Asymptotically optimum multialternative sequential procedures for discernment of processes minimizing average length of observations
Abstract
The problem of multialternative sequential discernment of processes is formulated in terms of conditionally optimum procedures minimizing the average length of observations, without any probabilistic assumptions about any one occurring process, rather than in terms of Bayes procedures minimizing the average risk. The problem is to find the procedure that will transform inequalities into equalities. The problem is formulated for various models of signal observation and data processing: (1) discernment of signals from background interference by a multichannel system; (2) discernment of pulse sequences with unknown time delay; (3) discernment of harmonic signals with unknown frequency. An asymptotically optimum sequential procedure is constructed which compares the statistics of the likelihood ratio with the meanweighted likelihood ratio and estimates the upper bound for conditional average lengths of observations. This procedure is shown to remain valid as the upper bound for the probability of erroneous partial solutions decreases approaching zero and the number of hypotheses increases approaching infinity. It also remains valid under certain special constraints on the probability such as a threshold. A comparison with a fixedlength procedure reveals that this sequential procedure decreases the length of observations to one quarter, on the average, when the probability of erroneous partial solutions is low.
 Publication:

USSR Rept Electron Elec Eng JPRS UEE
 Pub Date:
 January 1985
 Bibcode:
 1985RpEEE.......30F
 Keywords:

 Asymptotic Methods;
 Bayes Theorem;
 Multichannel Communication;
 Optimization;
 Sequential Control;
 Signal Detection;
 Data Processing;
 Interference Factor Table;
 Quality Control;
 Sampling;
 Communications and Radar