Journal of Global Positioning Systems

Vol. 18, No. 1, 2022

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JGPS Team Structure, Copyright and Table of Contents

1. An indoor magnetic field matching positioning solution based on consumer-grade IMU for smartphone

Jian Kuang, Taiyu Li and and Xiaoji Niu

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Magnetic field matching positioning (MFMP) has become one of the mainstream indoor positioning methods for mass application. However, the problem of the large workload of magnetic field mapping and the instability of the magnetometer bias remains to be solved. This paper designs an indoor MFMP scheme based on consumer-grade Inertial Measurement Units (IMUs). In the magnetic field mapping stage, the high-precision poses of the smartphone obtained by combining a foot-mounted IMU, a smartphone built-in IMU, and a few control points in the building are employed to generate a magnetic field grid map with high efficiency. In the real-time positioning stage, the relative trajectory generated by pedestrian dead reckoning (PDR) is used to improve the position discrimination of the magnetic field feature by adding spatial profile; and the differential magnetic field strength in the sensor frame (instead of in the reference frame) is used to achieve matching positioning that is immune to the magnetometer bias. The consistency of the magnetic field maps built using different smartphones show that the proposed magnetic mapping scheme achieves an average efficiency of 37 m2 /min and is not affected by the mapping trajectory and walking speed. The real-time positioning results using multiple smartphones show that the proposed MFMP algorithm is barely affected by the magnetometer bias, and can achieve an average RMS value of ±0.83 meters in a typical office scenario.

2. Estimation and analysis of BDS-3 multi-frequency differential code bias using MGEX observations

Haijun Yuan, Zhuoming Hu, Xiufeng He and Zhetao Zhang

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Differential code bias (DCB) significantly affects the ionosphere modeling, precise positioning, and navigation applications when using code observations. With the fully completed BeiDou navigation satellite system (BDS-3), there exist various DCBs of new frequencies and types which should be handled. However, limited types of DCB products for BDS-3 are provided by the analysis institutions (e.g., Chinese Academy of Science (CAS) and German Aerospace Center (DLR)). Hence, for some DCB corrections of new frequencies, they are generally generated by complex linear combinations, which are not friendly to users and may degrade the accuracy. In this study, the estimation method of DCB for BDS-3 is introduced first. Then, the BDS-3 observations from 40 globally distributed stations are selected to estimate the DCBs, including 19 types of DCBs of new frequencies for BDS-3. Moreover, the estimated DCBs are carefully analyzed in terms of inner consistency, external consistency, and stability. For the results of inner consistency, most closure error series are within 0.2 ns, and the closure error series of each satellite fluctuate near zero and have no obvious systematic deviations. For the results of external consistency, the mean deviations of estimated DCBs of each satellite are mainly within 0.3 ns and 0.2 ns for the common types of DCB products of CAS and DLR, respectively. For the results of stability, the mean values of monthly STDs for the estimated DCBs are all smaller than 0.12 ns, which exhibits good stability. The STDs of the directly estimated DCBs are generally smaller than that of the DCB combinations of DLR and CAS. In this sense, the directly estimated DCBs for BDS-3 exhibits good performance in terms of accuracy and stability in this study, which can further provide the DCB corrections for precise positioning and navigation applications.

3. A geometry-based ambiguity validation (GBAV) method for GNSS carrier phase observation

Wu Chen, Ying Xu, Duojie Weng and Shengyue Ji

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Integer ambiguity validation is an indispensable and critical step in GNSS carrier phase positioning for precise and reliable positioning applications. The crucial problems associated with any ambiguity validation methods are as follows. 1) The fixed ambiguity vector can be separated from all other ambiguity candidates under certain tests (separability). 2) The probability of fixing to wrong ambiguity combinations (mis-fixing) can be controlled to an acceptable level based on different application requirements. Traditional ambiguity validation methods, such as the R-ratio and the difference tests which use one statistical test to control both separability and misfixing rate, are widely used due to easier computation. The performances of these methods are generally acceptable. However, experiments show that these tests with a fixed threshold can cause either a small percentage of mis-fixing or overly conservative with long observation time. In this paper, we propose a new Geometry Based Ambiguity Validation (GBAV) method which uses two statistical tests to control geometry separability and mis-fixing probability separately. The thresholds for both tests can be strictly determined based on user requirements to control the quality of ambiguity resolution. Three 24-hour GNSS (GPS, BDS) datasets (two short baselines and one middle-range baseline) are processed using the proposed GBAV method, and compared with the popular R-ratio method. The results show that by giving proper control on the mis-fixing probability (0.01%), there is no mis-fixing case in all three datasets.

