Real-time prostate tracking during intensity-modulated arc radiotherapy requires a reliable prostate position signal during treatment. Many modern linear accelerators have a single gantry-mounted x-ray imager that could be used for intrafraction imaging of implanted prostate markers. The aim of this study was to develop a method to use such a single x-ray imager to estimate the three-dimensional (3D) prostate position in real time during arc treatment delivery and quantify the accuracy of this method in simulations based on 548 prostate trajectories for 17 patients measured with electromagnetic transponders. Imaging at 0.5, 1, 2 and 5 Hz during 360 degrees arc treatments of 1, 2 and 3 min duration was simulated by projecting the prostate position onto the rotating imager. When an image was acquired, a Gaussian probability density function (PDF) for the prostate position was first estimated by maximum likelihood optimization from the set of images acquired so far and then used to estimate the 3D prostate position from the projected position in the image. Since this method needed a PDF right from the onset of the treatment, an initial PDF was obtained with a series of pre-treatment images acquired in 10 s, 20 s or 30 s during a gantry rotation of 60 degrees , 120 degrees or 180 degrees . The accuracy of the estimations was quantified by calculating the root-mean-square (RMS) estimation error for each simulated treatment. The 3D RMS estimation error had a mean value of 0.22 mm and exceeded 1 mm in 0.8% of the cases for 1 min treatments with 5 Hz imaging and 20 s pre-treatment imaging. The position estimation accuracy degraded slightly with reduced imaging frequency or reduced pre-treatment imaging duration. Prolonged treatment duration of 2 and 3 min increased the mean 3D RMS errors to 0.27 mm and 0.30 mm, respectively. The single-imager trajectory estimation method would allow image-guided real-time prostate tracking based on standard equipment for modern linear accelerators.