1. Figure 3. Radial error distribution for the brightest star of a FOV with a fit shown in red (R2= 0:990) computed from the standard deviation of the distribution. matching algorithm is used due to its simplicity and effectiveness for large FOVs. The reference catalog is constructed as described by Houtz and Frueh.11First, the Yale Bright Star Catalog version 5 is loaded, which gives right ascension and declination for stars above magnitude 6.5 in J2000 coordinates along with other information. Right ascension and declination are converted to Cartesian coordinate unit vectors, with the x-axis pointing to the vernal equinox and the z-axis pointing to equatorial North. The Yale Bright Star Catalog contains binary stars as separate entries as well as several diffuse objects. Diffuse objects are eliminated, as are the dimmer members of pairs of stars whose unit vectors are less than 0:25◦apart. The visual magnitudes of the stars are also recorded. The exact visual magnitudes are not important, however. The visual magnitudes are used to order the stars’ unit vectors from brightest to dimmest. Then, based on the (rectangular) FOV for which the catalog is to be generated, the entire celestial sphere is scanned and virtually every possible FOV is evaluated. The process is to incrementally select a finite number of image centers and analytically evaluate all possible FOVs at those centers. The three brightest stars appearing in each image are placed in the catalog (duplicates are ignored). Due to the incremental nature of this technique, it is possible to miss some triangles, but the issue is easily fixed by limiting the size of each selected triangle such that the smallest circle on the unit sphere that contains all three indices of the triangle is smaller than a certain diameter. This diameter d is calculated as
2. The estimated pixel location of the ithstar in the image is related to the unit vector to this star expressed in the body frame,i~[i;xi;yi;z]T,accordingto