Astrometric Calibration and Estimate of the Systematic Error in WXM Localizations Obtained by the Chicago Bayesian Method

WXM gives GRB localizations in instrument coordinates. WXM localizations must be converted to celestial coordinates using spacecraft aspect information obtained by the optical cameras on HETE. We must therefore accurately determine the alignment of the WXM boresight with respect to that of the optical cameras, in order to accurately determine the celestial coordinates of WXM burst locations. We use a seven-parameter model that treats as free parameters the three Euler angles of a pure rotation, two horizontal shifts of the coded-aperture masks with respect to the detectors, and the heights of the masks above the two detectors. We determine the alignment by fitting the model to a set of 252 WXM localizations of Sco X-1 obtained between 23 April and 28 June 2001. We estimate the systematic error in WXM GRB locations by comparing the actual and the calculated locations of Sco X-1. We find that the systematic error corresponding to a 68.3% confidence region is 1.7$'$, and the systematic error corresponding to a 90% confidence region is 2.4$'$. We find that this astrometric solution also provides a satisfactory fit to an independent sample of SGR and XRB events. These results are consistent with the astrometric calibration and the systematic error in WXM localizations derived independently using the RIKEN localization method.