Clock Bias Research Articles

On theoretical and practical analyses of BDS-3/Galileo/GPS all-in-view and PPP time transfer with the consideration of satellite clock biases

On theoretical and practical analyses of BDS-3/Galileo/GPS all-in-view and PPP time transfer with the consideration of satellite clock biases

Near real-time multi-GNSS orbits, clock and observable-specific biases at Wuhan University

Near real-time multi-GNSS orbits, clock and observable-specific biases at Wuhan University

Grey modelling and real-time forecasting for the approximate non-homogeneous white exponential law BDS clock bias sequences

Precise forecasting of satellite clock bias is crucial for ensuring service quality and enhancing the efficiency of real-time precise point positioning (PPP).The grey model with many benefits is an excellent choice for predicting real-time clock bias. However, the absolute prediction error of a small number of satellites is very high in actual forecasting process. In order to address this issue, a non-homogeneous white exponential law grey model has been constructed specifically for predicting clock bias sequences with non-homogeneous class ratio approximating constants. Considering that any model is difficult to apply to different kinds of satellite clocks and clock bias signals, an adaptive selection strategy for forecast model is proposed to ensure more excellent prediction accuracy. Afterwards, a prediction scenario based on the observed products of the BeiDou satellite navigation system (BDS) is created to demonstrate the effectiveness of the approach described in this article. The outcomes of the method are then compared with those of a single grey model and the ultra-rapid predicted products. The outcomes demonstrate that this strategy’s prediction accuracy is less than 1 ns/day and that its prediction uncertainty is much decreased, which may improve data selection for real-time applications like real-time kinematics (RTK) and PPP.

Improvement of BDS-3 inter-frequency clock bias estimation and its application in multi-frequency precise point positioning

BDS-3 broadcasts five civilian signals, establishing a fundamental basis for multi-frequency real-time precise point positioning (RT PPP). Nevertheless, the existence of inter-frequency clock bias (IFCB) renders the current satellite clock error product unsuitable for multi-frequency PPP processing. Consequently, there is a critical need to conduct a thorough analysis of BDS-3 IFCBs and propose real-time service methods for RT PPP users. In this study, 8-day BDS-3 multi-frequency data obtained from 130 International GNSS Service (IGS) stations are employed to scrutinize the characteristics of BDS-3 IFCBs and validate the proposed real-time service method. The results disclose a noticeable disparity between the constant part of IFCBs computed using the differential code bias (DCB) product and those estimated from observations. The time-varying parts of different IFCBs, estimated using various combinations, are examined using the Fast Fourier Transform (FFT). The outcomes indicate that these IFCBs exhibit identical periods of 12, 6, and 4 h, although their fourth-period terms differ. To model the sequences of IFCBs, a polynomial with a fourth-order harmonic model is utilized, and the coefficients of the fitted model are subsequently transmitted for RT PPP processing. Experimental results show that the predicted accuracies of IFCBs for most satellites exceed 90 %, albeit with a noticeable decline as the prediction time increases. When applied in RT PPP for 20 IGS stations, the method significantly shortens the convergence time in dual-frequency and triple-frequency RT PPP when predicted IFCBs are provided. In the B1C/B2a, B1C/B3I, and B1I/B2a dual-frequency combinations, the average convergence times for RT PPP are reduced by 58 %, 46 %, and 59 %, respectively. In the B1I/B2a/B3I triple-frequency combinations, it is reduced by 48 %.

GNSS Spoofer Localization With Counterfeit Clock Bias Observables on a Mobile Platform

GNSS Spoofer Localization With Counterfeit Clock Bias Observables on a Mobile Platform

M_IFCB: a MATLAB-based software for multi‑GNSS inter‑frequency clock bias estimation and forecast

M_IFCB: a MATLAB-based software for multi‑GNSS inter‑frequency clock bias estimation and forecast

Global Navigation Satellite System Receiver Positioning in Harsh Environments via Clock Bias Prediction by Empirical Mode Decomposition and Back Propagation Neural Network Method.

This paper proposes a novel method to improve the clock bias short-term prediction accuracy of navigation receivers then solve the problem of low positioning accuracy when the satellite signal quality deteriorates. Considering that the clock bias of a navigation receiver is equivalent to a virtual satellite, the predicted value of clock bias is used to assist navigation receivers in positioning. Consequently, a combined prediction method for navigation receiver clock bias based on Empirical Mode Decomposition (EMD) and Back Propagation Neural Network (BPNN) analysis theory is demonstrated. In view of systematic errors and random errors in the clock bias data from navigation receivers, the EMD method is used to decompose the clock bias data; then, the BPNN prediction method is used to establish a high-precision clock bias prediction model; finally, based on the clock bias prediction value, the three-dimensional positioning of the navigation receiver is realized by expanding the observation equation. The experimental results show that the proposed model is suitable for clock bias time series prediction and providing three-dimensional positioning information meets the requirements of navigation application in the harsh environment of only three satellites.

