Exploiting Satellite Motion in ARAIM: Measurement Error Model Refinement Using Experimental Data

Abstract

In this work, a new time-sequential positioning and fault detection method is derived and analyzed for dualfrequency, multi-constellation Advanced Receiver Autonomous Integrity Monitoring (ARAIM). Unlike conventional 'snapshot' ARAIM, the sequential approach exploits changes in satellite geometry at the cost of slightly higher computation and memory loads. From the perspective of users on earth, the motion of any given GNSS satellite is small over short time intervals. But, the accumulated effect geometry variations of redundant satellites from multiple GNSS constellations can be substantial. This paper quantifies the potential performance benefit brought by satellite motion to ARAIM. It specifically addresses the following research challenges: (a) defining and experimentally validating raw GNSS code and carrier error models over time, consistent with established ARAIM assumptions, (b) designing estimators and fault-detectors capable of exploiting satellite motion for positioning, carrier phase cycle ambiguity estimation, and integrity evaluation, and (c) formulating these processes in a computationally-efficient implementation. A modular algorithm is designed, only requiring a minor augmentation of the snapshot airborne ARAIM multiple hypothesis solution separation (MHSS) algorithm. Other modifications to enable time-sequential ARAIM include additional ground segment performance commitments, and the inclusion of extra parameters in the broadcast integrity support message (ISM). Availability is analyzed worldwide for aircraft precision approach navigation applications. Results show substantial performance improvements for sequential ARAIM over snapshot ARAIM, not only to achieve 'localizer precision vertical' (LPV) requirements using depleted GPS and Galileo constellations, but also to fulfill much more stringent requirements including a ten-meter vertical alert limit.

Bounding Sequential Estimation Errors Due to Gauss-Markov Noise with Uncertain Parameters

“…However, when nominal GPS and Galileo constellations are depleted, LPV-200 can only be sparsely achieved using snapshot ARAIM [14]. 'Batch-ARAIM' addresses this limitation by processing measurements over time [3,4,15] using a sliding-window mechanism. One major challenge in batch ARAIM is to derive robust models of measurement errors over time.…”

“…One major challenge in batch ARAIM is to derive robust models of measurement errors over time. In prior work [4,15], a 'bias-plus-ramp' model was derived for satellite clock and orbit error dynamics using nine months of data. In parallel, assumptions were made on the time correlation of tropospheric and multipath errors.…”

“…In parallel, assumptions were made on the time correlation of tropospheric and multipath errors. Because no method was available to account for uncertainty in correlation time constants, the largest measured value was employed for multipath, and sensitivity to residual tropospheric delay was analyzed [3,4,15]. But multipath time constants can take a wide range of values as reported in Figures 21-22 of [5].…”

“…A specific example where recursive filtering is being explored is Vertical ARAIM, or V-ARAIM, which seeks to provide worldwide vertical guidance of aircraft using dual-frequency measurements from multiple GNSS constellations. It was shown recently that V-ARAIM performance can be improved significantly by processing time-sequences of measurements [3,4]. A major challenge with sequential estimation is how to conservatively account for time-correlated noise like GPS multipath.…”

Fault-Free Integrity Analysis of Mega-Constellation-Augmented GNSS

“…In this work, we focus on estimating the user position, clock bias, and cycle ambiguities using a batch weighted least squares (WLS) approach. This method can be implemented sequentially in a sliding window mechanism, and will leverage fault detection algorithms in future work [44,45,46].…”