The location of long-distance shortwave radiation sources is practically significant in national defense security. Shortwave multistation-positioning systems mainly include direction-of-arrival (DOA) and time-difference-of-arrival (TDOA) intersection locations. These two systems have their advantages and disadvantages in terms of performance. To combine the advantages of these two positioning technologies, this study focuses on the cooperative positioning problem based on DOA and TDOA measurements. First, the two-dimensional DOA and TDOA observation models are established for the over-the-horizon propagation scenario. Subsequently, the Cramér-Rao lower bound (CRLB) of positioning accuracy is derived in the presence of measurement errors in virtual ionosphere height. Aiming at the strong nonlinear characteristics of the observation equations, a new DOA/TDOA cooperative localization method is proposed. Finally, the asymptotic efficiency of the new estimator is proved using the first-order error analysis theory. The new method comprises two stages. In the first stage, the shortwave DOA observation equation is transformed into a pseudo-linear observation equation by introducing an auxiliary variable, as well as solving a quadratic equation with one unknown. Next, an optimization model with two quadratic equality constraints is constructed, and an iterative optimization algorithm based on matrix $~\bf{QR}$ decomposition is proposed to obtain an intermediate estimate of the emitter position. The second stage transforms the shortwave TDOA observation equation into a pseudo-linear observation equation by combining the intermediate estimates given in the first phase. Also, an iterative-constrained weighted-least-squares estimator based on the matrix decomposition is proposed again to localize the emitter. Simulation results show that the new cooperative localization method has good global convergence, the localization performance can reach the CRLB, and the obtained cooperative gain is quite high.