In this article, we consider the problem of trajectory optimization for an UAV, as well as the stationary target localization. Based on system observability condition and target localization error derived through grammian matrix and geometrical interpretations respectively, we design a trajectory and a control scheme. Under the control scheme, the UAV can move around the target with a desired radius to enhance the observability. Simulation results are presented to show the improvement in estimation of target position with bearing measurement bias.