A passive electro-optical tracker uses a two-band IR intensity ratio to discriminate high-speed projectiles and obtain a time-varying speed estimate from their time-varying temperature, as well as determining the trajectory back to the source of fire. In an omnidirectional system a hemispheric imager with an MWIR spectrum splitter forms two CCD images of the environment. Various methods are given to determine the azimuth and range of a projectile, both for clear atmospheric conditions and for nonhomogeneous atmospheric conditions. One approach uses the relative intensity of the image of the projectile on the pixels of a CCD camera to determine the azimuthal angle of trajectory with respect to the ground, and its range. A second uses a least squares optimization over multiple frames based on a triangle representation of the smeared image to yield a real-time trajectory estimate.