Once calculated, it is the distribution of this statistic that provides insight on the accuracy of the covariance.For the EKF to correctly calculate the covariance, error models associated with tracking data measurements must be accurately tuned. The Chi-square statistic is calculated to determine the realism of a covariance based on the prediction accuracy and the covariance values at a given point in time. It is also valuable when attempting to determine if the current orbital solution will meet mission requirements in the future.This paper examines the use of the Chi-square statistic as a means of evaluating filter performance. An accurate covariance is also useful for covariance propagation which is utilized in collision avoidance operations. This covariance can be useful for evaluating the overall performance of the tracking data measurements and the filter itself.

It also generates a covariance at each measurement. The filter incorporates force modelling, ground station and space network measurements to determine spacecraft states. This software uses an Extended Kalman Filter (EKF) to estimate the states of both spacecraft. The FDF has recently been tasked with delivering definitive covariance for each satellite.The main source of orbit determination used for these missions is the Orbit Determination Toolkit developed by Analytical Graphics Inc.

Both spacecraft are currently in the science phase of their respective missions. Both satellites are located in low Earth orbit (LEO), and are part of what is considered the A-Train satellite constellation. The Goddard Space Flight Center (GSFC) Flight Dynamics Facility (FDF) performs orbit determination (OD) for the Aqua and Aura satellites.

Under mild moment conditions, the limit is Gaussian for Î» = âˆž, Poisson for finite Î» > 0, and degenerate for Î» = 0.įilter Tuning Using the Chi-Squared Statistic Dataâ€¦ĭouble asymptotics for the chi-square statistic.Ĭonsider distributional limit of the Pearson chi-square statistic when the number of classes m n increases with the sample size n and. Four approaches were evaluated: calculating residuals, comparing cells, ransacking, and partitioning. This paper addresses the question of how one should follow a statistically significant chi-square test result in order to determine the source of that result. Your Chi-Square Test Is Statistically Significant: Now What?Īpplied researchers have employed chi-square tests for more than one hundred years.

Geogebra statistik histogram