Cycle Slip repair for single-frequency smartphone GNSS using the Best Integer Equivariant estimator

This paper proposes an instantaneous cycle slip repair method for single-frequency smartphone GNSS carrier phase measurements. In it, cycle slips are detected using a hybrid method that combines geometry-based and geometry-free cycle slip detection paradigms. A float value of the cycle slip is estimated after a Kalman filter (KF) update, and a cycle-slip repair is attempted as a form of integer ambiguity resolution problem using five different classes of estimators: (i) Integer Least Squares (ILS), (ii) Best Integer Equivariant (BIE) estimator (iii) Integer Aperture with Fixed Failure-rate Ratio Test (IA-FFRT) (iv) Partial Ambiguity Resolution (PAR) and (v) PAR with FF-RT. The PAR with FF-RT estimator uses a model-driven ratio test to select the subset of ambiguities chosen to be fixed. The performance of all five estimators is compared and analyzed using real smartphone GNSS carrier phase measurements. The variance of the fixed/repaired cycle slips is estimated. BIE and PAR-FFRT are the top-performing estimators, with PAR-FFRT offering the greatest precision improvement after repairing the float cycle slip ambiguities. BIE, on the other hand, has a 100% repair rate without the need for validation testing.