Practical Considerations in PSD Upper Bounding of Experimental Data

Abstract

In this paper, we develop a methodology to estimate the power spectrum of an experimentally-obtained data set for high-integrity modeling of Kalman filter (KF) input noise time correlation. In theory, power spectral density (PSD) upper-bounding can be used to determine time-correlated error models that guarantee bounds on the estimation error variance in recursive navigation algorithms such as KFs. This assumes that an empirical PSD is given. In practice, there is more than one way to determine a PSD from data. This PSD estimate depends on the number of samples in the data set, on the windowing process, and on the PSD frequency resolution. These parameters have an impact on the robustness of the PSD-upper-bounding model. In this paper, we analyze error model sensitivity to these parameters for example simulated random processes and for a one-year-long time-series of GPS orbit and clock ephemeris errors.