Measurement Error Time-Correlation Modeling for Safety-Critical Navigation

In this paper, we develop and evaluate two new methods to derive high-integrity models of measurement error time correlation from experimental data. These models enable the determination of sequential estimation error variance bounds in safety-critical navigation applications such as aircraft localization based on global navigation satellite systems and inertial navigation systems. We achieve tight bounding models from empirical data based on lagged product distributions instead of autocorrelation functions in the time domain and based on scaled periodogram distributions instead of power spectra in the frequency domain. We bound these distributions using first-order Gauss–Markov process (FOGMP) models, which provide a means to account for error time correlation and can be easily incorporated in linear estimators. To determine bounding models, we identify theoretical probability density functions of lagged products and derive the cumulative distribution function of scaled periodograms for FOGMPs. We implement and evaluate these two methods using simulated samples and experimental Global Positioning System data collected in a mild multipath environment.