A tracking system for tracking an expanded state of an object, the expanded state including a kinematic state indicative of one or a combination of a position and a velocity of a center of the object, and an extended state indicative of one or a combination of a dimension and an orientation of the object, the tracking system comprising: at least one processor; and a memory having instructions stored thereon that, when executed by the at least one processor, cause the tracking system to: receive measurements associated with at least one sensor, wherein the at least one sensor is configured to probe a scene including the object via one or multiple signal transmissions, the one or multiple signal transmissions configured to produce one or multiple measurements of the object per the transmission; execute a probabilistic filter iteratively tracking a belief on the expanded state of the object, wherein the belief is predicted using a motion model of the object and is updated using a compound measurement model of the object, wherein the compound measurement model includes multiple probabilistic distributions constrained to lie on a contour of the object with a predetermined relative geometrical mapping to the center of the object, wherein in each iteration of the iterative tracking, the belief on the expanded state is updated based on a difference between a predicted belief and an updated belief, wherein the updated belief is estimated based on probabilities of the measurements fitting each of the multiple probabilistic distributions, and mapped to the expanded state of the object based on the corresponding geometrical mapping; and track the expanded state of the object based on the updated belief on the expanded state. at least one processor; and a memory having instructions stored thereon that, when executed by the at least one processor, cause the tracking system to: receive measurements associated with at least one sensor, wherein the at least one sensor is configured to probe a scene including the object via one or multiple signal transmissions, the one or multiple signal transmissions configured to produce one or multiple measurements of the object per the transmission; execute a probabilistic filter iteratively tracking a belief on the expanded state of the object, wherein the belief is predicted using a motion model of the object and is updated using a compound measurement model of the object, wherein the compound measurement model includes multiple probabilistic distributions constrained to lie on a contour of the object with a predetermined relative geometrical mapping to the center of the object, wherein in each iteration of the iterative tracking, the belief on the expanded state is updated based on a difference between a predicted belief and an updated belief, wherein the updated belief is estimated based on probabilities of the measurements fitting each of the multiple probabilistic distributions, and mapped to the expanded state of the object based on the corresponding geometrical mapping; and track the expanded state of the object based on the updated belief on the expanded state. receive measurements associated with at least one sensor, wherein the at least one sensor is configured to probe a scene including the object via one or multiple signal transmissions, the one or multiple signal transmissions configured to produce one or multiple measurements of the object per the transmission; execute a probabilistic filter iteratively tracking a belief on the expanded state of the object, wherein the belief is predicted using a motion model of the object and is updated using a compound measurement model of the object, wherein the compound measurement model includes multiple probabilistic distributions constrained to lie on a contour of the object with a predetermined relative geometrical mapping to the center of the object, wherein in each iteration of the iterative tracking, the belief on the expanded state is updated based on a difference between a predicted belief and an updated belief, wherein the updated belief is estimated based on probabilities of the measurements fitting each of the multiple probabilistic distributions, and mapped to the expanded state of the object based on the corresponding geometrical mapping; and track the expanded state of the object based on the updated belief on the expanded state.