimization in order to detect and identify cycle slips on GNSS carrier phase observations from a single frequency receiver. This is done in a two-step process. It starts with a theoretical and very general approach to detect faults on measurements, as a binary decision. This is done with a theoretical distribution of a residual-based statistic (difference between observation models and measurements), and a comparison of the observed statistic with its theoretical distribution. In the case of detected fault, then comes step two of the process: by building multiple models and an optimization problem over a finite and discrete set of hypotheses, we are able to identify the observation where a fault was introduced. Following this theoretical approach to detect and identify faults, factor graph optimization is introduced. This is the strength of our approach: we are able to apply the procedure of detection and identification of faults for any factor graph, i.e., for any set of observations and states to estimate. Finally, the detection method is implemented in a GNSS simulator. We build a factor graph that estimates a receiver position from multiple carrier phase measurements. We apply the detection method to detect cycle slips on phase measurements. We show that, depending on the duration of the observation window, our detection method works for very small cycle slips, of one wavelength. We also compare Monte-Carlo simulations against theoretical probabilities of detection.