In this paper, a mathmatical model for the purpose of QRS detection is considered in the case of the occurence of nonoverlappjng pulse-shaped waveforms corrupted with white noise. The number of waveform, the arrival times, amplitudes, and widths of QRS complexes are regarded as random variables. The joint MAP estimation of all the unknown Quantities consists of linear filtering followed by an optimization procedure. Because the optimization procedure is time-consuming, this procedure is modified so that a threshold test is obtained.