[en] It is important to monitor tumor movement during radiotherapy. Respiration-induced motion affects tumors in the thorax and abdomen (in particular, those located in the lung region). For image-guided radiotherapy (IGRT) systems, it is desirable to minimize imaging dose, so external surrogates are used to infer the internal tumor motion between image acquisitions. This process relies on consistent correspondence between the external surrogate signal and the internal tumor motion. Respiratory hysteresis complicates the external/internal correspondence because two distinct tumor positions during different breathing phases can yield the same external observation. Previous attempts to resolve this ambiguity often subdivided the data into inhale/exhale stages and restricted the estimation to only one of these directions. In this study, we propose a new approach to infer the internal tumor motion from external surrogate signal using state augmentation. This method resolves the hysteresis ambiguity by incorporating higher-order system dynamics. It circumvents the segmentation of the internal/external trajectory into different phases, and estimates the inference map based on all the available external/internal correspondence pairs. Optimization of the state augmentation is investigated. This method generalizes naturally to adaptive on-line algorithms