Coordinated Positioning Method for Shortwave Anti-Multipath Based on Bayesian Estimation

Coordinated positioning based on direction of arrival (DOA)–time difference of arrival (TDOA) is a research area of great interest in beyond-visual-range target positioning with shortwave. The DOA estimation accuracy greatly affects the accuracy of coordinated positioning. With existing positioning methods, the elevation angle’s estimation accuracy in multipath propagation decreases sharply. Accordingly, the positioning accuracy also decreases. In this paper, the elevation angle is modeled as a random variable, with its probability distribution reflecting the characteristics of multipath propagation. A new coordinated positioning method based on DOA–TDOA and Bayesian estimation with shortwave anti-multipath is proposed. First, a convolutional neural network is used to learn the three-dimensional spatial spectrogram to make an intelligent decision on the number of single and multiple paths, and to obtain a probability distribution of the elevation angle under multiple paths. Second, the elevation angle’s estimated value is modified using the elevation angle’s probability distribution. The modified elevation angle’s estimated value is substituted into a DOA pseudo-linear observation equation, and the target position’s estimated value is obtained using the matrix QR decomposition iteration algorithm. Finally, a TDOA pseudo-linear observation equation is established using the target estimate obtained in the DOA stage, and the coordinated positioning result is obtained using the matrix QR decomposition iteration algorithm again. Simulation results demonstrated that the proposed method had a stronger anti-multipath capability than traditional methods, and it improved the coordinated positioning accuracy of the DOA and TDOA. Measured data were used to validate the proposed method.