The detection of an unresolved point source in clutter is the stressing problem for Infrared Search and Track (IRST) systems. The availability of temporally spaced snapshots of the same clutter background results in a data source that is three dimensional: azimuth, elevation, and time. Here the clutter in different frames will be assumed to consist of two components: one that is constant from frame to frame and one that is statistically independent between frames. The component that is statistically independent is due to the combination of sensor noise, pixel position jitter, and changes in the background. The constant component represents the part of the clutter that is temporally unvarying; it can be reduced by frame-to-frame differencing. The component that is statistically independent between frames can be reduced by frame averaging. Each of these techniques is optimum (in the mean squared sense) only for an isolated set of conditions on the clutter and target behavior. The general optimum linear processor will be referred to as the three dimensional matched filter. Averaging and differencing are limiting cases of this filter: averaging when the target velocity is zero and the independent component dominates, differencing when the target velocity is large and the constant component dominates. The assumption of a constant clutter component and constant intensity target lead to a fillet with infinite temporal extent. The temporal extent of the three dimensional matched filter must be constrained in practice since only a finite number of frames can be stored. This constraint combined with the assumptions on clutter structure has lead to a computationally efficient implementation of the optimum linear processor based on a finite number of frames of data. This processor, along with methods for predicting and comparing its performance to other multiframe processing schemes, is presented in this paper.