A New Approach for Modeling Correlated Gaussian Errors using Frequency Domain Overbounding
Steven Langel, Omar García Crespillo, Mathieu Joerger
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.
Topics & Concepts
Kalman filterCovarianceGaussian noiseNoise (video)AlgorithmCovariance matrixAutocorrelationFrequency domainComputer scienceCovariance functionMathematicsGaussian processCovariance intersectionGaussianStatisticsArtificial intelligencePhysicsMathematical analysisQuantum mechanicsImage (mathematics)Target Tracking and Data Fusion in Sensor NetworksGNSS positioning and interferenceInertial Sensor and Navigation