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The paper addresses the problem of adaptive manoeuvring targets tracking in clutter with a phased array radar. The tracking algorithm is based on the combination of the interacting multiple models (IMM) algorithm and the joint probabilistic data association filter (JPDAF), the resulting algorithm is named IMMJPDAF algorithm. Moreover, the phased array radar is a multifunction radar with the capability to select adaptively the sampling time interval; consequently, the tracking performance is improved. First, a complete comparative study between the IMMJPDAF algorithm and the multirate IMMJPDAF (MRIMMJPDAF) algorithm for tracking close manoeuvring targets with varying amounts of clutter density is presented. Then a description is made of the integration of a new fast method into the IMMJPDAF algorithm to adaptively select the next update time according to the targets motions. We call the resulting algorithm, the fast adaptive IMMJPDAF (FAIMMJPDAF) algorithm. Furthermore, an enhancement of the tracking accuracy in the FAIMMJPDAF algorithm is made by also taking into account the separation distance between targets in the selection of the next update time. The performance of the proposed algorithm, named improved fast adaptive IMMJPDAF (IFAIMMJPDAF) algorithm is assessed via Monte Carlo Simulations and compared with that of four algorithms that use an adaptive selection of the update time: FAIMMJPDAF algorithm, the adaptive IMMJPDAF that uses a modified version of the van Keuk criterion (MAIMMJPDAF), the adaptive IMMJPDAF that uses the original van Keuk method (AIMMJPDAF), and the IMMJPDAF (CIMMJPDAF) that uses a constant update time.