Compressed delayed-information projection for six-degree-of-freedom underwater vehicle navigation under delayed acoustic positioning
Abstract: Delayed acoustic positioning packets constrain historical navigation states, but a current-time update evaluates them against a mismatched state, whereas exact rewind/replay re-executes the intervening estimator history. This paper introduces compressed delayed-information projection (CDIP), a causal 15-state error-state Kalman filter (ESKF) treatment for delayed-acoustic unmanned underwater vehicle (UUV) navigation. CDIP retains a source-epoch snapshot and the historical-to-current cross-covariance, then projects the delayed source-epoch acoustic correction directly to the current state without full rewind/replay. Exact fixed-lag rewind/replay out-of-sequence-measurement (OOSM) processing serves as a high-fidelity accuracy reference. In 154 usable paired recordings at a fixed 1.5-s acoustic delay without an outage, CDIP reduced mean trajectory-position root-mean-square error (RMSE) from 1.062 m for the baseline to 0.456 m (57.1%). Its 0.456-m mean was 1.03% higher than the 0.451-m replay mean, while its measured mean per-update runtime was 99.2% lower (approximately 127-fold). A separate predeclared sweep across six fixed delays, with 30 paired recordings per delay, and a truth-supported 9-D consistency analysis bound the interpretation. Additional targeted experiments showed near-replay trajectory accuracy across 50-300-s acoustic outages while preserving sub-millisecond update cost. CDIP therefore provides a compact delayed-information treatment with an empirical accuracy-computation trade-off under the evaluated configuration; the evidence does not establish statistical equivalence or non-inferiority relative to replay.