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This paper gives a computationally efficient algorithm for estimating the state of an arbitrary number of mut—tiple systems in the presence of false measurements. It combines the Viterbi algorithm with the Kalman filter for state estimation. The algorithm does not require that the target systems exist at all times or that the probability that a target system is detected he unity. An example is given showing that the algorithm is effective even for high numbers of false measurements and a low probability of detection, compared to a con-ventional algorithm (PDA).