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In an embedded system with limited processing resources, as the number of tasks grows, they interfere with each other through preemption and blocking while waiting for shared resources such as CPU time and memory. The main task of an Any-Time Kalman Filter (AKF) is real-time state estimation from measurements using available processing resources. Due to limited computational resources, the AKF may have to select only a subset of all the available measurements or use out-of-sequence measurements for processing. This paper addresses the problem of measurement selection needed to implement AKF on systems that can be modeled as double-integrators, such as mobile robots, aircraft, satellites etc. It is shown that a greedy sequential selection algorithm provides the optimal selection of measurements for such systems given the processing constraints.