Multi-Process Stochastic Error Models for DFMC GBAS Carrier Smoothed Code Processing and Preliminary Airborne Results

Gary A. McGraw, Maria Caamano

Abstract:	Carrier phase (CP) smoothing of code pseudorange (PR) measurements is an important means to mitigate PR noise and multipath, especially for high-accuracy Global Navigation Satellite Systems (GNSS) precision approach and landing applications like Ground-Based Augmentation Systems (GBAS) and Space-Based Augmentation Systems (SBAS). Traditionally, statistical error bounding of smoothed PR errors has been done assuming that carrier smoothed code (CSC) filters are in steady-state conditions. With emerging dual frequency multi-constellation (DFMC) applications, such as the proposed GBAS approach service type E (GAST-E), it is desirable to be able to statistically bound the smoothed error throughout CSC filter convergence. Building on recent developments in error bounding of correlated error sources in integrated navigation applications, this paper proposes the use of Gauss-Markov processes for modeling multipath and other correlated errors in CSC processing along with white noise and random bias terms. The paper provides a general theoretical development of this approach and then looks at specific examples for root-mean-square (RMS) over-bounding of airborne DFMC GBAS measurements obtained from flight test campaigns on different air transport class aircraft. Results for two model sets are shown: a “three-term model” consisting of a single first-order Gauss-Markov (FOGM) process along with bias and noise components and a “four-term model” with two FOGM processes plus bias and noise components. The four-term error model is able to provide a significantly less conservative RMS over-bound to the observed CSC errors during both filter convergence and steady-state conditions. These results demonstrate the feasibility of using linear stochastic models for statistical error bounding of airborne GNSS errors although the final form of the model and associated parameters to incorporate into future standards will require further validation efforts.
Published in:	Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025) September 8 - 12, 2025 Hilton Baltimore Inner Harbor Baltimore, Maryland
Pages:	158 - 177
Cite this article:	McGraw, Gary A., Caamano, Maria, "Multi-Process Stochastic Error Models for DFMC GBAS Carrier Smoothed Code Processing and Preliminary Airborne Results," Proceedings of the 38th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2025), Baltimore, Maryland, September 2025, pp. 158-177. https://doi.org/10.33012/2025.20266
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In