The Journal of Global Positioning Systems

A major error component of Global Positioning System (GPS) is the ionospheric delay. Ionopspheric error can be reduced by a dual frequency receiver using a linear combination technique that can not be applied with a single frequecy receiver. However, an accurate ionospheric error modeling for single-frequency receiver is required. Due to the nonlinearity of the ionospheric error, a highly nonlinear wavelet network (WN) method is proposed in this paper. The main objective of the paper is to develop a short-term prediction model based on a short dataset. Therefore, five GPS stations with five days of ionospheric datasets along with time and location were employed to develop the proposed WN-based ionospheric model. Four days of datasets were employed to develop the model and one day of dataset was employed to test the prediction accuracy. To validate the WN-based ionospheric model, a comparison was made between the developed WN-based ionospheric model and the CODE, JPL and IGS Global Ionospheric Map (GIM) models. It is shown that the Root-Mean-Squared (RMS) errors of the developed WN-based ionospheric model are 2.51 TECU, 2.75 TECU and 2.50 TECU (Total Electronic Content Unit) with percentage errors of about 3.4%, 3.8% and 3.4% when compared with the CODE, JPL and IGS GIM models.

Triple-frequency GNSS has been intensively studying in the past decades, especially with the open service of China’s BeiDou system. In this review, we will address the ambiguity resolution, benefits gained from additional frequency signals compared to the dual-frequency GNSS signals, as well as analyse the challenges of triple-frequency GNSS for future development. We first review and compare the three carrier ambiguity resolution models of geometry-based, geometry-free, geometry-ionosphere-free (GIF). The benefits gained from triple-frequency GNSS are then comprehensively examined with respect to dual-frequency case, including the improved ambiguity resolution, extra-widelane based RTK, the augmented RTK service, the shortened PPP convergence, the improved availability and reliability. In addition, some challenges are discussed from both theoretical and practical aspects to open eyes for future research.

Integer ambiguity resolution of carrier-phase measurements from a single receiver can be implemented by applying additional satellite corrections (products) to mitigate unmodelled satellite equipment delays. Interoperability of different PPP-AR products would allow the PPP user to transform independently generated PPP-AR products to obtain multiple fixed solutions of comparable precision and accuracy with limited changes required to user PPP measurement processing software. The ability to provide multiple solutions would increase the reliability of the solution for, e.g., real-time processing; if there were an outage in the generation of one set of PPP-AR products, the user could instantly switch streams to a different provider. There are currently three main public providers of real-time products that enable PPP-AR. These include School of Geodesy and Geomatics at Wuhan University (SGG-WHU), Natural Resources Canada (NRCan) and Centre National d’Etudes Spatiales (CNES). The presented research examines the PPP-AR products generated from the FCB (Fractional Cycle Bias) model and IRC (Integer Recovery Clock) model that have been transformed into the DC (Decoupled Clock) format and applied within the PPP user solution. Interoperability of the different PPP-AR products is a challenging task due to the public availability of different quality of products, limited literature documenting the conventions adopted within the network solution of the providers and unclear definitions of the corrections. The novelty of the research is in the analysis of using the transformed products. The convergence time (time to first fix and time to a pre-defined performance level), position precision (repeatability), position accuracy and solution outliers are examined. Equivalent performance was noted utilizing the different methods. Of the four solutions, FCB products had the highest accuracy. This is attributed to the products being generated using final IGS orbit and clock products. To confirm this, FCBs generated using GRG orbit and clock products were also examined and comparable performance was observed between the FCBs and IRC (GRG) products. The least accurate solution was obtained using the IRC (CNT) products, which was due to the products being archived real time products.

Although the Kalman filter (KF) is widely used in practice, its estimated results are optimal only when the system model is linear and the noise characteristics of the system are already exactly known. However, it is extremely difficult to satisfy such requirement since the uncertainty caused by the inertial instrument and the external environment, for instance, in the aided inertial navigation. In practice almost all of the systems are nonlinear. So the nonlinear filter and the adaptive filter should be considered together. To improve the filter accuracy, a novel adaptive filter based on the nonlinear Cubature Kalman filter (CKF) and the Variance-Covariance Components Estimation (VCE) was proposed in this paper. Here, the CKF was used to solve the nonlinear issue while the VCE method was used for the noise covariance matrix of the nonlinear system real-time estimation. The simulation and experiment results showed that better estimated states can be obtained with this proposed adaptive filter based on the CKF.

