Probability of Anomaly Expressions for Random Waveform Registration

Registration by integral-square error correlation of one-dimensional discrete-time waveforms which are treated as random processes with specified autocorrelation functions is considered. An important design parameter for this class of problems is the probability of anomaly (a false dip in the correlation function) because it gives an indication of system immunity to gross registration errors. Explicit expressions for this parameter are not possible, so bounds and appoximations must be derived. Two upper bounds and an approximation for the probability of anomaly are derived here. The use of these expressions is illustrated by an example. The relative utility of these performance indicators is shown for the example by comparison with actual values of the probability of anomaly obtained by computer simulation.