Multi-pass phase-differential GNSS ambiguity fixing for post-processing applications

Traditional parameter estimation like Kalman filtering is mostly based on the assumption that all states/parameters and observations are defined in continuous multi-dimensional space. GNSS ambiguity fixing however is breaking this assumption: the previously float ambiguity estimates are fixed to integer values, for example using the integer-least-squares method. Furthermore, the error of an ambiguity fix is essentially binary: the fix is correct, or not, it is usually of little interest how incorrect a bad fix is. Similarly, outliers of raw GNSS observations are commonly flagged, or not flagged, based on some predefined threshold – also breaking the continuity assumption. The traditional Extended Kalman Filter (EKF) framework in combination with RTS smoothing (also called Kalman smoothing) may therefore fail to produce optimal results, even in the absence of (significant) linearization errors. On the other hand, once a correct fix is successfully established after some convergence time, this is obviously information that should be made available to epochs in the past: as long as a satellite is continuously tracked by the receiver without any loss-of-lock or cycle slip, the ambiguity must always be constant by definition. Therefore, a newly established ambiguity fix not only applies to the upcoming epochs, but also to those epochs of the convergence phase before the fix.In this paper, we present results from a GNSS test data evaluation using iMAR’s post-processing software suite iPosCal-SURV. The test data set consists of a large variety of kinematic scenarios, including very challenging urban canyons. A Kalman Filter is embedded into an iterative process that walks over the entire multi-GNSS multi-base data set iteratively, using multiple passes. An ambiguity memory is used in order to make double-differenced ambiguity fix information available to the upcoming passes. Consider for example three passes: forward-reverse-forward. The second (reverse) pass can use the entire fixing information of the first pass, which will in general allow additional fixes during the second pass. The third pass can then use all the accumulated fixing information of the first two passes, enabling even more successful ambiguity fixes. Real-world examples indicate, that the fixing rate may even benefit from using six or more passes, in particular under very challenging GNSS conditions. Results are shown for both GNSS-only processing, and the tightly-coupled integration of GNSS and a navigation-grade IMU.