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A simplified model is proposed for predicting the nonlinear dynamic response of vertically loaded tapered piles in the time domain, in which the tapered pile is divided into several frustum segments and the four-spring is used for the simulation of the soil–pile interaction. The differential equations for the tapered pile are given and solved by the finite difference method. The vertical dynamic response of a typical tapered pile is investigated, and the consistency of the computational results compared with the finite element results convincingly verifies the reliability of the proposed simplified model. Then, recommended segment numbers, considering the computational efficiency and accuracy requirements for the dynamic analysis of tapered piles, are given. And parametric studies are also carried out to investigate the effect of soil and pile parameters on the nonlinear dynamic response of the tapered pile. The results show that soil nonlinearity significantly affects the vertical dynamic characteristics of the tapered pile. And the tapered pile shows better dynamic characteristics than the cylindrical pile with the same volume and pile length. In addition, the properties of the soil along the upper part of the tapered pile have a more considerable effect on the dynamic response of the tapered pile. These results help to further improve the theory of nonlinear dynamic response analysis of tapered piles and promote its widespread application in engineering practice.

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 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.

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.