In this Letter, considering the configuration of small antenna array aperture used for special usage, the authors proposed a target trajectory estimation method by unambiguous phase differences with prior knowledge on target velocity from a single fixed passive sensor. First, they developed the maximum likelihood estimator of the target trajectory parameters based on unambiguous phase differences and then deduce the corresponding Cramer-Rao lower bound. Furthermore, in terms of the error in prior knowledge on target velocity, the influence of target velocity mismatch on trajectory parameters estimation is analysed. Finally, they evaluated the performance of the proposed method and validated the correctness of their analysis via numerical simulation.