We present a technique for continuous generation of volumetric images during SBRT using periodic kV imaging and an external respiratory surrogate signal to drive a patient-specific PCA motion model. Using the on-board imager, kV radiographs are acquired every 3 seconds and used to fit the parameters of a motion model so that it matches observed changes in internal patient anatomy. A multi-dimensional correlation model is established between the motion model parameters and the external surrogate position and velocity, enabling volumetric image reconstruction between kV imaging time points. Performance of the algorithm was evaluated using 10 realistic eXtended CArdiac-Torso (XCAT) digital phantoms including 3D anatomical respiratory deformation programmed with 3D tumor positions measured with orthogonal kV imaging of implanted fiducial gold markers. The clinically measured ground truth 3D tumor positions provided a dataset with realistic breathing irregularities, and the combination of periodic on-board kV imaging with recorded external respiratory surrogate signal was used for correlation modeling to account for any changes in internalexternal correlation. The three-dimensional tumor positions are reconstructed with an average root mean square error (RMSE) of 1.47 mm, and an average 95 th percentile 3D positional error of 2.80 mm compared with the clinically measured ground truth 3D tumor positions. This technique enables continuous 3D anatomical image generation based on periodic kV imaging of internal anatomy without the additional dose of continuous kV imaging. The 3D anatomical images produced using this method can be used for treatment verification and delivered dose computation in the presence of irregular respiratory motion.