Wuhan University
School of Geodesy and Geomatics
Since the Selective Availability was turned off, the velocity and acceleration can be determined accurately with a single GPS receiver using raw Doppler measurements. The carrier-phase-derived Doppler measurements are normally used to... more
Since the Selective Availability was turned off, the velocity and acceleration can be determined accurately with a single GPS receiver using raw Doppler measurements. The carrier-phase-derived Doppler measurements are normally used to determine velocity and acceleration when there is no direct output of the raw Doppler observations in GPS receivers. Due to GPS receiver clock drifts, however, a GPS receiver clock jump occurs when the GPS receiver clock resets itself (typically with 1 ms increment/ decrement) to synchronize with the GPS time. The clock jump affects the corresponding relationship between measurements and their time tags, which results in non-equidistant measurement sampling in time or incorrect time tags. This in turn affects velocity and acceleration determined for a GPS receiver by the conventional method which needs equidistant carrier phases to construct the derived Doppler measurements. To overcome this problem, an improved method that takes into account, GPS receiver clock jumps are devised to generate non-equidistantderived Doppler observations based on non-equidistant carrier phases. Test results for static and kinematic receivers, which are obtained by using the conventional method without reconstructing the equidistant continuous carrier phases, show that receiver velocity and acceleration suffered significantly from clock jumps. An airborne kinematic experiment shows that the greatest impact on velocity and acceleration reaches up to 0.2 m/s, 0.1 m/s 2 for the horizontal component and 0.5 m/s, 0.25 m/s 2 for the vertical component. Therefore, it can be demonstrated that velocity and acceleration measurements by using a standalone GPS receiver can be immune to the influence of GPS receiver clock jumps with the proposed method.
[1] Nowadays more and more high-rate real-time GPS data become available that provide a great opportunity to contribute to earthquake early warning (EEW) system in terms of capturing regional surface displacements, as an independent... more
[1] Nowadays more and more high-rate real-time GPS data become available that provide a great opportunity to contribute to earthquake early warning (EEW) system in terms of capturing regional surface displacements, as an independent information source, useful for promptly estimating the magnitude of large destructive earthquake. In our study, we demonstrate the performance of the real-time ambiguity-fixed precise point positioning (PPP) approach using 5 Hz GPS data collected during El Mayor-Cucapah earthquake (Mw 7.2, 4 April 2010). The PPP-based displacements show to agree with accelerometer-based displacement at centimeter level. The key for successfully obtaining high precision displacements is the efficient ambiguity resolution. PPP with ambiguity fixing can result in correct permanent co-seismic offsets and correct recovery of moment magnitude and fault slip inversion at levels comparable to post-processing.
- by Bofeng Guo
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Real-time precise GNSS satellite orbit and clock products are the prerequisite of real-time GNSS-based applications. To obtain real-time GNSS satellite orbit and clock, three approaches exist currently, namely, the prediction-estimation... more
Real-time precise GNSS satellite orbit and clock products are the prerequisite of real-time GNSS-based applications. To obtain real-time GNSS satellite orbit and clock, three approaches exist currently, namely, the prediction-estimation approach, the prediction-correction approach and the estimation approach. Different from the former two approaches, which are based on the predicted orbit, the last approach estimates orbit and clock in an integrated way, thus it is the most rigorous one. However, the simultaneously estimation of both orbit and clock parameters makes it very time-consuming. In this contribution, the extended Kalman filter with parallel computation proposed for real-time GPS satellite clock estimation (Gao, et al., 2017) is introduced to improve the computational efficiency. In the introduced method, the epoch observations are processed sequentially and the covariance update process is accelerated with the Open Multi-Processing. With observation data from about 70 globally distributed stations spanning days 001-003 of 2018, the real-time GPS orbit and clock are estimated for validation. The epoch average processing time of the introduced method achieves around 2.9 s on average with 16 CPU cores, while that of the traditional method without Open Multi-Processing is about 4.1 s. When compare the estimated orbit and clock to the IGS final products, the daily constellation-mean RMS of orbit achieve 2.7, 5.7, 4.9 cm for the radial, along-track
In this paper, the admittance function between seafloor undulations and vertical gravity gradient anomalies were derived. Based on this admittance function, bathymetry model of 1 minute resolution were predicted from vertical gravity... more
In this paper, the admittance function between seafloor undulations and vertical gravity gradient anomalies were derived. Based on this admittance function, bathymetry model of 1 minute resolution were predicted from vertical gravity gradient anomalies and ship soundings in the experimental area from northwest Pacific. The accuracy of the model is evaluated using ship soundings and existing models, including ETOPO1, GEBCO, DTU10 and V15.1 from SIO. The model’s STD is 69.481m, comparable with V15.1 which generally believed to have the highest accuracy.