4. Comparative analysis of data quality and performance index for BDS-3 constellation

Zhipeng Ding1, Kaifei He1, Ming Li1, Yu Wu1, Yue Zhang1,Jinquan Yang

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The global BeiDou-3 Navigation Satellite System (BDS-3) was completed in July 2020. In terms of data processing, the final positioning and baseline solving results will be affected by the quality of the raw observation data. Therefore, it is necessary to analyse and evaluate the data quality of the complete BDS-3 constellation and its service performance. Based on all observing satellites and the open signals from MGEX stations that can track BDS-3, improved software is used to analyse the complete BDS-3 constellation and signals. Moreover, the service performance of BDS-3 is evaluated using self-developed software. The geometric configuration of the complete BDS-3 constellation is found to be slightly better than that of GPS. However, the overall multipath error is about 10 cm higher than that of GPS, although the increased choke of the measured maritime data effectively weakens the multipath error. The pseudorange multipath error of each signal runs in the order B1I>B2a>B2b>B3I>B2a+B2b>B1C; other quality indicators exhibit little difference among bands. In terms of service performance, the carrier phase residuals are 0.17-0.48cm. After data convergence, the relative positioning performance fluctuates around 5 cm of the “true value”, although the fluctuations in the vertical direction are up to 10 cm.

5. Innovative formulation in discrete Kalman filtering with constraints - A generic framework for comprehensive error analysis

Jianguo Wang, Benjamin Brunson and Baoxin Hu

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This manuscript establishes a generic framework for comprehensive error analysis in discrete Kalman filtering with constraints, which systematically provides a complete set of algorithmic formulas along with demonstrating an alternative process of theoretical analytics of discrete Kalman filter. This constructive work aims extensively to standardize the formulation of Kalman filter with constraints. In analogy to the similar framework for standard discrete Kalman filter (without any constraints), the proposed framework specifically considers: model formulation vs. the error sources, the solution of the state and process noise vectors, the residuals for the process noise vector and the measurement noise vector, the redundancy contribution of the predicted state vector, process noise vector and measurement vector, and other relevant essential aspects, of which some of the features are essential to comprehensive error analysis, but are nonexistent yet in the primary algorithm in Kalman filtering with constraints. Besides, the algorithmic form of the Extended Kalman filter with constraints is also provided for practical purpose. At the end, specific remarks about the developed framework are given to emphasize on its usage to a certain extend.

6. Bio-inspired Map Construction based on Brain Navigation Mechanism for Indoor Robots

Yixuan Long, Fang Ye, Yibing Li, Qian Sun

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ABSTRACTS OF PHD DISSERTATIONS

