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This paper describes a method for utilizing reflected Global Positioning System (GPS) signals to form an image of targets within a region of interest. The principle is based upon a type of bi-static synthetic aperture radar (SAR) in which a matched filter technique is employed to perform the image reconstruction. This method relies upon the fact that each component of the received signal resulting from a reflection from an individual target is subjected to a unique chirp. A major challenge to be tackled is the appalling signal to noise ratio associated with the received reflected GPS signals. Another difficulty is the masking of the reflected signals by power in the tails of the autocorrelation function of the direct signals which cannot be totally suppressed. Moreover, the reconstruction method results in an undesirable point spread function (PSF) which seriously smears the reconstructed image. We simulate the entire GPS signal generation and image reconstruction process as faithfully as possible within the limitations of the available computational effort. We are able to demonstrate that a spatial resolution of the order of the LI wavelength (19 cm) is theoretically possible from realistic observation distances provided that sufficient coherent correlator integration time is allowed and that the direct signals can be sufficiently suppressed. For the rather simplified organization of targets within the simulation we are able to show that the image smeared by the PSF is able to be cleaned by means of a Wiener filter based deconvolution method.