- by Minzhang HU
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There are different ways to construct adaptive Kalman filtering (AKF) algorithms. This paper proposes an innovative way to simultaneously estimate the variance matrix R of the measurement vector and the variance matrix Q of the process... more
There are different ways to construct adaptive Kalman
filtering (AKF) algorithms. This paper proposes an
innovative way to simultaneously estimate the variance
matrix R of the measurement vector and the variance
matrix Q of the process noise vector based on the
variance-covariance component estimation by taking the
advantages of the measurement residuals and the process
noise residuals (Wang, 1997, 2009; Wang et al, 2009)
and the measurement redundancy contribution (Ou,
1989). The core of the novel AKF algorithm lies in the
projection of the system innovation vector into the three
groups of residuals: the residuals of the measurement
vector, the residuals of the process noise vector and the
residuals of the predicted state vector exclusive of the
effect of the process noise. The simulated and real GPS
data in kinematic relative positioning mode were used to
demonstrate the performance of the proposed adaptive
Kalman filter. The results from the simulated datasets
confirm to the simulated variance-covariance
components well. The results from real kinematic GPS
datasets are also provided and discussed.
filtering (AKF) algorithms. This paper proposes an
innovative way to simultaneously estimate the variance
matrix R of the measurement vector and the variance
matrix Q of the process noise vector based on the
variance-covariance component estimation by taking the
advantages of the measurement residuals and the process
noise residuals (Wang, 1997, 2009; Wang et al, 2009)
and the measurement redundancy contribution (Ou,
1989). The core of the novel AKF algorithm lies in the
projection of the system innovation vector into the three
groups of residuals: the residuals of the measurement
vector, the residuals of the process noise vector and the
residuals of the predicted state vector exclusive of the
effect of the process noise. The simulated and real GPS
data in kinematic relative positioning mode were used to
demonstrate the performance of the proposed adaptive
Kalman filter. The results from the simulated datasets
confirm to the simulated variance-covariance
components well. The results from real kinematic GPS
datasets are also provided and discussed.
- by Jiming Guo and +1
- •
There are different ways to construct adaptive Kalman filtering (AKF) algorithms. This paper proposes an innovative way to simultaneously estimate the variance matrix R of the measurement vector and the variance matrix Q of the... more
There are different ways to construct adaptive Kalman
filtering (AKF) algorithms. This paper proposes an
innovative way to simultaneously estimate the variance
matrix R of the measurement vector and the variance
matrix Q of the process noise vector based on the
variance-covariance component estimation by taking the
advantages of the measurement residuals and the process
noise residuals (Wang, 1997, 2009; Wang et al, 2009)
and the measurement redundancy contribution (Ou,
1989). The core of the novel AKF algorithm lies in the
projection of the system innovation vector into the three
groups of residuals: the residuals of the measurement
vector, the residuals of the process noise vector and the
residuals of the predicted state vector exclusive of the
effect of the process noise. The simulated and real GPS
data in kinematic relative positioning mode were used to
demonstrate the performance of the proposed adaptive
Kalman filter. The results from the simulated datasets
confirm to the simulated variance-covariance
components well. The results from real kinematic GPS
datasets are also provided and discussed.
filtering (AKF) algorithms. This paper proposes an
innovative way to simultaneously estimate the variance
matrix R of the measurement vector and the variance
matrix Q of the process noise vector based on the
variance-covariance component estimation by taking the
advantages of the measurement residuals and the process
noise residuals (Wang, 1997, 2009; Wang et al, 2009)
and the measurement redundancy contribution (Ou,
1989). The core of the novel AKF algorithm lies in the
projection of the system innovation vector into the three
groups of residuals: the residuals of the measurement
vector, the residuals of the process noise vector and the
residuals of the predicted state vector exclusive of the
effect of the process noise. The simulated and real GPS
data in kinematic relative positioning mode were used to
demonstrate the performance of the proposed adaptive
Kalman filter. The results from the simulated datasets
confirm to the simulated variance-covariance
components well. The results from real kinematic GPS
datasets are also provided and discussed.
