This paper presents a new ultrashort baseline (USBL) tightly coupled integration technique to enhance error estimation in low-cost strapdown inertial navigation systems (INSs), with application to underwater vehicles. In the proposed strategy, the acoustic array spatial information is directly exploited in an extended Kalman filter (EKF) implemented in a direct feedback structure. Instead of using the USBL position fixes or computed range and elevation/bearing angles to correct the INS error drifts, as in classical loosely coupled strategies, the novel tightly coupled strategy directly embeds in the EKF the round-trip-time and time-difference-of-arrival of the acoustic signals arriving at the onboard receivers. The enhanced performance of the proposed filtering technique is evidenced both through extensive numerical simulations and with experimental data obtained in field tests at sea. The tightly coupled filter is also shown to be able to operate closer to theoretical performance lower bounds, such as the posterior Cramér-Rao lower bound, using Monte-Carlo simulations. This paper details the design and description of an USBL/INS prototype to be used as a low-cost navigation system, including the acoustic processing and positioning system, fully developed in-house. The developed system validates the usage of the proposed technique with real data in real world operation scenarios, and its enhanced performance compared to classical strategies is evaluated experimentally (median improvement level of 15% in typical operating conditions). Improved and faster convergence to nominal trajectories from multiple initial conditions, as well as enhanced accelerometer and rate gyros estimation capabilities, are also demonstrated experimentally for the new tightly coupled filter.