On-orbit servicing missions in geostationary orbit with intersatellite separations less than 1 km pose a problem for ground-based electro-optical space surveillance sensors. The close separations between the objects subtend angles comparable to the size of turbulence (seeing) cells of Earth's atmosphere. Speckle interferometry using a cross-spectrum approach was explored as a means to overcome atmospheric turbulence to enable measurement of relative positions of on-orbit servicing satellites without the use of adaptive optics and to enable unambiguous positioning of the secondary satellite. A test of this approach using collocated geostationary satellites, acting as on-orbit servicing proxies, found that cross-spectrum measurements can obtain in-track and cross-track relative position precisions better than 100 m when the satellites' apparent angular separations were less than 5 arcseconds. Simulations indicate that the radial position estimates requires 3 h of observation data in order to converge and points to a need for longer observation periods to estimate relative orbits. Brightness differences between the objects did not pose a significant observational limitation as brightnesses of mprimary = 10.2, Δm = 0.3 and mprimary = 9.1, Δm = 1.5 were speckled successfully with relative position estimates obtained.