Resolving a variable number of hypotheses with multiple sensors

Author

Gubner, John A. ; Scharf, Louis L.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Wisconsin-Madison, Madison, WI, USA

fYear

2012

fDate

5-8 Aug. 2012

Firstpage

504

Lastpage

507

Abstract

A family of multi-sensor detection problems is proposed in which the number of hypotheses to be resolved can be traded off against the probability of error, the signal-to-noise ratio (SNR), and the number of sensors. Using large deviations and an approximation of the large deviation rate function, it is shown that the number of hypotheses resolvable at a specified error probability is proportional to the square root of the product of the SNR and the number of sensors, and the constant of proportionality depends on the logarithm of the desired error probability. Similar analysis shows that the SNR required to resolve a specified number of hypotheses at a specified error probability is proportional to the square of the number of hypotheses to be resolved and inversely proportional to the number of sensors. Examples are included to illustrate the results.

Keywords

approximation theory; error statistics; sensor fusion; SNR; error probability; hypotheses variable number; large deviation rate function approximation; multiple sensors; multisensor detection problems; signal-to-noise ratio; Approximation methods; Educational institutions; Error probability; Random variables; Sensors; Signal resolution; Signal to noise ratio; Detection; hypothesis resolution; large deviations;

fLanguage

English

Publisher

ieee

Conference_Titel

Statistical Signal Processing Workshop (SSP), 2012 IEEE

Conference_Location

Ann Arbor, MI

ISSN

pending

Print_ISBN

978-1-4673-0182-4

Electronic_ISBN

pending

Type

conf

DOI

10.1109/SSP.2012.6319744

Filename

6319744