Integrity Monitoring for Network RTK Users with Enhanced Computational Performance
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Integrity monitoring (IM) is a vital task for precise real-time positioning in road transportation, autonomous driving, and drones, where safety is essential. IM has the main tasks of detection and exclusion of faulty observations and ensuring that the continuity and integrity requirements of the positioning system are met, otherwise alert the user to switch to another system. The traditional receiver-autonomous-integrity-monitoring (RAIM) methods have evolved into the new advanced RAIM (ARAIM) methodology that takes into consideration the use of multi-constellation multi-frequency data with the capability of monitoring simultaneous multiple faults. The ARAIM method has been originally developed primarily for aviation based on the use of the single-point positioning method, which can achieve accuracy typically less than 10 m, or with augmentation at a few m. However, applications such as navigation of drones, or autonomous driving require better accuracy at the dm-level or better, such as for the in-lane accuracy. Such a level of accuracy requires the use of more precise methods such as precise point positioning (PPP), real-time kinematic (RTK), or Network RTK. However, PPP has a serious limitation related to the need for approximately 30 minutes of initialization time for the solution to converge. Therefore, the use of Network RTK (NRTK), with its widespread coverage over most populated areas in developed countries and many others, would be attractive. In our previous work, we discussed integrity monitoring for PPP-RTK and RTK. We also discussed the vulnerabilities from different sources and those at the network stations and at the user, in addition to discussing the observation and stochastic models, and the formulation of the integrity monitoring algorithm. In this contribution, we shift the focus to the user side of Network RTK, assuming the use of the Virtual Reference Station (VRS) methodology. In our algorithm, on one hand, although fixed ambiguity resolution is used, wrong ambiguity solutions are not included in the integrity risk budget, otherwise, the probability of misleading information has to increase to accommodate the failure rate (1- success rate) considered in the ambiguity validation task. On the other hand, at the user side, no fault budget needs to be assigned to the spatially correlated errors, i.e. the orbital errors and atmospheric (ionosphere and troposphere) delays, due to the short baseline length employed in the VRS approach that is typically less than 5 km, and the use of double-difference observations.
In this contribution, two approaches that can improve the IM computational load are proposed. This improvement of the computational load is necessary for real-time applications, where testing subsets of measurements needs to apply multiple parallel processing filters. Firstly, in the VRS methodology, a NRTK station is typically being selected by the Network Center as the nearest station within the network to compute the VRS observations for a specific user. We utilize the known position of this NRTK station to detect and identify faulty satellite observations by comparing the true range between this known station and the satellites with their undifferenced observations. For phase observations, the ambiguities are considered temporally constant and are identified within an initialization period after rising of a satellite. This process is not user-specific. For the specific user, however, the expected normalized residuals of the undifferenced observations at its VRS are predicted, which are computed as the residuals at the NRTK station adjusted by the corrections of the spatially correlated errors (orbital errors and the troposphere and ionosphere delays) at the VRS. This process can be done either by the NRTK network center within the process of computing the observations at the VRS, or alternatively by the user if the user reconstructs the VRS observations (according to the VRS methodology used). This information, comprising information of detected faults and the expected observation residuals at the VRS is sent to the user via the NTRK message, and is considered valid within a short period of a few minutes, and accordingly being updated by this rate. The user utilizes the information of faults detected by the NRTK station since the source of the vulnerabilities related to the satellites would be common, and any faults detected at the reference station would be most likely experienced by the user, except for those due to the user-specific environment. Note that in the VRS approach, vulnerabilities due to the troposphere and ionosphere delays are common between the VRS and the user owing to their short distance, and therefore can be ignored as double-difference observations are used. The information on faults detected by the NRTK station is utilized, serving the selection of the pivot satellite and other satellites to use, combined with the application of the detection test in the observation domain for all-satellites in view, i.e. using the Chi-square test employing the sum of squared normalized-double-differenced observation residuals as the test statistic. The outcome of this process is either accepting the observations and proceeding to computations of the Protection levels or testing only single satellites for further fault identification if the detection test does not pass, without the need to consider multiple satellite faults, which tremendously reduces the computational load. For identification and to further reduce the number of tested subsets, similar normalized undifferenced observation residuals from the all satellite-in-view solution are computed at the user end, which is compared to those computed above at the VRS for the same satellites, and their ratio is ranked for all observations. The algorithm benefit from this information and the computation of the correlation coefficient between observation errors of each satellite to perform testing only for the most vulnerable observation type of the satellite, i.e. the one with the highest ratio, such that only this observation is tested (i.e. excluded along with its highly correlated observations when forming the observation subset). Accordingly, one test is performed per satellite, thus reducing the number of subsets if all observations of the satellite form their own subsets (note that, e.g., for dual-frequency data there are four observations per satellite, 2 code plus 2 phase observations). The Chi-square test is applied for the subsets excluding the suspected observation(s) at a time. The subset with the least p_value among those which may not pass the test is considered first for exclusion. Furthermore, a new approach that significantly improves the computation time of the measurement-update of Kalman gain in the filter processing is presented where only one matrix inversion is applied for all filters with measurement subsets. This reduction in the processing time is achieved at the expense of a suboptimal approximation of using the covariance matrix of the predicted states of the all-in-view observations when considering the subsets, leading to a small increase in the protection level. However, with NRTK, the protection level is still at a few dm, significantly below the alert limit.
Test results for a kinematic test run in a mixed open-sky and suburban environments demonstrate the benefit of the proposed approach compared to traditional methods in reducing the computation time. With integrity risks of 10^-5 and 10^-6, availability of integrity monitoring, i.e. when PL is tested against a selected alert limit of 1.625m. Comprehensive results are presented in the paper.
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