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The problem of tracking a target using a sequence of infrared (IR) images is addressed. A Bayes-closed estimation algorithm developed by Kulhavy is shown to be well suited to the IR tracking problem. Due to the form of the model for the radiation intensity pattern on the IR focal plane array, closed-form expressions are found for the reduced sufficient statistics (RSS) which are used to approximate the true posterior density in the Kulhavy algorithm. An estimate of the target state is then derived via a reconstruction formula from the RSS. For comparison, both a previously developed IR tracking algorithm based on an extended Kalman filter (EKF) and the new RSS-based method are used to track a target through a sequence of IR images. It is shown that the RSS algorithm can maintain track in high velocity scenarios where the EKF diverges.