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An adaptive-update-rate target-tracking algorithm is proposed for a phased-array radar. The algorithm is based on the interacting-multiple-model (IMM) algorithm. The purpose of this IMM algorithm is twofold: to estimate and predict the target states; and to estimate the level of the dynamic process noise. The estimate of the process-noise level is used to determine the update interval adapted to the changing target dynamics. The update interval is determined so that the number of track updates per unit time in reflection of beam-positioning losses can be reduced. The proposed algorithm is implemented for a phased-array radar tracking and evaluated with Monte Carlo simulations on various trajectories. The evaluation results of the proposed algorithm are presented and compared with the results of the `cube-root filter'