The traditional leader-follower Unmanned Aerial Vehicle (UAV) formation cooperative positioning (CP) algorithm, based on relative ranging, requires at least four leader UAV positions to be known accurately, using relative distance with leader UAVs to achieve the unknown position follower UAV’s high-precision positioning. When the number of the known position leader UAVs is limited, the traditional CP algorithm is not applicable. Aiming at the minimum cooperative unit, which consists of a known position leader UAV and an unknown position follower UAV, this paper proposes a CP method based on the follower UAV’s moving vector. Considering the follower UAV can only acquire the single distance with the leader UAV at each distance-sampling period, it is difficult to determine the follower UAV’s spatial location. The follower UAV’s moving vector is used to construct position observation of the follower UAV’s inertial navigation system (INS). High-precision positioning is achieved by combining the follower UAV’s moving vector. In the process of CP, the leader UAV obtains a high-precision position by an INS/Global Positioning System (GPS) loosely integrated navigation system and transmits its position information to the follower UAV. Based on accurate modeling of the follower UAV’s INS, the position, velocity and heading observation equation of the follower UAV’s INS are constructed. The improved extended Kalman filtering is designed to estimate the state vector to improve the follower UAV’s positioning accuracy. In addition, considering that the datalink system based on radio signals may be interfered with by the external environment, it is difficult for the follower UAV to obtain relative distance information from the leader UAV in real time. In this paper, the availability of the relative distance information is judged by a two-state Markov chain. Finally, a real flight test is conducted to validate the performance of the proposed algorithm.