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This paper deals with the management of multimode sensors such as multifunction radars. We consider the problems of multitarget radar scheduling formulated as multivariate partially observed Markov decision process (POMDPs). The aim is to compute the scheduling policy to determine which target to choose and how long to continue with this choice so as to minimize a cost function. We give sufficient conditions on the cost function, dynamics of the Markov chain target and observation probabilities so that the optimal scheduling policy has a threshold structure with respect to the multivariate TP2 ordering. This implies that the optimal parameterized policy can be estimated efficiently. We then present stochastic approximation algorithms for estimating the best multilinear threshold policy.