A mixed-integer least-squares formulation of the GNSS snapshot positioning problem

Eyal Waserman, Sivan Toledo*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper presents a formulation of snapshot positioning as a mixed-integer least-squares problem. In snapshot positioning, one estimates a position from code-phase (and possibly Doppler-shift) observations of global navigation satellite system (GNSS) signals without knowing the time of departure (timestamp) of the codes. Solving the problem allows a receiver to determine a fix from short radio-frequency snapshots missing the timestamp information embedded in the GNSS data stream. This is used to reduce the time to first fix in some receivers, and it is used in certain wildlife trackers. This paper presents two new formulations of the problem and an algorithm that solves the resulting mixed-integer least-squares problems. We also show that the new formulations can produce fixes even with huge initial errors, much larger than permitted in Van Diggelen's widely-cited coarse-time navigation method.

Original languageEnglish
Pages (from-to)1267-1283
Number of pages17
JournalJournal of Navigation
Issue number6
StatePublished - 26 Nov 2021


FundersFunder number
Israel Science Foundation


    • Doppler
    • GNSS
    • integer ambiguity resolution
    • satellite navigation


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