The effect of correlation on accumulated detection probability

A sonar model frequently used for accumulating probability of detection over a succession of independent opportunities is modified by the introduction of correlation between opportunities. Two Guassian models, Markov and unit-memory, are investigated. Monte Carlo calculations of accumulated detection probability and mean hold time are presented. The calculations of mean hold time can be used to estimate the correlation. The loss of accumulated detection probability compared with the independent model can then be estimated from the calculations of accumulated detection probability. Compared to the case of independent opportunities, nonzero correlation imposes a performance penalty which is modest when opportunities are weakly correlated but grows rapidly with increasing correlation.