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Sensor measurements derived from passively observed transient signals radiated by a target are non-Gaussian and may also be nonstationary due to their dependence on tracking geometry. Moreover, transients are usually observed in clutter, so there is also a possibility of false detections. A technique that incorporates a deterministic annealing procedure into a robust M-estimator, referred to as the annealing M-estimator, is applied to determine the target motion parameters based on such measurements. This technique is compared to standard robust M-estimators using several scenarios with different tracking geometry and is found to give more accurate parameter estimates.