A Mixed Integer Least-Squares Formulation of the GNSS Snapshot Positioning Problem

TL;DR

This paper formulates the GNSS snapshot positioning problem as a mixed-integer least-squares problem, enabling rapid position fixes from short radio-frequency snapshots without time-stamp data, improving initial fix robustness.

Contribution

It introduces two novel formulations and an algorithm for solving the mixed-integer least-squares problem in GNSS snapshot positioning, enhancing accuracy and robustness.

Findings

Can produce fixes with large initial errors

Reduces time to first fix in GNSS receivers

Applicable to wildlife tracking and rapid positioning

Abstract

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 observations of a Global Navigation Satellite Systems (GNSS) 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 time-stamp information embedded in the GNSS data stream. This is used to reduced 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.