Cycle Slip Repair for Single-Frequency Smartphone GNSS Using the Best Integer Equivariant Estimator

Naman Agarwal and Kyle O'Keefe

Peer Reviewed

Abstract:	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. Keywords— cycle slip, smartphone, GNSS, Kalman Filter, BIE, PAR
Published in:	2025 IEEE/ION Position, Location and Navigation Symposium (PLANS) April 28 - 1, 2025 Salt Lake Marriott Downtown at City Creek Salt Lake City, UT
Pages:	1536 - 1543
Cite this article:	Agarwal, Naman, O'Keefe, Kyle, "Cycle Slip Repair for Single-Frequency Smartphone GNSS Using the Best Integer Equivariant Estimator," 2025 IEEE/ION Position, Location and Navigation Symposium (PLANS), Salt Lake City, UT, April 2025, pp. 1536-1543.
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