Probability density functions for the projected area of a tumbling or precessing target are employed as prior distributions in the derivations of signal plus noise distributions for an ir scanner. The analysis treats several cases for known and unknown pulse arrival times using a matched filter and also an unspecified filter, where the sensor noise is stationary and Gaussian. The signal pulse shape is variously Gaussian or unspecified. The paper also provides the characteristic functions and detection probabilities corresponding to the signal plus noise densities.