As part of the Thinking Telescopes project, a long-term Space Situational Awareness effort at the Los Alamos National Laboratory, we developed efficient algorithms for detecting and localizing unresolved moving sources in wide-field astronomical images. Our approach is based on pixel-by-pixel differencing of two images after one image has been convolved to match the point spread function of the other. The input images are obtained with the telescope tracking at the sidereal rate, and therefore stars are imaged as point sources and moving objects streak. The algorithm first identifies islands of connected pixels above a significance threshold in difference images where static sources have been removed. The next step is line detection and fitting light profiles of streaked sources using empirical models. he main objective is to optimize the accuracy of the measured streak end points while keeping the required computation reasonably fast. To this end we apply a series of progressively more sophisticated estimators until the result is no longer improved due to noise limitations. The final astrometry for sufficiently bright streaks takes into account the local point spread function for a particular location within the wide -field image. We found efficient 1D and 2D algorithms for fitting models of moving point sources (infinitely thin lines convolved with the point spread function). The 2D algorithm based on the iterative locally linearized fit parameterized with sub-pixel locations of both ends provides up to an order of magnitude improvement in accuracy over the 1D algorithm by removing the bias in the orientation of the streak. Other advantages of the new approach include: the ability to accurately measure very short streaks, much better sensitivity for faint objects, better convergence (after about two iterations), and eliminating the need for interpolation of the original image and 1D projection. These algorithms have been tested on real and simulated ground-based images of Earth satellites. They are robust and have a potential to significantly improve the utility of cost-effective space surveillance systems that rely on commodity imaging and computing hardware.