Estimation of pulse heights and arrival times

The problem is studied of estimating the arrival times and heights of pulses of known shape observed with white additive noise. The main difficulty is estimating the number of pulses. When a maximum likelihood formulation is employed for the estimation problem, difficulties similar to the problem of estimating the order of an unknown system arise. The problem may be overcome using Rissanen's shortest data description approach. An estimation algorithm is described, and its consistency is proved. The results are illustrated by a simulation study using an example from seismic data processing also studied by Mendel.