An adaptive robust strategy based on hypothesis testing for satellite clock bias short-term forecasting

The study of short-term forecasting of satellite clock bias (SCB) is important to promote the development of real-time precise point positioning, and the Kalman filter model has certain advantages over other models in the single forecast model. However, the filtering performance will be degraded by the model bias, and a fading factor is constructed to control the effect brought by the model bias. Considering that the fading factor may cause the covariance matrix to be abnormally inflated or even invalid when the observed information is unreliable, the chi-square test is introduced as a test indicator. At the current epoch moment, the fading factor or robust estimation is conditionally applied based on the result of the hypothesis test. An improved IGGIII weight function is used by the robust estimation, which simplifies the solution of the parametric robust solution. BeiDou satellite navigation system-3 satellite clock bias data with different clock types were selected for the analysis of fitting accuracy and forecasting accuracy, and the experimental results showed that the proposed algorithm can well eliminate the anomalous perturbation phenomenon caused by model deviation and improve the fitting accuracy. The comparison of forecast accuracy between the proposed strategy and GM(1,1), quadratic polynomial, and autoregressive integrated moving average (ARIMA) models at 3, 6, and 12 h intervals reveals that the proposed strategy consistently demonstrates optimal forecast accuracy.

Enhancing satellite clock bias prediction in BDS with LSTM-attention model

Enhancing satellite clock bias prediction in BDS with LSTM-attention model

Time transfer via single‐record TDoA measurements of GNSS satellites using direct cross‐correlation and relative pilot code phases

AbstractRadar systems are evolving towards distributed receiver networks. As individual stations might be separated too far to install a cable link, novel methods are required to synchronise individual data records in the time domain. State‐of‐the‐art GNSS receivers disciplining a highly stable oscillator are able to output a timing signal with several nanosecond accuracy solely using non‐proprietary signals. However, they typically require a stable environment and become a major cost factor for receiver networks with a high number of nodes. A method is presented to passively synchronise data records via GNSS raw signals in a single record requiring only a GNSS antenna, an analogue‐to‐digital converter and computation hardware. The clock bias is estimated via the common view method with either full raw signal correlation or software‐based code correlation of individual signals from the GPS, Galileo and BeiDou constellation with sub‐nanosecond precision.

Clock-modeling-constrained Epoch Relative Positioning for GPS coseismic displacement estimation

High-rate GNSS technology is invaluable for capturing surface displacements. However, vertical displacement is strongly linked to zenith tropospheric delay (ZTD) and receiver clock bias, compromising accuracy and impeding the detection of weak seismic waves. Some GNSS stations, fortunately, feature high-stability oscillators, enabling receiver clock modeling instead of epoch-wise estimation. This paper introduces an epoch relative positioning approach (ERP)with receiver clock modeling (CMC-ERP) to enhance coseismic displacement accuracy. Applied to earthquakes in Japan and the United States, the method improves vertical displacement accuracy by 24% to 61%. Furthermore, P-wave arrival times are determined by processing displacement sequences extracted through both CMC-ERP and ERP methods using STA/LTA. Compared to theoretical arrival times calculated by TauP software, CMC-ERP accuracy is enhanced by 74%–99%, further confirming its effectiveness.

Smart forwarding deceptive jamming distribution optimal algorithm

AbstractWith the frequent occurrence of drone black flying in large stadiums and airports, the requirement of precise electromagnetic interference to achieve unmanned aerial vehicle (UAV) displacement and forced landing in these protected area became urgent. Since traditional suppression jamming will affect normal communication, and forwarding deceptive jamming has coverage hole, a smart forwarding deceptive jamming distribution optimal algorithm (SFDJDO) is proposed. It gives a mapping error scale factor and the optimal distribution of multistation forwarding equivalent mapping to solve the problem of distortion on the mapping scale caused by different distribution methods and reduces the influence of the mapping errors and the differences between the virtual and real point neighborhoods of the jamming source. A comparison of the proposed SFDJDO method to the existing jamming source distribution optimisation method is conducted in the aspect of area mapping and trajectory mapping. The findings reveal that when the GNSS receiver clock bias is within the capture range, SFDJDO demonstrates significant enhancements in mapping precision and jamming success rates.

