GPS Solutions

The inter-frequency bias of PRN25 was noticed by the scientific community and considered to be caused by thermal variations. The inter-frequency bias leads to an apparent inter-frequency clock bias (IFCB), which could be obtained using the difference of two ionosphere-free phase combinations (L1/L2 and L1/L5). We present an efficient approach derived from the epoch-differenced strategy for fast estimation of IFCBs for Block IIF satellites. For the analysis, data from 32 stations from the IGS network spanning 10 months (DOY 213, 2011–153, 2012) are processed. The processing times show that the epoch-differenced method is more efficient than the undifferenced one. In order to study the features of IFCB, a harmonic analysis is performed by using a FFT (fast Fourier transformation), and significant periodic variations with the periods of 12, 6 and 8 h are noticed. The fourth-order period is determined by comparing the performances of the model with different periods. After determination, a harmonics-based function of order 4 is used to model the IFCB, and the single-day amplitudes and phases are estimated for the 10 months from a least squares fit. Based on the estimated results, the characterization of IFCB is discussed. The algorithm is incorporated into the MGPSS software developed at SHAO (Shanghai Astronomical Observatory, Chinese Academy of Sciences) and used to monitor the IFCB variations of GPS and COMPASS systems in near real time.

Since carrier phase multipath cannot be easily captured or mitigated, especially in real-time and kinematic applications, it is necessary to assess the multipath significance. We propose a real-time multipath detection method using dual-frequency carrier-to-noise-power-density ratio (C/N0). The proposed method takes full account of the relationship between the multipath and C/N0. Specifically, when the multipath effects are significant, the C/N0 behaviors not only deviate from the nominal values, but also differ in frequencies. Therefore, a combination test consisting of two statistics is developed. One is based on the C/N0 and the other is based on the differenced C/N0 between frequencies (∆C/N0). In addition, as an indispensable component of the multipath detection, a procedure for modeling the nominal C/N0 and ∆C/N0 functions is proposed. This procedure is based on a rigorous evaluation in terms of statistical properties. To validate the effectiveness of the proposed method, both static and kinematic experiments were carried out under environments with distinct levels of reflective and diffractive multipath. The results show that this method can effectively detect the multipath significance, and the two statistics are both indispensable. In addition, the modeling procedure improves the reliability of multipath detection with the minimal detectable multipath as small as 0.05 cycles, providing a great potential in high-precision applications.

Digital beamforming (DBF) has been studied to obtain automatic beam steering towards desired signals and simultaneous elimination of multipath and jamming signals at GNSS receivers, which is made possible by spatial and temporal digital signal processing. In this paper, the limitations of conventional multipath and jamming suppression techniques, which have been proven and widely used in GPS, are investigated. Different DBF algorithms suitable for GNSS applications are investigated theoretically. New ideas for future development of DBF are presented. The implementation of digital beamforming in FPGA/DSP for practical application environments is also discussed.

The Global Positioning System (GPS) and Wide Area Augmentation System (WAAS) provide lower power signals that are susceptible to interference. The potential exists for a person or organization to jam GPS or WAAS signals, causing a loss of service over a large area. Accidental interence by extraneous radio transmissions on the GPS frequency also can cause loss of service. Jamming has become a serious issue for GPS, and the U. S. military is making a significant effort to mitigate jamming effects. While jamming is a major concern of the military, interference is of a no lesser concern to the civilian sector. In fact, with varying emphasis both jamming and interference are concerns of the entire GPS user community. This article explores jamming and interference threats to the GPS. We provide a general overview of the GPS signal structure, discuss jamming effects on the GPS, and consider mitigating options. © 1999 John Wiley & Sons, Inc.

Zero velocity update technology (ZUPT) has frequently been used as a tool to reduce divergence when the inertial navigation system (INS) is working in pure inertial mode. In general, the normal gravity model is adopted to calculate the gravity vector, and the effect of gravity disturbance is neglected. We present a new point of view to explain the influence of gravity disturbance on INS and point out that gravity disturbance is one of the most significant error sources of the high-precision INS. Two real-time gravity disturbance compensation methods are proposed. An about 110-km-long vehicle test has been conducted in mountainous terrain with a drastic change of gravity disturbance. The test results proved the correctness of the new explanation and the feasibility of the two on-line compensation algorithms for land vehicles. With gravity disturbance compensation in conjunction with ZUPTs, the total horizontal error at the end of the test was reduced from 8.93 to 3.75 m, and the elevation error was reduced from 1.63 to 0.80 m.

