TY - JOUR
T1 - A mixed-integer least-squares formulation of the GNSS snapshot positioning problem
AU - Waserman, Eyal
AU - Toledo, Sivan
N1 - Publisher Copyright:
Copyright © 2021 The Author(s). Published by Cambridge University Press on behalf of The Royal Institute of Navigation..
PY - 2021/11/26
Y1 - 2021/11/26
N2 - 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.
AB - 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.
KW - Doppler
KW - GNSS
KW - integer ambiguity resolution
KW - satellite navigation
UR - http://www.scopus.com/inward/record.url?scp=85114324150&partnerID=8YFLogxK
U2 - 10.1017/S0373463321000709
DO - 10.1017/S0373463321000709
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AN - SCOPUS:85114324150
SN - 0373-4633
VL - 74
SP - 1267
EP - 1283
JO - Journal of Navigation
JF - Journal of Navigation
IS - 6
ER -