A SEQUENTIAL PROCEDURE FOR MULTIHYPOTHESIS TESTING
Carl W. Baum
Venugopal V. Veeravalli
Abstract
The sequential testing of more than two hypotheses has important
applications in direct-sequence spread spectrum signal acquisition,
multiple-resolution-element radar, and other areas. A useful
sequential test which we term the MSPRT is studied in this paper. The
test is shown to be a generalization of the Sequential Probability
Ratio Test. Under Bayesian assumptions, it is argued that the MSPRT
approximates the much more complicated optimal test when error
probabilities are small and expected stopping times are large. Bounds
on error probabilities are derived, and asymptotic expressions for the
stopping time and error probabilities are given. A design procedure
is presented for determining the parameters of the MSPRT. Two
examples involving Gaussian densities are included, and comparisons
are made between simulation results and asymptotic
expressions. Comparisons with Bayesian fixed sample size tests are
also made, and it is found that the MSPRT requires two to three times
fewer samples on average.