Gravity Model Error Considerations for High-Integrity GNSS-aided INS Operations
Timothy G. Needham and Michael S. Braasch, Ohio University
Location: Big Sur
GNSS-aided inertial systems are typically used to achieve accurate and reliable position, velocity, and attitude estimates in a wide variety of aerospace applications. When utilized in a safety-critical operation such as civil aviation, every potential error source must be characterized for its potential contribution to hazardously misleading information. The standards-making body, RTCA, facilitates working groups that develop requirements and test criteria in the form of Minimum Operational Performance Standards (MOPS). Existing standards address the usage of navigation grade inertial units in long-range operations such as oceanic flight. Currently, RTCA SC-159 WG-2C is developing a new MOPS that, in addition to addressing a wider range of inertial units, will also address coasting during GNSS outages to increase continuity in operations such as non-precision approach. As part of this effort, the effect of gravity mis-modeling on the navigation system during short-term GNSS outages is being investigated from a certification perspective.
The performance of safety-critical systems during periods of GNSS unavailability is becoming increasingly important as the potential for GNSS interference also increases. For certification purposes, the navigation system must be properly stressed/tested using realistic worst case scenarios. Previous gravity modeling work by the authors  demonstrated that large gradients in the deflection of the vertical (DOV) can lead to horizontal position errors that are a significant fraction of an RNP 0.3 lane width. This paper extends the previous work in two main areas: a) global analysis of DOV magnitude and gradient; and b) statistical characterization of low, medium and high-order gravity model performance.
The Earth Gravitational Model 2008 (EGM2008) produced by the National Geospatial-Intelligence Agency provides the highest fidelity publicly available global model of the geoid complete to degree and order 2159 (by contrast, the previous standard, EGM96, was complete only to degree order 360). In this paper EGM2008 is used to generate global DOV contour plots focused specifically on the high-integrity civil aviation application. Unlike most DOV analyses that concentrate on two or three-sigma statistics, the current analysis focuses on the rare cases of large DOV magnitudes and gradients. Unlike noise analyses, these cases of large DOV are tied to physical locations on or above the earth. A given user will encounter these worst cases every time they pass through (or attempt to land at) these locations.
In addition to analyzing worldwide DOV’s, gravity model performance is examined. Specifically, the EGM2008 model is analyzed in terms of commission and omission errors . Commission error is the error due to the use of imperfect measurement data, and omission error is the error due to finite resolution. EGM2008 provides estimates of its commission error, but these estimates have not been analyzed from the aforementioned perspective of civil aviation. This paper analyzes and describes the regions where the model is known to be less accurate thus potentially requiring increased restrictions on safety-critical operations. The paper also presents an analysis that provides reasonable bounds on the magnitude and frequency of omission error in the model.
For users implementing low or medium-order models (due to constraints including computational complexity and/or IMU performance), this paper presents the statistics of the gravity model error both for typical/benign and rare DOV cases. Statistical models are derived that users may implement in an aiding filter to account for the gravity model error.
Finally, this paper presents methodologies for testing gravity models in GNSS-aided inertial systems. Both deterministic and statistical testing methods are described and compared. The results of this work are intended to help manufacturers and regulators understand the impact of gravity mis-modeling and testing considerations for safety-certification.
 Needham, T. and M. Braasch, “Impact of Gravity Modeling Error on Integrated GNSS/INS Coasting Performance,” AIAA/IEEE Digital Avionics Systems Conference (DASC), St. Petersburg, FL, Sept 2017.
 Pavlis, N., Holmes, S., Kenyon, S. and J. Factor, “The Development and Evaluation of the Earth Gravitational Model 2008 (EGM2008),” Journal of Geophysical Research: Solid Earth (1978-2012), Volume 117, Issue B4, April 2012.