7. High precision positioning for pedestrian navigation in dense urban environments

Luo Huan

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Due to reflections or blockages of GNSS satellite signals by buildings and infrastructures, urban positioning with GNSS is a great challenge. Traditional receiver autonomous integrity monitoring (RAIM) based methods are insufficient to obtain positioning solutions with high accuracy in urban canyons where the majority of satellite signals may be contaminated by multipath interference and non-line-of-sight (NLOS) reception. This thesis will focus on the positioning performance improvement for pedestrians using lowcost devices in urban canyons. With the help of three-dimension (3D) city models, GNSS positioning performance can be improved by predicting visibility or path delays of satellite signals. Shadow matching is a 3D-mapping-aided (3DMA) approach utilizing SNR of satellite signals, which is available in position (NMEA format data) and measurement (raw GNSS measurement data) domains with a wide range of applications. However, the performance of shadow matching will be degraded when it fails to distinguish the grids of neighboring streets, or when it is affected by dynamic interference or 3D model errors. A new weighting method, grid weight smoothing and clustering (GWSC) method, is proposed to improve the performance of grid identification, and experiments in Hong Kong streets showed that the newly proposed method improved the cross-street accuracy of shadow matching from 19.4m to 2.1m with a large improvement rate (IR) of 89.2%, significantly outperforming the weighted average (WA)-based method of 15.3m accuracy, which had an IR of 21.1%. NLOS correction-based approach is another 3DMA method to improve overall positioning performance by simulating reflected paths of satellite signals in the measurement domain. Diffraction, which is also a type of NLOS, is not considered in the conventional reflection model. In this study, we apply the radio signal diffraction models to develop an improved NLOS correction-based approach using a more comprehensive reflection model considering more types of NLOS, along with the GWSC method in weighting. Through experiments, the estimated delays were consistent with the received errors, where over 95% of signals showed estimated errors below 15m. Moreover, the improved approach achieved accuracy of 7.4-15m in static tests, and 11.9m in kinematic tests, compared with up to 86.4m by the conventional GNSS method in typical Hong Kong streets. The proposed method showed a significant IR between 62.7% and 89.7% of positioning accuracy in all experiments in urban canyons. The computation load with city 3D models is very high as it needs to consider different satellite constellations at different time. Moreover, many cities may not have public 3D models available. In this study, a novel approach, named multi-epoch offset searching (MEOS), which does not need 3D city models, is proposed to mitigate multipath effects. With the implementation of measurement smoothing and the GWSC method, the new approach can provide high-precision positioning solutions for pedestrians in urban canyons. It is showed that the approach achieved accuracy of within 9m and 15m in several static and kinematic tests, respectively, compared to the poor accuracy, up to 57.7m and 27.5m, from raw GNSS outputs from conventional low-cost GNSS devices. The proposed method has significant IRs up to 88.3% in static tests, while its IR reached 47.6% in kinematic tests. To make the positioning system more stable and robust, multiple techniques are integrated with sensors existing in the smartphones. The integration of GNSS-based approaches and pedestrian dead reckoning (PDR) technology improves the positioning availability and further reduces the positioning errors. Further integrating Bluetooth-low-energy (BLE) into the system makes the positioning system more flexible and effective. Owing to the proposal of BLE-based heading estimation and improvement of step detection, this integration system achieved a high accuracy of within 5m in outdoor and seamless areas.

8. Research on the Underwater Vehicle Navigation Based on Bayesian Filter

Huimin Liu

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The underwater multi-sensor integrated navigation technology provides guarantees for the long-term and large-scale execution of underwater vehicle diving missions. In multi-source navigation information fusion, observational models and navigation sensor noise are spatially and temporally complex. It is of great theoretical interest and practical value for constructing accurate functional and stochastic models. In this paper, we focus on the fusion of multi-source navigation information for underwater vehicles and work on high-precision long-baseline acoustic system filter design, nonlinear filtering, colored noise filtering, integrated navigation fault-tolerant design, and multi-vehicle coordinated navigation. The work and results of this study are as follows. The paper is divided into seven chapters and is structured as follows: Chapter 1 introduces the research status of common commercial underwater navigation sensors at home and abroad, the development status of filtering theory under the framework of Bayesian filtering and the research status of underwater integrated navigation filtering at home and abroad, introduces the research content and technical route of the paper, and gives the chapter division of the paper. Chapter 2 presents the filtering principle for underwater multi-sensor integrated navigation. Definitions and transformation relations have been studied for commonly used underwater integrated navigation systems, Strapdown inertial navigation systems, Doppler logs, acoustic USBL systems, LBL systems, and pressure sensor and measurement error models. In this paper, we introduce the underwater navigation sensor noise analysis method and its mathematical foundations in the framework of Bayesian filtering. In Chapter 3, sound velocity estimation and sound velocity error correction methods in LBL acoustic localization are investigated. Considering the delayed nature of acoustic propagation, we study the acoustic delay of LBL systems and analyze the PDOP problem in acoustic localization. The underwater carrier navigation filter algorithm is designed based on the LBL/INS loose-binding and tight-binding modes, and the simulation experiments are designed to validate it. Section 4 presents the application of the Bayesian filtering algorithm to nonlinear systems corresponding to the specific operational context of underwater integrated navigation. In this paper, we introduce SINS fast alignment problem under large misalignment angle, USBL/DVL integrated navigation under depth constraint, CKF based compact combination algorithm for SINS/USBL, and localization problem for nonlinear ranging equations when acoustic ranging is short, which are validated by simulations and experiments.

