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We define and evaluate methods to perform robust network monitoring using trajectory sampling in the presence of report loss. The first challenge is to reconstruct an unambiguous set of packet trajectories from the reports on sampled packets received at a collector. In this paper we extend the reporting paradigm of trajectory sampling to enable the elimination of ambiguous groups of reports, but without introducing bias into any characterization of traffic based on the surviving reports. Even after the elimination, a proportion of trajectories are incomplete due to report loss. A second challenge is to adapt measurement based applications (including network engineering, path tracing, and passive performance measurement) to incomplete trajectories. To achieve this, we propose a method to join multiple incomplete trajectories for inference, and analyze its performance. We also show how applications can distinguish between packet and report loss at the statistical level.