In this study, we combined a time-differenced carrier phase (TDCP)-based global positioning system (GPS) with an inertial navigation system (INS) to form an integrated system that appropriately considers noise correlation. The TDCP-based navigation system can determine positions precisely based on high-quality carrier phase measurements without difficulty resolving integer ambiguity. Because the TDCP system contains current and previous information that violate the format of the conventional Kalman filter, a delayed state filter that considers the correlation between process and measurement noise is utilized to improve the accuracy and reliability of the TDCP-based GPS/INS. The results of a dynamic simulation and an experiment conducted to verify the efficacy of the proposed system indicate that it can achieve performance improvements of up to 70% and 60%, respectively, compared to the conventional algorithm.

Many strategies for treating dual-frequency cycle slip, which can seriously affect the performance of a carrier-phase-based positioning system, have been studied over the years. However, the legacy method using the Melbourne-Wübbena (MW) combination and ionosphere combination is vulnerable to pseudorange multipath effects and high ionospheric storms. In this paper, we propose a robust algorithm to detect and repair dual-frequency cycle slip for the network-based real-time kinematic (RTK) system which generates high-precision corrections for users. Two independent and complementary carrier-phase combinations, called the ionospheric negative and positive combinations in this paper, are employed for avoiding insensitive pairs. In addition, they are treated as second-order time differences to reduce the impact of ionospheric delay even under severe ionospheric storm. We verified that the actual error distributions of these monitoring values can be sufficiently bounded by the normal Gaussian distribution. Consequently, we demonstrated that the proposed method ensures high-integrity performance with a maximum probability of missed detection of 7.5 × 10⁻⁹ under a desired false-alarm probability of 10⁻⁵. Furthermore, we introduce a LAMBDA-based cycle slip compensation method, which has a failure rate of 1.4 × 10⁻⁸. Through an algorithm verification test using data collected under a severe ionospheric storm, we confirmed that artificially inserted cycle slips are successfully detected and compensated for. Thus, the proposed method is confirmed to be effective for handling dual-frequency cycle slips of the network RTK system.

Regional augmentation systems for a global navigation satellite system (GNSS) provide an ionospheric map correction to the user in order to remove the ionospheric delay error. Measurements are collected from multiple reference stations to estimate the ionospheric map. During this process, the pseudorange measurement error of a reference station causes an error in the correction, which is more evident at edge areas and causes a large error for low-elevation satellites. In this study, an ionospheric modeling algorithm was developed that uses the carrier phase with the pseudorange to greatly reduce the error. The integer-resolved double-difference carrier phase can be obtained through ambiguity resolution method, and the measurement is directly utilized in ionospheric modeling. The performance of the developed method was tested in simulations and with real data for validation. The results of users at various locations showed that the method effectively improved the accuracy of the correction.

The covariance of real-time global positioning system (GPS) orbits has been drawing attention in various fields such as user integrity, navigation performance improvement, and fault detection. The international global navigation satellite system (GNSS) service (IGS) provides real-time orbit standard deviations without correlations between the axes. However, without correlation information, the provided covariance cannot assure the performance of the orbit product, which would, in turn, causes significant problems in fault detection and user integrity. Therefore, we studied real-time GPS orbit covariance characteristics along various coordinates to effectively provide conservative covariance. To this end, the covariance and precise orbits are estimated by means of an extended Kalman filter using double-differenced carrier phase observations of 61 IGS reference stations. Furthermore, we propose a new method for providing covariance to minimize loss of correlation. The method adopted by the IGS, which neglects correlation, requires 4.5 times the size of the covariance to bind orbit errors. By comparison, our proposed method reduces this size from 4.5 to 1.3 using only one additional parameter. In conclusion, the proposed method effectively provides covariance to users.

In this paper, using the additional relation between tropospheric delay and height variation, we combined multiple carrier phase corrections from multiple reference stations of Network RTK. The Low-order Surface Method (LSM) is used as a base correction interpolation method. The LSM including height difference is also considered and its gradient coefficients are calculated as minimum-norm solutions. Real GPS data from multiple reference station network are collected and Compact RTK and Master-Auxiliary Concept (MAC) corrections are generated. Finally, generated corrections are tested for various correction interpolation methods including proposed algorithm and their performances are compared.