The problem of detection in the presence of a slowly varying not neces
sarily Gaussian noise is treated in this paper by introducing the gene
ralized Linear tests and the generalized quantiles test statistic T(i
). Detectors based on these tests combine the good qualities of order
and partition statistics, i.e., increased efficiency and ease of imple
mentation. Using an array of M sensors, the T(i) statistic, which com
bines the power of rank tests, and the robustness of partition tests,
is extended to its multivariate counterpart, and its performance is ev
aluated for small signal-to-noise-ratio environments.