Multitarget positioning technology, such as FMCW millimeter-wave radar, has broad application prospects in autonomous driving and related mobile scenarios. However, it is difficult for existing correlation algorithms to balance high resolution and low complexity, and it is also difficult to ensure the robustness of the positioning algorithm using an aging antenna. This paper proposes a super-resolution and low-complexity positioning algorithm based on the orthogonal matching pursuit algorithm that can achieve more accurate distance and angle estimation for multiple objects in a low-SNR environment. The algorithm proposed in this paper improves the resolving power by two and one orders of magnitude, respectively, compared to the classical FFT and MUSIC algorithms in the same signal-to-noise environment, and the complexity of the algorithm can be reduced by about 25–30%, with the same resolving power as the OMP algorithm. Based on the positioning algorithm proposed in our paper, we use the PSO algorithm to optimize the arrangement of an aging antenna array so that its angle estimation accuracy is equivalent to that observed when the antenna is intact, improving the positioning algorithm’s robustness. This paper also further realizes the use of the proposed algorithm and a single-frame intermediate frequency signal to estimate the position angle information of the object and obtain its motion trajectory and velocity, verifying the proposed algorithm’s estimation ability when it comes to these qualities in a moving scene. Furthermore, this paper designs and carries out simulations and experiments. The experimental results verify that the positioning algorithm proposed in this paper can achieve accuracy, robustness, and real-time performance in autonomous driving scenarios.