An Effective Robust Total Least-Squares Solution Based on "Total Residuals" for Seafloor Geodetic Control Point Positioning

Global Navigation Satellite System/Acoustic (GNSS/A) underwater positioning technology is attracting more and more attention as an important technology for building the marine Positioning, Navigation, and Timing (PNT) system. The random error of the tracking point coordinate is also an important error source that affects the accuracy of GNSS/A underwater positioning. When considering its effect on the mathematical model of GNSS/A underwater positioning, the Total Least-Squares (TLS) estimator can be used to obtain the optimal position estimate of the seafloor transponder, with weak consistency and asymptotic unbiasedness. However, the tracking point coordinates and acoustic ranging observations are inevitably contaminated by outliers because of human mistakes, failure of malfunctioning instruments, and unfavorable environmental conditions. A robust alternative needs to be introduced to suppress the adverse effect of outliers. The conventional Robust TLS (RTLS) strategy is to adopt the selection weight iteration method based on each single prediction residual. Please note that the validity of robust estimation depends on a good agreement between residuals and true errors. Unlike the Least-Squares (LS) estimation, the TLS estimation is unsuitable for residual prediction. In this contribution, we propose an effective RTLS_Eqn estimator based on "total residuals" or "equation residuals" for GNSS/A underwater positioning. This proposed robust alternative holds its robustness in both observation and structure spaces. To evaluate the statistical performance of the proposed RTLS estimator for GNSS/A underwater positioning, Monte Carlo simulation experiments are performed with different depth and error configurations under the emulational marine environment. Several statistical indicators and the average iteration time are calculated for data analysis. The experimental results show that the Root Mean Square Error (RMSE) values of the RTLS_Eqn estimator are averagely improved by 12.22% and 10.27%, compared to the existing RTLS estimation method in a shallow sea of 150 m and a deep sea of 3000 m for abnormal error situations, respectively. The proposed RTLS estimator is superior to the existing RTLS estimation method for GNSS/A underwater positioning.