This report cicals with the problcm of determining the trajectory of a spacecraft from on-board optical measurents without a priori information. Only sufficient information to determine the trajectory is used, and it is assumed that this preliminary estimate will be improved later by the use of differential corrections and redundant data. Five basic types of measurements, representing instruments considered feasible or within the state of the art, are considered. The effects of random and bias type measurement errors and interpolation errors arising from nonsimultaneous measurements are analyzed. Only observations of the central body and two stars are considered. Within certain limitations all five types of measurements will give satisfactory results. Two important factors discussed in the report are the proper choice of stars and the calibration for eliminating bias errors.