This paper designs, evaluates, and tests a tractable priority-index policy for scheduling target updates in a discrete-time multitarget tracking model, which aims to be close to optimal relative to a discounted or average performance objective accounting for tracking-error variance and measurement costs. The policy is to be used by a sensor system composed of M phased-array radars coordinated to track the positions of N targets moving according to independent scalar Gauss-Markov linear dynamics, which therefore allows for the use of the Kalman Filter for track estimation. The paper exploits the natural problem formulation as a multiarmed restless bandit problem (MARBP) with real-state projects subject to deterministic dynamics by deploying Whittle's (1988) index policy for the MARBP. The challenging issues of indexability (existence of the index) and index evaluation are resolved by applying a method recently introduced by the first author for the analysis of real-state restless bandits. Computational results are reported demonstrating the tractability of index evaluation, the substantial performance gains that the Whittle's marginal productivity (MP) index policy achieves against myopic policies advocated in previous work and the resulting index policies suboptimality gaps. Further, a preliminary small scale computational study shows that the (MP) index policy exhibits a nearly optimal behavior as the number of distinct objective targets grows with the number of radars per target constant.