- by Jianguo Wang and +1
- •
The noise in GPS coordinate time series is known to follow a power-law noise model with different components (white noise, flicker noise, and random walk). This work proposes an algorithm to estimate the white noise statistics, through... more
The noise in GPS coordinate time series is known to follow a power-law noise model with different components (white noise, flicker noise, and random walk). This work proposes an algorithm to estimate the white noise statistics, through the decomposition of the GPS coordinate time series into a sequence of sub time series using the empirical mode decomposition algorithm. The proposed algorithm estimates the Hurst parameter for each sub time series and then selects the sub time series related to the white noise based on the Hurst parameter criterion. Both simulated GPS coordinate time series and real data are employed to test this new method; the results are compared to those of the standard (CATS software) maximum-likelihood (ML) estimator approach. The results demonstrate that this proposed algorithm has very low computational complexity and can be more than 100 times faster than the CATS ML method, at the cost of a moderate increase of the uncertainty (∼5%) of the white noise amplitude. Reliable white noise statistics are useful for a range of applications including improving the filtering of GPS time series, checking the validity of estimated coseismic offsets, and estimating unbiased uncertainties of site velocities. The low complexity and computational efficiency of the algorithm can greatly speed up the processing of geodetic time series.
In the analysis of some specific time series (e.g., Global Positioning System coordinate time series, chaotic time series, human brain imaging), the noise is generally modeled as a sum of a power-law noise and white noise. Some existing... more
In the analysis of some specific time series (e.g., Global Positioning System coordinate time series, chaotic time series, human brain imaging), the noise is generally modeled as a sum of a power-law noise and white noise. Some existing softwares estimate the amplitude of the noise components using convex optimization (e.g., Levenberg-Marquadt) applied to a log-likelihood cost function. This work studies a novel cost function based on an approximation of the negentropy. Restricting the study to simulated time series with flicker noise plus white noise, we demonstrate that this cost function is convex. Then, we show thanks to numerical approximations that it is possible to obtain an accurate estimate of the amplitude of the colored noise for various lengths of the time series as long as the ratio between the colored noise amplitude and the white noise is smaller than 0.6. The results demonstrate that with our proposed cost function we can improve the accuracy by around 5% when compared with the log-likelihood ones with simulated time series shorter than 1400 samples.
In this paper, we investigate the performance of different position estimation methods which make use of time-of-arrival (TOA) of ultra wideband (UWB) signals for low cost/low complexity UWB systems. We first propose a simple and robust... more
In this paper, we investigate the performance of different position estimation methods which make use of time-of-arrival (TOA) of ultra wideband (UWB) signals for low cost/low complexity UWB systems. We first propose a simple and robust two-stage, non-coherent TOA estimation approach. We then explore positioning algorithms utilizing both non-iterative and iterative techniques. A review of positioning in distributed networks is also performed and a positioning algorithm is proposed for node location in multi-hop distributed networks. Furthermore, we consider smoothing techniques to improve accuracy when tracking moving objects and we propose the use of sinc functions to smooth the estimate of the mobile position in order to achieve both good accuracy and low complexity. The system modelled and investigated corresponds to an actual test environment in a ski field where skiers are tracked.
