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Kilovoltage intrafraction monitoring (KIM) is a method allowing to precisely infer the tumour trajectory based on cone beam computed tomography (CBCT) 2D-projections. However, its accuracy is deteriorated in the case of highly mobile tumours involving hysteresis. A first adaptation of KIM consisting of a prior amplitude based binning step has been developed in order to minimize the errors of the original model (phase-KIM). In this work, we propose enhanced methods (KIM sub-arc optim and phase-KIM sub-arc optim ) to improve the accuracy of KIM and phase-KIM which relies on the selection of the optimal starting CBCT gantry angle. Aiming at demonstrating the interest of our approach, we carried out a simulation study and an experimental study: we compared the accuracy of the conventional versus sub-arc optim methods on simulated realistic tumour motions with amplitudes ranging from 5 to 30 mm in 1 mm increments. The same approach was performed using a lung dynamic phantom generating a 30 mm amplitude sinusoidal motion. The results show that for in-silico simulated motions of 10, 20 and 30 mm amplitude, the three-dimensional root mean square error (3D-RMSE) can be reduced by 0.67 mm, 0.91 mm, 0.94 mm and 0.18 mm, 0.25 mm, 0.28 mm using KIM sub-arc optim and phase-KIM sub-arc optim respectively. Considering all in-silico simulated trajectories, the percentage of errors larger than 1 mm decreases from 21.9% down to 1.6% for KIM (p < 0.001) and from 6.6% down to 1.2% for phase-KIM (p < 0.001). Experimentally, the 3D-RMSE is lowered by 0.5732 mm for KIM and by 0.1 mm for phase-KIM. The percentage of errors larger than 1 mm falls from 39.7% down to 18.5% for KIM and from 23.2% down to 11.1% for phase-KIM. In conclusion, our method efficiently anticipates CBCT gantry angles associated with a significantly better accuracy by using KIM and phase-KIM., (© 2020 IOP Publishing Ltd.)