Outliers and multipath effects significantly affect the positioning accuracy and reliability of the global navigation satellite system (GNSS), which must be handled properly in real-time kinematic (RTK) positioning, especially for low-cost devices. In this study, an extended robust estimation method (EIGG3) considering the multipath effects is proposed for RTK positioning. The carrier-to-noise power density ratio ( $C/N0$ ) template function is introduced, and then, an extended shrinking factor of the bifactor equivalent weight is proposed, where one five-segment processing strategy considering the multipath effects is used. Two dedicated experiments, including one static experiment and one kinematic vehicle experiment, were carried out to evaluate the performance of the EIGG3 method in terms of positioning availability, accuracy, and ambiguity resolution. For the static experiment, the improved percentage of the EIGG3 method is 62.7%, 61.6%, and 52.1% compared to the traditional robust estimation method for the positioning accuracy in the $E$ -, $N$ -, and $U$ -directions, respectively. Also, the EIGG3 method can further improve the performance of ambiguity resolution. For the kinematic vehicle experiment, the EIGG3 method 15.4% improvements for positioning accuracy in an urban environment, and even 23.9% improvements can be obtained in some typical scenarios.

Global Navigation Satellite System-Acoustic (GNSS-A) technology has been widely used in ocean engineering and ocean environmental science. Accurate sound travel time modeling is essential for GNSS-A seafloor positioning. Currently, half of the two-way travel time (TWTT) has been used as an approximation for the one-way travel time (OWTT). In this work, the time error of the approximate OWTT is investigated under different survey configurations, and a sequential GNSS-A seafloor positioning method using the extended Kalman filter (EKF) is developed to investigate the impact of sound travel time modeling. Simulations show that the time error induced under the static survey configuration is less than 0.6 ms; the time error induced under the circle survey configuration with a stable inclination angle is stable, but the time error of the line survey configuration can reach 28 ms. As confirmed through field experiments, sequential GNSS-A seafloor positioning using TWTT modeling is more stable than OWTT modeling. The positioning residuals of TWTT modeling are similar to those of OWTT modeling under the circle configuration but at least 2 times less than those of OWTT modeling under the line survey configuration. Furthermore, the average positioning residuals of OWTT and TWTT modeling can be greatly reduced for a survey configuration combining circular and linear tracks. These findings provide a feasible method for improving the precision and efficiency of GNSS-A seafloor positioning.

Multipath is a major source of unmodeled errors that will hinder high-precision and high-reliability positioning, navigation, and timing in the Global Navigation Satellite System (GNSS). Traditional methods mainly focus on how to model the multipath effects well, little attention has been paid to the reliability of the multipath corrections which may exist abnormal values, especially under complex observation conditions. In this paper, a robust pseudorange and carrier phase multipath hemispherical map considering the uncertainty based on the least-squares collocation (LSC) is proposed. First, the posterior residuals and the corresponding mean standard deviations are applied to establish the MHM correction model and its precision model, respectively. Second, the robust MHM approach based on the LSC is deduced including the real-time differenced (RTD) and real-time kinematic positioning (RTK) modes. The results show that for the designed experiment, the root mean square error (RMSE) values of the proposed method are improved by 13.4%, 16.4%, and 13.1% compared to the traditional MHM method in RTD, RTK float, and RTK fixed solutions, respectively. In the field test, accuracy at the decimeter and centimeter levels can be improved by the proposed method in RTD and RTK solutions, respectively. It proves that the proposed method considering the uncertainty is robust especially under complex observation conditions.

Probability of collision between non-cooperative space object (NCSO) and the reference spacecraft (RS) has been increased drastically over the past few decades. The traditional method is difficult to identify the maneuvering of non-cooperative space object. In the present paper, not only positions and velocities, but also accelerations of non-cooperative space object are estimated as parameters by the extended Kalman filtering based on setting up the state linear equation and measurement model of the non-cooperative space object. The algorithm for predicting collision probability is derived from position error ellipsoid, and the algorithm for determining maneuvering probability is derived from maneuvering acceleration and its error ellipsoid, which can be employed to identify whether the upcoming space object is being maneuvered. An epoch Earth-centered inertial (EECI) coordinate system is suggested to replace Earth-centered inertial (ECI) to simplify coordinate transformation. Finally, a set of simulations were conducted to validate the proposed algorithms with the simulated measurement data of the reference spacecraft space-borne millimeter-wave (MMW) radar.

Sea level monitoring is particularly important in coastal areas that are vulnerable to marine disasters. It was recently demonstrated that the global navigation satellite system multipath reflectometry (GNSS-MR) technique, which uses multipath signals reflected from the sea, can be applied to determine the sea level. However, this approach does not provide sufficient accuracy or equally spaced sampling to meet the actual sea level monitoring requirements for certain stations. To solve the deficiency of the traditional GNSS-MR technique, the least squares method, which is based on sliding time windows, was applied. Using the sliding windows to combine the quad-constellation multi-GNSS retrieval can effectively improve the accuracy and time resolution of sea level retrieval, but insufficient data or a lack of data in some time ranges and missing overflights in some timeframes can lead to the calculation of faults in these time windows, causing the estimated loss of corresponding sampling points. In this study, we used a robust regression solution strategy based on multi-GNSS sea level retrieval and an improved variational mode decomposition (IVMD) algorithm to process sea level retrieval after robust regression. BRST and HKQT stations are located on the western coast of France and the northern coast of Hong Kong. The two stations can both receive satellite observation data from the four satellite systems. Through the experiment, using data retrieved from the BRST and HKQT stations, the results of this study demonstrate that the IVMD method based on multi-GNSS sea level retrieval can further improve the accuracy to <10 cm and can achieve 10 min equal interval sampling. This is significant for using GNSS-MR technology to detect sea level height and monitor sea level change and could be applied to other sites.

This paper proposes an accurate quantitative segmentation method by analyzing the probability distribution of tracking variance and strict derivation based on the tracking loop theory. The segmentation points are taken as characteristics of phase lock loop (PLL) and frequency lock loop (FLL) performances, and the two factors that cause the performance difference are discriminator gain and filtering coefficient, which denote proportional and integration coefficients, respectively. The filtering coefficients lead to a difference of 2.5 dB-Hz between the FLL and PLL. Moreover, through the analysis of the normalized bandwidth and phase margin, it is found that the integration time and bandwidth need a dynamic balance to achieve the best performance. Finally, the simulation results and real data are in good agreement with the theoretical analysis results. The minimum mean error rate of the deviation between the real data and the theoretical data is only 1.8%. In the proposed method, the influence of external hardware factors on the tracking loop is removed, and the loop design factors are modeled directly. Instead of testing the denoising performance based on the ranging and angle measuring error after location calculation, the filter coefficient is proposed to evaluate the processing performance of the tracking loop objectively and directly at the theoretical level, which proposes a new performance evaluation method at the theoretical level. The results presented in this study provide theoretical support for the design of a new-type tracking loop with enhanced performances.