Real-time high-precision baseline measurement of satellite formation flying based on GNSS

With the establishment of the Chinese space station, a series of space science missions will be conducted in its vicinity. One of the extended tasks for the in-orbit service of space station is the formation flying of small satellites centered around the space station. Satellite formations can perform simultaneous three-dimensional observations of the space station, generating three-dimensional images and monitoring and assessing the status of critical components of the space station. The real-time and accurate relative position measurement is one of the key issues in formation flying. It is a fundamental prerequisite for maintaining and reconfiguring formation configurations, collision avoidance and safety assurance. GNSS-based relative positioning is a low-cost and high-precision measurement method, which is not constrained by light, weather, or relative attitude of satellites. This study introduces a novel approach to determine the relative position of satellites based on single-epoch Global Navigation Satellite System (GNSS) carrier phase difference measurements. Unlike traditional methods, the proposed technique eliminates the need for precise ephemeris and clock bias files and does not require historical observation data. The algorithm avoids the complexity associated with full cycle ambiguity jumps, facilitating real-time, high-precision calculations of relative position baseline vectors. Special attention is given to the influence of Geostationary Earth Orbit (GEO) satellites in the BeiDou Navigation Satellite System (BDS), and measures are taken to mitigate their impact on measurement accuracy by adjusting their observation weights. Our newly developed GNSS-based real-time measurement module, designed for high-quality GNSS signal reception and data communication, was tested on terrestrial and simulated low-orbit platforms. Remarkably, over baselines ranging from 10 m to 9.3 km, while traditional pseudorange differential measurements showed errors up to 1.5571 m, our proposed method consistently held errors under 5 cm and ensured computational speeds within 0.1 s per epoch. High-dynamic zero-baseline tests further validated its potential, with errors less than 1 cm. The innovations encapsulated in this work, resonating with the evolving trends of miniaturized and scalable satellites, present a cost-efficient and real-time solution for inter-satellite relative position measurement. This promises a new horizon in satellite formation technology, with future endeavors focusing on on-orbit experiments.

BDS-3 six-frequency precise point positioning: effects of receiver-dependent inter-frequency clock bias and multi-frequency contributions

We find that there is time-varying bias at the receiver in BDS-3 multi-frequency phase observations, which will lead to receiver-dependent inter-frequency clock bias (RIFCB) and damage the rigor of BDS-3 multi-frequency precise point positioning (PPP) model. A unified RIFCB correction method compatible with uncombined and ionospheric-free combined PPP models using any BDS-3 frequencies is proposed. The contributions of multi-frequency integration to BDS-3 static and kinematic PPP performance are evaluated. The results indicate that the RIFCB amplitude can reach 1 dm. If the RIFCB correction is ignored, the phase observation residuals present a systematic bias. RIFCB has potential effects on precise time transfer, ionospheric monitoring, and fractional cycle bias estimation. Experimental results show that the long-term frequency stability of time transfer can be improved by correcting RIFCB. The joint use of all BDS-3 six-frequency signals can significantly shorten the convergence time, and the positioning accuracy can also be slightly improved.

Improved SSA-Based GRU Neural Network for BDS-3 Satellite Clock Bias Forecasting.

Satellite clock error is a key factor affecting the positioning accuracy of a global navigation satellite system (GNSS). In this paper, we use a gated recurrent unit (GRU) neural network to construct a satellite clock bias forecasting model for the BDS-3 navigation system. In order to further improve the prediction accuracy and stability of the GRU, this paper proposes a satellite clock bias forecasting model, termed ITSSA-GRU, which combines the improved sparrow search algorithm (SSA) and the GRU, avoiding the problems of GRU's sensitivity to hyperparameters and its tendency to fall into local optimal solutions. The model improves the initialization population phase of the SSA by introducing iterative chaotic mapping and adopts an iterative update strategy based on t-step optimization to enhance the optimization ability of the SSA. Five models, namely, ITSSA-GRU, SSA-GRU, GRU, LSTM, and GM(1,1), are used to forecast the satellite clock bias data in three different types of orbits of the BDS-3 system: MEO, IGSO, and GEO. The experimental results show that, as compared with the other four models, the ITSSA-GRU model has a stronger generalization ability and forecasting effect in the clock bias forecasting of all three types of satellites. Therefore, the ITSSA-GRU model can provide a new means of improving the accuracy of navigation satellite clock bias forecasting to meet the needs of high-precision positioning.