9. Research on LiDAR/INS/ODO/GNSS vehicle integrated navigation algorithm based on graph optimization

Le Chang

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With the rapid development of digital earth and smart city, the demand for localization-based services is becoming urgent. However, continuous, accurate, and reliable positioning navigation in complex environments is a common key technical issue that need to be solved. While GNSS positioning deteriorates or even fails in urban canyons; the positioning error of low-cost INS quickly diverges over time; LiDAR has poor positioning availability when environmental features are insufficient. In order to improve the positioning and navigation service capabilities, China plan to build a more ubiquitous, more integrated, and smarter national comprehensive PNT (Positioning, Navigation, and Timing) system in 2035. And the multi-sensor information fusion is one of the key components of the comprehensive PNT. Since the insufficient vertical resolution of the low-beam LiDAR causes the degradation of LiDAR odometry in some environments, we propose a feature point-based probability map matching method, which combines the advantages of matching by feature point with a probability map. The process extracts the ground feature points and the non-ground feature points by segmentation. A probability map with different resolutions will be constructed to deal with those features, respectively, with a higher vertical resolution for the ground feature and a higher horizontal resolution for the non-ground part. Scan matching by a probability map constructed by feature points minimizes the dependence on the line and surface features in the environment. It has been compared with the well-known open-source LiDAR odometry, i.e. Cartographer and LeGO-LOAM. Evaluations were carried out in different feature scenes. In the areas with rich line and surface features, the positioning accuracy of the proposed method is better than Cartographer, primarily the positioning result on the elevation and horizontal attitude. In areas lacking line and surface features or with the ramped ground, the positioning error of LeGO-LOAM is larger than the proposed method, and it even crashed in some challenging scenarios.

10. Attitude estimation methods using low-cost GNSS and MEMS MARG sensors and their integration

Wei Ding

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For low-cost magnetic, angular rate, and gravity (MARG) sensors based on the microelectromechanical system (MEMS) technology, the sensor errors and measurement noises are significantly large. Attitude errors by integrating gyro data accumulate rapidly. When the vehicle is quasi-static, the roll and pitch angles can be determined by accelerometer measurements which use the local gravity as the reference. The magnetometer is resorted to generate heading information by measuring the geomagnetic field. However, the accelerometer and magnetometer measurements can be deteriorated by the vehicle maneuver and ambient artificial magnetic disturbances, respectively. Thereby a quaternion-based error state Kalman filter (ESKF) is developed to fuse the MEMS MARG sensor measurements for accuracy improved attitude estimation. The error state vector constitutes attitude error and gyro bias variation. the gyro-measured angular rates are used to continuously propagate the vehicle’s three-dimensional attitude quaternion in its sampling rate, whilst accelerometer and magnetometer measurements are employed for the state correction. Disturbances such as external accelerations and magnetic anomalies are excluded, and the measurement noise covariance matrix is adaptively adjusted according to the innovations. Global navigation satellite system (GNSS) based attitude estimation shows time-independent error characteristics. The pitch and heading angles can be determined using a single GNSS antenna based on the time differenced carrier phase (TDCP) observations or derived from a moving baseline formed between two firmly mounted GNSS antennas. The major challenges of the former include cycle slips, carrier phase discontinuity, and slow vehicular velocity which should be excluded from attitude estimation. Whereas the integer ambiguity resolution is indispensable for the latter, the baseline length constrained least-squares ambiguity decorrelation adjustment (C-LAMBDA) method can be applied.

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Last Modified: March, 2022