The Real-Time Kinematic (RTK) positioning algorithm is a promising positioning technique that can provide real-time centimeter-level positioning precision in GNSS-friendly areas. However, the performance of RTK can degrade in GNSS-hostile areas like urban canyons. The surrounding buildings and trees can reflect and block the Global Navigation Satellite System (GNSS) signals, obstructing GNSS receivers’ ability to maintain signal tracking and exacerbating the multipath effect. A common method to assist RTK is to couple RTK with the Inertial Navigation System (INS). INS can provide accurate short-term relative positioning results. The Extended Kalman Filter (EKF) is usually used to couple RTK with INS, whereas the GNSS outlying observations significantly influence the performance. The Robust Kalman Filter (RKF) is developed to offer resilience against outliers. In this study, we design an algorithm to improve the traditional RKF. We begin by implementing the tightly coupled RTK/INS algorithm and the conventional RKF in C++. We also introduce our specific implementation in detail. Then, we test and analyze the performance of our codes on public datasets. Finally, we propose a novel algorithm to improve RKF and test the improvement. We introduce the Carrier-to-Noise Ratio (CNR) to help detect outliers that should be discarded. The results of the tests show that our new algorithm’s accuracy is improved when compared to the traditional RKF. We also open source the majority of our code, as we find there are few open-source projects for coupled RTK/INS in C++. Researchers can access the codes at our GitHub.

The detection and repair of the cycle slip is a key step for high precision navigation and positioning in indoor environments. Different methods have been developed to detect and repair cycle slips for carrier phase processing. However, most approaches are designed to eliminate the effects of the ionosphere in an outdoor environment, and many of them use pseudorange (code) information that is no longer suitable for indoor multipath environments. In this paper, a method based on the geometry-free combination without the pseudorange data is proposed to detect and fix cycle slips. A ground-based navigation system is built for data collection. Unlike the traditional dual-frequency cycle slip detection method, the Beidou B1, GPS L1 carrier phase combination is used instead of the B1, B2, or L1, L2 carrier phase combination, Ublox is used for data collecting. For fixing the cycle slips quickly, an improved adaptive Particle Swarm Optimization (PSO) algorithm is employed. We compared the performance of the new method with the existing two methods using simulated data in different conditions. The results show that the proposed method has better performance than other methods.

Carrier phase measurements play a more critical role in achieving precise positioning for lower noise and insensitivity to multipath error over code (pseudorange) measurements. Real-time kinematic (RTK) is the most used precise positioning technique. However, the application costs are increased due to the demands for differential base stations. The undifferenced precise point positioning (PPP) does not require differential station assistance but is typically for static use. This paper proposes a dynamic continuous constrained phase (DCCP) method based on factor graph optimization for kinematic positioning without differential stations, even in the presence of cycle slips. The precise velocity estimated via integral doppler and the time correlation of phase ambiguity are regarded as the probability constraints in the factor graph. A real-world experiment was carried out to verify the feasibility of the DCCP method. Experimental results show that the proposed method had a better performance than the kinematic PPP method and window carrier phase (WCP) optimization method with 0.034m standard deviation and 1.338m mean error. It is our hope that this approach provides new insight into the study of other time-correlated state estimation problems.

The real-time kinematic positioning technique (RTK) and visual–inertial odometry (VIO) are both promising positioning technologies. However, RTK degrades in GNSS-hostile areas, where global navigation satellite system (GNSS) signals are reflected and blocked, while VIO is affected by long-term drift. The integration of RTK and VIO can improve the accuracy and robustness of positioning. In recent years, smartphones equipped with multiple sensors have become commodities and can provide measurements for integrating RTK and VIO. This paper verifies the feasibility of integrating RTK and VIO using smartphones, and we propose an improved algorithm to integrate RTK and VIO with better performance. We began by developing an Android smartphone application for data collection and then wrote a Python program to convert the data to a robot operating system (ROS) bag. Next, we established two ROS nodes to calculate the RTK results and accomplish the integration. Finally, we conducted experiments in urban areas to assess the integration of RTK and VIO based on smartphones. The results demonstrate that the integration improves the accuracy and robustness of positioning and that our improved algorithm reduces altitude deviation. Our work can aid navigation and positioning research, which is the reason why we open source the majority of the codes at our GitHub.

The positioning accuracy of a ground-based system in an indoor environment is closely related to the geometric configuration of pseudolites. This paper presents a simple closed-form equation for computing the weighted horizontal dilution of precision (WHDOP) with four eigenvalues, which can reduce the amount of calculation. By comparing the result of WHDOP with traditional matrix inversion operation, the effectiveness of WHDOP of the proposed simple calculation method is analyzed. The proposed WHDOP has a linear relationship with the actual static positioning result error in an indoor environment proved by the Pearson analysis method. Twenty positioning points are randomly selected, and the positioning variance and WHDOP of each positioning point have been calculated. The correlation coefficient of WHDOP and the positioning variance is calculated to be 0.82. A pseudolite system layout method based on a simulated annealing algorithm is proposed by using WHDOP, instead of Geometric dilution of precision (GDOP). In this paper, the constraints of time synchronization are discussed. In wireless connection system, the distance between master station and slave station should be kept within a certain range. Specifically, for a given indoor scene, many positioning target points are randomly generated in this area by using the Monte Carlo method. The mean WHDOP value of all positioning points corresponding to the synchronous pseudolite layout is used as the objective function. The results of brute force search are compared with the method, which proves the accuracy of the new algorithm.

Precise carrier phase positioning is a widely used technique in vehicle navigation, localization, and mapping, which utilizes pseudorange and carrier phase measurements with the extended Kalman filter (EKF) to estimate position, velocity, and ambiguities. For highly accurate vehicle positioning requirements, propagation errors of measurements need to be considered, especially the ionospheric delay, which is the most significant error source. In EKF, a priori information of different error characteristics can be fully utilized as constraints to obtain more precise state estimation results, even when no corrections are available. This paper aims to improve the positioning accuracy for vehicle navigation and proposes a spherical harmonic function (SHF)-based undifferenced and uncombined (UDUC) carrier phase positioning method for vehicles to fit the ionospheric delays of multiple satellites in a single formula and reduce the marginal effect caused by polynomials. Better positioning results are expected compared to traditional UDUC and polynomial fitting approaches. The feasibility of the proposed method is tested on a kinematic dataset from a real-world car test. The experimental results show that the proposed method outperforms the traditional UDUC and polynomial fitting methods, respectively, with a root mean square error of 0.860 m and a standard deviation of 0.579 m when using broadcast ephemeris. In summary, the results demonstrate that the proposed method is highly beneficial for precise vehicle navigation.