** Accession Number : **AD0712508

**Title : **TWO-DIMENSIONAL POINT RESOLUTION,

**Corporate Author : **NAVAL RESEARCH LAB WASHINGTON D C

** Personal Author(s) : **Owens,M. E. B.
;
Kullback,J. H.

**Report Date : **11 SEP 1970

**Pagination or Media Count : **13

**Abstract : **A hypothesis test has been designed for a situation which arises when multiple sensors observe the positions and only the positions of vessels in a specified region of the ocean. Given that two sensors each observe the position of a vessel, the problem is to determine whether the sensors observed the position of the same vessel or the positions of different vessels. Assuming the observations occur at the same time and the observation errors are normally distributed with known covariance matrices, it is a simple matter to design a test to test the null hypothesis that the observations refer to the same vessel against the alternative hypothesis that the observations refer to different vessels. This test is designed to have a fixed but arbitrary probability of the type 1 error (concluding that the observations refer to different vessels when they actually do not). Remaining is the question of the probability of the type 2 error (concluding that the observations refer to the same vessel when they actually do not). Without a complete statistical description of the processes, one cannot answer this question exactly. The authors have only assumed that the number of vessels in any subregion is a Poisson random variable having for the parameter the product of a constant and the area of the subregion, the constant being the expected number of vessels per unit area. Under this condition the least upper bound for the probability of the type 2 error is expressed as an explicit function of the error covariance matrices, the probability of the type 1 error, and the expected number of vessels per unit area. (Author)

**Descriptors : **
(*NAVAL VESSELS, POSITION FINDING), (*OCEAN SURVEILLANCE, STATISTICAL TESTS), DETECTORS, RANDOM VARIABLES, DISTRIBUTION FUNCTIONS, MATRICES(MATHEMATICS), PROBABILITY DENSITY FUNCTIONS, PROBABILITY, ERRORS

** Subject Categories : **MILITARY INTELLIGENCE

**Distribution Statement : **APPROVED FOR PUBLIC RELEASE