This paper links the polarization-sensitive-array signal detection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic PARAFAC signal detection algorithm. The proposed PARAFAC signal detection algorithm fully utilizes the polarization, spatial and temporal diversities, and supports small sample sizes. The PARAFAC algorithm does not require direction-of-arrival (DOA) information and polarization information, so it has blind and robust characteristics. The simulation results reveal that the performance of blind PARAFAC signal detection algorithm for polarization sensitive array is close to nonblind MMSE method, and this algorithm works well in array error condition.