GMP-Overbound Parameter Determination for Measurement Error Time Correlation Modeling

Sandeep K. Jada and Mathieu Joerger

Abstract: In this paper, we develop a new method to determine parameter values for high-integrity models of measurement error time correlation. The method builds upon prior research on error correlation modeling, where an upper bound on the estimation error variance is derived given limits on the measurement error variance and correlation time constant. In this paper, we provide the means to derive these limits from experimental data. First, rather than working with autocorrelation functions, we consider “lagged products,” which are products of samples taken at different times in a data sequence: we derive a closed form expression of the lagged products probability density function for first order Gauss Markov Processes (FOGMP). These FOGMP models are then used to bound the sample cumulative distribution function (CDF), thereby providing bounds on the mean sample time correlation while accounting for all sample quantiles at all lag times. We illustrate and analyze this approach using simulated and experimental data, and show that it applies even with sparse, unknown (non-GMP) time-correlated data.
Published in: Proceedings of the 2020 International Technical Meeting of The Institute of Navigation
January 21 - 24, 2020
Hyatt Regency Mission Bay
San Diego, California
Pages: 189 - 206
Cite this article: Jada, Sandeep K., Joerger, Mathieu, "GMP-Overbound Parameter Determination for Measurement Error Time Correlation Modeling," Proceedings of the 2020 International Technical Meeting of The Institute of Navigation, San Diego, California, January 2020, pp. 189-206.
https://doi.org/10.33012/2020.17137
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