Asymptotically Efficient Solutions for TOA-FOA Localization With Clock Bias and Drift

Asymptotically Efficient Solutions for TOA-FOA Localization With Clock Bias and Drift

ASSESSMENT OF STEC ESTIMATION QUALITY USING GNSS PPP FIXED

Abstract. GNSS (Global Navigation Satellite System) data can be used for geodetic remote sensing, particularly for monitoring the ionosphere in the context of Space Weather. One of the important parameters derived from GNSS measurements for ionospheric analysis is the Slant Total Electron Content (STEC). By utilizing GNSS data from multiple frequencies or even a single frequency, the STEC can be computed using an appropriated linear combination, like geometry free. However, when computing an ionospheric gradient between two IPP (Ionospheric Pierce Point) from the same satellite, the precision of the STEC estimate can become a limiting factor. In some cases, the uncertainty in the estimate may be greater than the actual gradient value itself. This poses challenges, especially for augmentation systems like GBAS (Ground Based Augmentation System), where accurate ionospheric gradients are crucial. An alternative approach to improve these limitations is to estimate the STEC using a different approach, like Precise Point Positioning (PPP). For such case, the coordinates of the GNSS stations are constrained to known values (PPP-Fixed), while other parameters such as clock biases, tropospheric delays, and ionospheric delays (including STEC) can be estimated. The results of an experiment carried out to assess the quality of STEC for such application are presented and have shown good results. Ionospheric gradients are agreed in the mm level.

Adverse effects of receiver clock bias and drift on NavIC user position coordinates and their mitigation

We investigated the effects of receiver clock bias and drift on NavIC receiver position coordinates at a low latitude station and proposed a mitigation technique. For this, Five weeks data of Accord IRNSS-GPS-SPS (AIGS) receiver are considered. Error in each position coordinates (X, Y and Z) is estimated and observed that the maximum error occurred in user position Z-coordinate. CEP for 2D position is analyzed and observed that the Circular Error Probability (CEP) values are high in Z coordinate of YZ and ZX planes. Further, it is noticed that the timing of sudden enhancement of both clock bias and drift parameters coincides with the periodic anomaly of the X, Y and Z coordinates. The error in individual position coordinates is minimized by applying 6th order Butterworth low pass filter resulting in improved position accuracy. If such errors are not mitigated, the position estimation of the receiver becomes highly erroneous.

Approximate Maximum-Likelihood RIS-Aided Positioning

A reconfigurable intelligent surface (RIS) allows a reflection transmission path between a base station (BS) and user equipment (UE). In wireless localization, this reflection path aids in positioning accuracy, especially when the line-of-sight (LOS) path is subject to severe blockage and fading. In this paper, we develop a RIS-aided positioning framework to locate a UE in environments where the LOS path may or may not be available. We first estimate the RIS-aided channel parameters from the received signals at the UE. To infer the UE position and clock bias from the estimated channel parameters, we propose a fusion method consisting of weighted least squares over the estimates of the LOS and reflection paths. We show that this approximates the maximum likelihood estimator under the large-sample regime and when the estimates from different paths are independent. We then optimize the RIS phase shifts to improve the positioning accuracy and extend the proposed approach to the case with multiple BSs and UEs. We derive Cramér–Rao bound (CRB) and demonstrate numerically that our proposed positioning method approaches the CRB.

Reconstructed estimation method of the multi-frequency GNSS inter-frequency clock bias

In consideration of contributions from both carrier phase and pseudorange observations during computation, this study introduces a reconstructed method for estimating the multi-frequency global navigation satellite system (GNSS) inter-frequency clock biases (IFCB). Diverging from conventional approaches that separately calculate the time-varying and constant parts of IFCBs using carrier phase and pseudorange observations, the reconstructed method directly utilizes their combination to estimate satellite IFCBs. To validate the efficacy of the presented approach, 7 d observations from 87 International GNSS Service (IGS) stations are analyzed, with a specific focus on triple-frequency GPS, multi-frequency BDS-3, and Galileo IFCBs, aiming to scrutinize their distinctive characteristics. Furthermore, the performances of satellite IFCB estimation are investigated in both precise point positioning (PPP) and single-point positioning (SPP) using 35 IGS stations over 3 d. The results demonstrate that IFCBs of GPS BLOCK IIIA satellites exhibit centimeter-level variations, distinguishing them from BLOCK IIF counterparts. The Galileo IFCBs vary from millimeter to centimeter level, while those of BDS-3 reach a centimeter level. These variations significantly impact GPS PPP convergence performances but have minimal effects on Galileo and BDS-3 PPP. SPP performances are slightly enhanced when the time-varying IFCB part are taken into account. Additionally, we note disparities in the constant parts of satellite IFCBs computed with differential code bias (DCB) products, reconstructed, and pseudorange observation-based methods, particularly for BDS-3 C2I/C6I-C1P/C5P and C2I/C6I-C1P/C6I combinations. The differences of IFCB estimated with different strategies, SPP and PPP performances show that the reconstructed method is better than others, and the IFCB accuracy decreases when computed with satellite DCB products.