Affected by dynamic changes in the complex marine environment, ultrashort baseline (USBL) systems may exhibit continuous gross errors in underwater target positioning, resulting in the distortion of the target coordinates. To effectively detect and eliminate continuous gross errors in USBL underwater acoustic positioning, a robust sequential adaptive Kalman filter (RSAKF) algorithm is proposed in this paper. The RSAKF algorithm employs sequential filtering to decompose all measurement updates into multiple submeasurement updates and uses the fading memory weighted average method to estimate the one-step prediction mean square error of the metrics for each submeasurement update. Then, the RSAKF algorithm adopts an adaptive correction method of submeasurement noise variance, which eliminates the influence of continuous gross errors through a more targeted adaptive correction of each submeasurement noise variance. The effectiveness of the algorithm was quantitatively analyzed using a USBL positioning simulation experiment, and the results showed that the continuous gross errors rejection rate of the RSAKF algorithm reached 84.12%. The point error of the RSAKF algorithm is improved by 62.65%, 46.76%, 36.09%, and 26.48% compared with the KF, KF based on Huber (HKF), KF based on IGGIII (IGGKF), and the maximum correntropy Kalman filter (MCKF), respectively. The USBL positioning ROV experiment was conducted in the South China Sea, and the results showed that the RSAKF has the best filtering accuracy. Simulation and actual measurement experiments verified that the RSAKF algorithm can effectively eliminate the influence of continuous gross errors.