Polarimetric detection for vector-sensor array in quaternion Gaussian proper noise

The passive polarimetric detection problem for vector-sensor array is formulated based on quaternion. The quaternion-formed detectors are deduced and analyzed in the presence of different quaternion proper noise. The properness of quaternion Gaussian noise, especially for the C-proper and Q-proper cases in this paper, is discussed based on the second order statistics (SOS) of the complex components of quaternion noise. Numerical simulations and statistical analysis demonstrate that the C-proper, Q-proper and complex detectors are equivalent in the Q-proper case, and that the Q-proper detector behaves poorer than C-proper and complex detectors in the C-proper case.