Speckle tracking is used with synthetic aperture radar (SAR) images to estimate displacements, in ways that support or integrate interferometric measurements. This letter derives Fisher information expressions for the displacement estimation using coherent speckle tracking, for the multi-image scenario with an arbitrary coherence structure. Previous results were limited to image pairs. An estimator that approaches the theoretical bound is also proposed, establishing a link with phase estimation for multi-image SAR interferometry. The derivation of the Fisher information is given in the general case when the coherence is a function of the frequency.