CONTENTS 



INTRODUCTION... page 5 



HISTORICAL BACKGROUND... 5 



BINOMIAL HIGH-RESOLUTION TWO-STAGE DETECTION. 

 Glossary of Symbols... 8 

 General Description... 9 

 Distribution of Signal and Noise... 10 

 Binomial Fixed-Sample-Size Testing... 12 

 False-Alarm Rate (FAR). ..73 

 Sample Sizes... 7 4 

 Resolution... 15 

 N and the Average Scanning Rate... 16 



ANALYSIS OF SPECIAL CASES... 21 

 General Description... 21 

 A Sequential Test for Stage A... 21 

 Detector Optimization... 22 

 Comparison of Systems... 32 



MULTIPLE-RANGE-BIN FIRST-STAGE... 38 



APPLICATIONS INVOLVING CHANGES IN ENERGY... 45 



CONCLUDING REMARKS... 45 



REFERENCES... 46 



ILLUSTRATIONS 



1 Multiple-stage detection, block diagram... page 6 



2 ?i{K, S) vs threshold K, fixed-sample test.. .23 



3 Effect of varying coarseness of resolution in first stage... 16 



4 PjjvsN for Na= 1,2, 3... 18 



5 Cumulative detection probability vs N, an approximation... i9 



6 N^ + optimum /Vg vs iV... 20 



7 avsEo(n), sequential test... 23 



8 Pq vs N, fixed-sample stages... 24 



9 Pq vs N, first stage sequential... 25 



10 Per-stage miss probabilities vs Ng... 26 



11 Pq vs range... 27 



12 Optimum Ng vs Po... 28 



13 Optimum a^ ws Pq...29 



14 pg/p^ vsPd...30 



15 Pb/P_4 vs N... 31 



