## 1 Introduction  
During radiation therapy, intrafractional tumor motion poses a significant challenge in accurately irradiating the tumor and minimizing healthy tissue irradiation. This becomes more challenging when the tumor has a large range of motion and undergoes shape deformation due to respiratory and cardiac activities (e.g., lung and liver tumors) [1; 2; 3]. To minimize healthy tissue irradiation while treating mobile tumors, intrafractional tumor tracking (i.e., following the tumor with a treatment beam) has been widely studied in the past. For target monitoring (i.e., estimating the target position as a function of time) in intrafractional tumor tracking, various approaches have been proposed, which can be categorized into two types: non-invasive and invasive. One non-invasive approach is infrared-based monitoring (e.g., Varian Real-time Position Management (RPM) system); during treatment, the location of an external marker block placed on the patient's surface is monitored by an infrared camera system [4; 5]. This information is used to estimate the internal tumor position based on the correlation between the location of the marker block and the tumor centroid, where the correlation is established prior to the treatment using planning computed tomography (CT) images [4]. Another non-invasive approach is optical surface monitoring (e.g., AlignRT system), which uses multiple high-definition cameras to project structured light patterns on the patient such that motion can be estimated [5; 6]. During treatment, the real-time detected patient surface is compared with a reference surface, often obtained from the simulation CT [6], and this information is used to estimate the tumor position based on the correlation between the alignment of the patient and the alignment of the tumor determined by an additional system [5]. Invasive approaches include X-ray image-based methods, which come in different hardware configurations of stereoscopic imaging and can be combined with external monitoring [6]. The CyberKnife system uses both external and internal tumor surrogates to estimate tumor positions during beam delivery. The patient wears a vast containing external markers that are monitored by a camera system to update the patient's external motion. Metallic surrogates are also surgically inserted near the tumor and are imaged by two orthogonal kilovoltage X-ray systems. During treatment, the tumor position is estimated by the assumed correlation between the patient's external motion and the location of internal surrogates, where the correlation is established prior to the treatment and periodically updated using the X-ray images. Real-time tumor tracking radiotherapy (RTRT) and Vero systems use metallic seeds as internal tumor surrogates, which are monitored during treatment by two orthogonal diagnostic X-ray systems in fluoroscopic mode. These images are used to estimate the internal tumor's position [6]. With information from target monitoring, various tracking methods can be used for beam delivery, which include robotic tracking through CyberKnife Synchrony [7], gimbaled tracking through BrainLab Vero [8; 9], couch tracking [10], and multi-leaf collimator (MLC) tracking [11; 12]. These methods have the potential for margin reduction, particularly for targets affected by respiratory motion where the internal target volume (ITV) is reduced [13]. Most of the currently available target monitoring methods are based on indirect tracking through the use of internal or external tumor surrogates [6]. Reliance on surrogates, however, has been shown to be problematic because implanted seeds can migrate from their initial positions [14], good correlations between internal tumor motion and external surrogate displacement are assumed while mismatches between tumor and surrogateshave been shown [15; 16], and any tumor shape deformation is unknown during tracking. A hybrid radiotherapy-magnetic resonance (MR) system known as linac-MR [17; 18; 19; 20] overcomes these limitations by enabling intrafractional MR imaging of a tumor.