A New Approach for Modeling Correlated Gaussian Errors using Frequency Domain Overbounding

Abstract

This paper presents a new method to overbound Kalman filter (KF) based estimate error distributions in the presence of uncertain, time-correlated noise. Each noise component is a zero-mean Gaussian random process whose autocorrelation sequence (ACS) is stationary over the filtering duration. We show that the KF covariance matrix overbounds the estimate error distribution when the noise models overbound the Fourier transform of a windowed version of the ACS. The method is evaluated using covariance analysis for an example application in GPS-based relative position estimation.