Title :
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
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;
Conference_Titel :
Statistical Signal Processing Workshop (SSP), 2012 IEEE
Conference_Location :
Ann Arbor, MI
Print_ISBN :
978-1-4673-0182-4
Electronic_ISBN :
pending
DOI :
10.1109/SSP.2012.6319744
