A system for tracking an expanded state of a moving object including a kinematic state indicative of a position of the object and an extended state indicative of one or combination of a dimension and an orientation of the object, the system comprising: at least one sensor configured to probe a scene including a moving object with multiple signal transmissions to produce multiple measurements of the object per the transmission; a memory configured to store values of truncation intervals for truncating a probabilistic distribution; a processor configured to execute a probabilistic filter tracking a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a center-truncated distribution having truncation intervals providing smaller probability for the measurements at the center of the center-truncated distribution inside of the truncation intervals and larger probability for the measurements outside of the truncation intervals, wherein the center-truncated distribution is a truncation of an underlying untruncated distribution according to the truncation intervals, wherein the probabilistic filter is configured to estimate the center-truncated distribution that fits the measurements and to produce mean and variance of the underlying untruncated distribution corresponding to the center-truncated distribution, such that the mean of the underlying untruncated distribution indicates the position of the object in the expanded state and the variance of the underlying untruncated distribution indicates the dimension and the orientation of the object in the expanded state; and an output interface configured to output the expanded state of the object. at least one sensor configured to probe a scene including a moving object with multiple signal transmissions to produce multiple measurements of the object per the transmission; a memory configured to store values of truncation intervals for truncating a probabilistic distribution; a processor configured to execute a probabilistic filter tracking a joint probability of the expanded state of the object estimated by a motion model of the object and a measurement model of the object, wherein the measurement model includes a center-truncated distribution having truncation intervals providing smaller probability for the measurements at the center of the center-truncated distribution inside of the truncation intervals and larger probability for the measurements outside of the truncation intervals, wherein the center-truncated distribution is a truncation of an underlying untruncated distribution according to the truncation intervals, wherein the probabilistic filter is configured to estimate the center-truncated distribution that fits the measurements and to produce mean and variance of the underlying untruncated distribution corresponding to the center-truncated distribution, such that the mean of the underlying untruncated distribution indicates the position of the object in the expanded state and the variance of the underlying untruncated distribution indicates the dimension and the orientation of the object in the expanded state; and an output interface configured to output the expanded state of the object. <EOS>