In multi-sensor systems, time synchronization between sensors is a significant challenge, and this issue is particularly pronounced in underwater integrated navigation systems incorporating acoustic positioning. Such systems are highly susceptible to time delay, which can significantly degrade accuracy when measurement and fusion moments are misaligned. To address this challenge, this paper introduces a tightly coupled navigation framework that integrates a passive inverted ultra-short baseline (piUSBL) acoustic positioning system, a strapdown inertial navigation system (SINS), and a depth gauge under precise time synchronization. The framework fuses azimuth and slant range from the piUSBL with depth data, thereby avoiding poor vertical-angle observability in planar arrays. A novel delay measurement strategy is introduced, combining synchronized timing with acoustic signal processing, which redefines delay-traditionally an unobservable error-into a quantifiable parameter, enabling explicit estimation of both acoustic propagation and system processing delays. Simulations and field experiments confirm the feasibility of the proposed method, with delay-compensated navigation reducing RMSE by 40.45% and maximum error by 32.55%. These findings show that precise delay measurement and compensation not only enhance underwater navigation accuracy but also establish a generalizable framework for acoustic positioning integration, offering valuable insights into time alignment and data fusion in latency-sensitive multi-sensor systems.

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