The code-phase divergences, which are minimal for GPS, GLONASS, and Galileo satellites, are commonly found in BeiDou Navigation Satellite System (BDS) Geostationary Orbit (GEO), Inclined GeoSynchronous Orbit (IGSO) and Medium Earth Orbit (MEO) satellites. Several precise positioning applications which use code observations are severely affected by these code biases. We present an analysis of code bias based on multipath (MP) combination observations. To mitigate the effect of BDS code bias on precise positioning, we proposed a periodical correction method using a low-pass filter for BDS GEO, IGSO and MEO satellites. The auto-correlation of MP series over long periods is analyzed to obtain the periods of the dominant repeating components for three types of BDS satellites. The periods of the dominant daily repeating components are close to 86,160 s for BDS GEO and IGSO satellites while 603,120 s for MEO satellites. The zero phase-shift low-pass filter was used to extract the low-frequency components of MP series and then low-frequency components are applied to mitigate the code bias periodically. The developed correction methods can make a more remarkable improvement for the accuracy of MP series, compared to the current elevation-dependent correction models. Data sets collected at 50 Global Navigation Satellite System (GNSS) ground stations including 15 of the International GNSS Monitoring and Assessment System (iGMAS) and 35 of the Multi-GNSS Experiment (MGEX) stations are employed for this study. To analyze the influence of code bias on precise positioning and validate the effectiveness of the correction methods, some applications such as single point positioning (SPP), wide-lane (WL) ambiguity analysis and Uncalibrated Phase Delays (UPDs) estimation are conducted. After applying the proposal correction method to the code observations, SPP solutions outperform the uncorrected ones in term of positioning accuracy. The positioning accuracy decreased by 0.28 and 0.1 m in the north and east components and the improvements are more significant for the U components decreased by 0.42 m. In addition, the systematic variations of Melbourne-Wübbena (MW) combination are greatly removed and the convergence time of the MW series are decreased. Moreover, significant improvement is also achieved in terms of the usage rate and residuals of UPDs estimation.

This paper presents a novel two-step camera calibration method in a GPS/INS/Stereo Camera multi-sensor kinematic positioning and navigation system. A camera auto-calibration is first performed to obtain for lens distortion parameters, up-to-scale baseline length and the relative orientation between the stereo cameras. Then, the system calibration is introduced to recover the camera lever-arms, and the bore-sight angles with respect to the IMU, and the absolute scale of the camera using the GPS/INS solution. The auto-calibration algorithm employs the three-view scale-restraint equations (SRE). In comparison with the collinearity equations (COL), it is free from landmark parameters and ground control points (GCPs). Therefore, the proposed method is computationally more efficient. The results and the comparison between the SRE and COL methods are presented using the simulated and road test data. The results show that the proposed SRE method requires less computation resources and is able to achieve the same or better accuracy level than the traditional COL.

WiFi and Bluetooth are two most commonly used short range wireless communication technologies. Recent years, with increasing number of WiFi and Bluetooth mobile terminals, tags, and other devices, a demand for integration and coexistence of these two technologies including their positioning function is booming. In this paper, we firstly investigate the interferences between WiFi and Bluetooth signals from the signal and protocol perspectives. Secondly, the principle of fingerprinting approach for WiFi positioning is introduced. In order to evaluate the performance of WiFi fingerprinting coexisted with Bluetooth, both occurrence-based and Weibull-based approaches are utilized for generating the database. Field tests present the interference in the WiFi and Bluetooth coexistence environments. A WiFi mobile device with a Bluetooth device nearby obtains poor positioning results due to the interference. Weibull-based database has more robust performance than occurrence-based database in the coexistence environments.

Improving a priori stochastic models of the process and measurement noise vectors in Kalman Filer (KF) has always been a challenge. As one preferable technique to address this challenge, the variance component estimation (VCE) applied on the Kalman Filter’s process and measurement noise covariance matrix (Q & R) has been proved in plenty of applications. Unsurprisingly, VCE was expected to re-establish the stochastic model about the random errors in the IMU’s measurements in a multisensor integrated positioning and navigation system applying Kalman Filter. However, in the conventional error states-based GPS aided inertial navigation system (GPS/INS), the stochastic model tuning is difficult for the IMU’s measurements due to the amalgamation of the observables from inertial sensor and other aiding sensors. This paper proposes a generic method for the stochastic model tuning about the random errors in IMU measurements together with other sensors. The core of this novel approach is based on an innovative multisensor integration strategy which deploys upon the vehicle’s generic kinematic model and takes the IMU’s output as raw measurements in Kalman Filter (IMU/GNSS Kalman Filter). As a result, the statistical orthogonality between random error vectors of any two sensors enables the separate but parallel statistics collection of each individual random error source. Given these independent statistics corresponding to each error source, the VCE technique iteratively tunes all stochastic model of the process and measurement noise vectors. The success of the VCE algorithm is shown through a real dataset involving GPS and inertial sensors.

Multipath affects the shape of the correlation function and results in biased pseudorange measurements and erroneous navigation solutions. Antenna array processing, which uses signal spatial characteristics, is an effective method to mitigate various types of interference signals. However, the performance of most of the distortionless beamforming techniques degrades in multipath conditions due to the correlation between the desired Line of Sight (LOS) signal and multipath signals. This paper characterizes the performance of different beamforming techniques to mitigate multipath signals through the processing and analysis of simulated and actual data. The main novelty is the investigation of multipath mitigation performance of practically realizable antenna array-based GNSS receivers when the beamforming process is completely integrated into the tracking module after de-spreading. Beamforming techniques such as Delay And Sum (DAS) beamforming, Minimum Power Distortionless Response (MPDR) with and without spatial smoothing are considered. A novel multi-antenna simulator test-bed is developed to generate multipath signals for a multi-antenna platform. A software multi-antenna GPS receiver incorporating different beamforming techniques is then developed to generate pseudorange measurements and position solutions. Carrier-to-Noise ratio (C/N0), pseudorange errors and position solutions before and after beamforming are compared to show the effectiveness of different beamforming techniques to mitigate multipath. Results with simulated and actual GPS signals show improved performance using the MPDR beamformer with spatial smoothing. The utilization of spatial processing results in a pseudorange error reduction of up to 60 % and a position error reduction of up to 30 %.