This study investigates the sub-daily polar motion (PM) derived from different estimation interval solutions ranging from 5 min/2 h. By analyzing a 3-year continuous time series of the PM estimates using Global Positioning System (GPS) observations, we conclude that PM should be parameterized as piecewise constant for intervals no longer than 30 min, while piecewise linear parameterization is more appropriate for longer intervals. The inconsistencies between the estimates and the background sub-daily PM model become more pronounced as the estimation intervals become shorter. The results demonstrate that applying continuity constraints enhances the accuracy of PM rate parameter estimation by approximately 20%. However, it is noteworthy that continuity constraints significantly modify and smooth the high-frequency content of the signal in PM. Therefore, when employing piecewise linear estimation, it is not recommended to use continuity constraints. Moreover, we find that sub-daily PM estimates are influenced by artificial signals, primarily caused by the resonance between the earth rotation and satellite revolution periods. These resonance signals are more obvious as the estimation interval becomes shorter, particularly at 4.8 and 8-h periods in the prograde and retrograde spectra, respectively. Finally, we implemented a sub-daily PM series with a 5-min temporal resolution and examined the recovery of the tidal coefficients for 38 tides. Overall, the residual signal amplitudes were generally small, with most of the main ocean tides below 5 μas. The largest residual signals were observed for S1 and K1 terms, with amplitudes of 13.1 and 18.0 μas, respectively.

Computerized ionospheric tomography (CIT) is an ill-posed inverse problem owing to insufficient data acquisition. Therefore, the ionospheric electron density (IED) distributions cannot be reconstructed accurately. Although many attempts have been made to deal with this issue, there is still a long way to go before it can be completely overcome. Specifically, the inverted IEDs of voxels without observational information show a strong dependence on initial values, which affects the overall accuracy of CIT. Taking this into account, a new three-dimensional CIT model is developed, based on a backpropagation neural network. The neural network model is trained using the characteristics and inverted IEDs of voxels with observational information, and then, the IEDs of voxels without observational information are predicted again. Careful validation of the proposed model is performed by conducting numerical experiments with GPS simulation and real data under both quiet and disturbed ionospheric conditions. Compared with the traditional non-neural network method in the simulation experiment, the proposed method offers improvements of 62.0 and 56.89% in root mean square error and the mean absolute error for those voxels without observational information, respectively, while it offers improvements of 30.98 and 26.67% for all voxels of the whole region. In the real data experiment, the IEDs of the control groups obtained by the proposed method are compared with the target IEDs for all periods. The result presents correlation coefficient greater than 0.96 between this predicted IEDs and the target IEDs for all periods, and this further certifies the feasibility of the proposed method. Additionally, the latitude–longitude maps and profiles of the ionospheric electron density also show that the ill-posedness problem has a significantly weaker effect for those voxels without observational information.

The rapid development of the BeiDou Satellite Navigation System (BDS) and other Global Navigation Satellite System (multi-GNSS) constellations provides a great opportunity to contribute to earthquake early warning systems in terms of capturing displacement and velocity waveforms for the estimation of magnitude and fault slip inversion. In this study, we demonstrate the capability of BDS and the benefit of multi-GNSS for real-time capturing seismic waveforms using the combined high-rate BDS + GPS + GLONASS data collected during the 2017 Mw 6.5 Jiuzhaigou earthquake. For this event, we found that the displacements, derived from BDS precise point positioning (PPP) are better than that of Global Positioning System-only (GPS) results, especially in the east and vertical components with improvements of 43% and 23%. While the velocity waveforms from BDS present a comparable performance with GPS. the multi-GNSS fusion can significantly improve the accuracy by 47%, 55%, and 28% in the east, north, and vertical components compared with GPS-only results. The BDS and multi-GNSS derived displacement waveforms agree quite well with those obtained from integrating the acceleration, with accuracy at the millimeter level. In addition, the theoretical permanent displacement field calculated from a finite-fault slip model is selected as an independent reference, and the differences between GNSS derived permanent displacements and theoretical permanent displacements are mostly less than 1 mm. Therefore, we conclude that the BDS and multi-GNSS fusion can significantly contribute to the real-time capture of accurate seismic waveforms and that it has the potential to benefit for earthquake early warning and rapid geohazard assessment.