Delayed acoustic position measurements describe past states but may reach an underwater vehicle after its navigation estimate has advanced. This paper presents compressed delayed-information projection (CDIP), a causal delayed-update method implemented in a 15-dimensional error-state Kalman filter (ESKF). CDIP retains source-associated inertial measurement unit (IMU) snapshots and maintains current-to-snapshot cross-covariances, projecting delayed corrections without repeated full-from-start filtering. In 154 paired simulation recordings with synthetic horizontal-position fixes delayed by 1.5~s, CDIP reduced mean trajectory-position root-mean-square error (RMSE) from 1.062~m for a reception-time Baseline to 0.456~m (57.1\%). Its mean RMSE approached that of full-from-start Replay (0.451~m), with 99.2\% lower mean core-loop time per processed IMU step for the tested implementations. A six-delay sweep, scheduled permanent-loss outages of 50--300~s, and packet-erasure tests further characterized sensitivity to measurement timing and availability. A separate 256-trial nonlinear synthetic assessment identified departures from the prespecified calibration criterion for CDIP and two fully augmented ESKF references. Together, these results demonstrate an accuracy--computation trade-off for causal underwater navigation under the evaluated delayed-measurement simulation conditions.

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