Stochastic Modeling of Gravity Compensation Error in GNSS-Aided Inertial Navigation Systems

GNSS-aided inertial navigation systems (INS) are used in a variety of aerospace applications as robust sources of position, velocity, attitude, and time. Due to the safety-critical nature of civil aviation applications, navigation systems must be rigorously tested to ensure they will not output hazardously misleading information (HMI). RTCA, a standards-making organization, develops documents containing requirements and testing guidance for manufacturers of equipment installed on aircraft. RTCA Special Committee 159 has organized a working group (WG-2C) to develop a new Minimum Operational Performance Standard (MOPS) that addresses GNSS-aided INS. The new MOPS will accommodate a wide performance range of inertial sensors (e.g., tactical as well as navigation grade), and it will cover accuracy and integrity coasting performance during GNSS outages. As part of the focus on coasting performance during GNSS outages, WG-2C is investigating the effects of gravity modeling error on the aided-inertial solution. The portion of gravity deflection not accounted for in the navigation system by a model or database results in horizontal acceleration error that integrates to become velocity and position error. Previous research by the authors [1] has shown that unmodeled gravity deflections can induce up to 200 meters of position error, which is a non-negligible portion of an RNP 0.3 or less lane-width. Additional work by the authors [2] showed that even if a worldwide high fidelity model such as EGM2008 is used, the commission and omission errors of the model still remain in the acceleration estimates after compensation. This paper first presents deflection of the vertical (DOV) profiles for real RNP airport approaches to demonstrate realistic severe situations for GNSS-coasting. Next, low and high order gravity models are implemented and the statistics of the residuals are studied. Finally, system identification techniques are used to analyze the gravity model residuals and develop stochastic processes that are statistically representative of these residuals. Second-order autoregressive models are identified, and model parameters are dynamically drawn from the numerically derived statistical distributions to account for the non-stationary nature of the residuals.