Error statistics of asteroid optical astrometric observations

Astrometric uncertainty is a crucial component of the asteroid orbit determination process. However, in the absence of rigorous uncertainty information, only very crude weighting schemes are available to the orbit computer. This inevitably leads to a correspondingly crude characterization of the orbital uncertainty and in many cases to less accurate orbits. In this paper we describe a method for carefully assessing the statistical performance of the various observatories that have produced asteroid astrometry, with the ultimate goal of using this statistical characterization to improve asteroid orbit determination. We also include a detailed description of our previously unpublished automatic outlier rejection algorithm used in the orbit determination, which is an important component of the fitting process. To start this study we have determined the best fitting orbits for the first 17,349 numbered asteroids and computed the corresponding O-C astrometric residuals for all observations used in the orbit fitting. We group the residuals into roughly homogeneous bins and compute the root mean square (RMS) error and bias in declination and right ascension for each bin. Results are tabulated for each of the 77 bins containing more than 3000 observations; this comprises roughly two thirds of the data, but only 2% of the bins. There are several interesting results, including substantial bias from several observatories, and some distinct non-Gaussian characteristics that are difficult to explain. Several limitations of our approach and possible future improvements are discussed. The correlation of errors among observations taken closely together in time is in many cases an important issue that has rarely been considered. We have computed the mean correlation between observations with varying time separations and obtained empirical functions that model the results. This has been done for several observatories with very large data sets (the remainder has been lumped into a single mixed batch). These functions could be used for estimating correlation coefficients among different observations of the same observatory, supplying a new observation weighting scheme based upon an empirically tested observational error model. (C) 2003 Elsevier Inc. All rights reserved.