Robust Modeling of Geodetic Altitude from Barometric Altimeter and Weather Data

Vertical navigation is crucial for safe aircraft separation, which have been traditionally based on flight altitude levels. This altitude information is normally called standard pressure altitude since it is computed from airborne pressure measurements performed by barometers and is referenced to the International Standard Atmosphere (ISA) Mean Sea Level (MSL) isobar surface. On the other hand, robust geodetic altitude navigation is fundamental for airport nearness operations with tighter requirements and plays a key role for new applications like Urban Air Mobility (UAM). However, the deviations of standard pressure altitude from true geodetic altitude can reach up to several hundreds of meters and therefore its application is limited to relative vertical navigation. The barometric measurements can nevertheless still be used to determine geodetic altitude if additional weather information like pressure and temperature is available and some transformations are applied. This paper first presents a methodology to compute geodetic altitude from a corrected pressure altitude obtained with airborne pressure measurements and external weather data. Flight data is used to assess the achievable geodetic altitude accuracy from 20 flight hours with the German Aerospace Center (DLR) Dassault Falcon 20-ES aircraft. Second, one linear model is derived to mitigate residual errors that dependent on flight dynamics. Finally, and based on the available flight data, first robust stochastic error models are proposed to support the adoption of barometric pressure measurements for safe geodetic altitude navigation. In particular, two models are derived. The first one provides a Gaussian overbound for the computed geodetic altitude so that it can be used either directly as altitude information or in combination with other sensors in snapshot (e.g., least-squares) estimators. The second is a dynamic model that bounds the power spectral density of the error with a first-order Gauss Markov process. In this way this model can be easily incorporated in a sequential estimator, like a Kalman filter, and in combination with other sensors.