- by Kegen Yu and +1
- •
- Engineering, Technology, Signal Processing, Location Tracking
Over the last years the scientific community has been using the auto regressive moving average (ARMA) model in the modeling of the noise in GPS time series (daily solution). This work starts with the investigation of the limit of the ARMA... more
Over the last years the scientific community has been using the auto regressive moving average (ARMA) model in the modeling of the noise in GPS time series (daily solution). This work starts with the investigation of the limit of the ARMA model which is widely used in signal processing when the measurement noise is white. Since a typical Global Positioning System (GPS) time series consists of geophysical signals (e.g., seasonal signal) and stochastic processes (e.g., coloured and white noise), the ARMA model may be inappropriate. Therefore, the application of the fractional auto regressive integrated moving average (FARIMA) model is investigated. The simulation results using simulated time series as well as real GPS time series from a few selected stations around Australia show that the FARIMA model fits the time series better than other models when the coloured noise is larger than the white noise. The second fold of this work focuses on fitting the GPS time series with the family of Levy α-stable distributions. Using this distribution, a hypothesis test Dr. Jean-Philippe Montillet formerly at the Australian National University, now at the Cascadia Hazards Institute, is developed to eliminate effectively coarse outliers from GPS time series, achieving better performance than using the rule of thumb of n standard deviations (with n chosen empirically).
- by Kegen Yu and +1
- •
- Applied Mathematics, Geology, Mathematical Geosciences
The paper provides an evaluation of a noncoherent tWB system, which is suitable for low complexity, cost and data rate tWB wireless sensor networks with
This paper presents a new approach for smoothing long time series of position estimates of ground GNSS (global navigation satellite system) receivers. The fractional Brownian motion (fBm) model is employed to describe the position... more
This paper presents a new approach for smoothing long time series of position estimates of ground GNSS (global navigation satellite system) receivers. The fractional Brownian motion (fBm) model is employed to describe the position coordinate estimates that have long-range dependencies. A new and low-complexity method is proposed to estimate the Hurst parameter and the simulation results show that the new method achieves good accuracy and low complexity. A modified leaky least mean squares (ML-LMS) estimator is proposed to filter the long time series of the position coordinate estimates, which uses the Hurst parameter estimates to update the filter tap weights. Simulation results demonstrate that this ML-LMS estimator outperforms the classic LMS estimator considerably in terms of both accuracy and convergence.
Fractional Brownian motion (fBm) is an important mathematical model for describing a range of phenomena and processes. The properties of discrete time fBm (dfBm) when m equals 1 and 2 have been reported in the literature. This paper... more
Fractional Brownian motion (fBm) is an important mathematical model for describing a range of phenomena and processes. The properties of discrete time fBm (dfBm) when m equals 1 and 2 have been reported in the literature. This paper focuses on analysis of auto-covariance matrix of the m-th order (m > 2) of a dfBm process and the error associated with the approximation of a large dimensional auto-covariance matrix. Applying matrix theory and analysis, we also generalize the asymptotic properties of the eigenvalues of the auto-covariance matrix. Based on the analysis, two theorems and one lemma are proposed and their proofs are provided.
- by Jean-Philippe Montillet and +1
- •
This work deals with the development of pre-filtering techniques for low-cost devices using high data rate communications. Many positioning algorithms have been recently revisited in a centralized architecture scenario, where a cheap... more
This work deals with the development of pre-filtering techniques for low-cost devices using high data rate communications. Many positioning algorithms have been recently revisited in a centralized architecture scenario, where a cheap Mobile Sensor is surrounded by N Base Stations. The overview of the system is composed of two blocks: a Smoothing Filters and a Positioning Block. In the Smoothing Filters block, different algorithms such as smoothing filter, Recursive Least Squares and Maximum-Likelihood are developed to process multiple Time-of-Arrival measurements before triangulating the position of the Mobile Sensor. The positioning algorithms are the Taylor Series, Direct Method and Spherical Interpolation.
- by Jean-Philippe Montillet and +1
- •
- Mobile Sensors, Time of Arrival
This paper focuses on location accuracy enhancement and performance comparison for global navigation satellite systems (GNSS) based positioning in light multipath propagation environments. The well-known linear iterative least-squares... more
This paper focuses on location accuracy enhancement and performance comparison for global navigation satellite systems (GNSS) based positioning in light multipath propagation environments. The well-known linear iterative least-squares (LS) estimator algorithm performs the location of a ground (mobile) terminal. A sliding window and subspace decomposition (SD) based approach is proposed to generate coefficients for weighting the pseudorange measurements between the ground receiver and a set of satellites. Simulation results with real pseudorange measurement data (recorded at two different scenarios) demonstrate that the proposed SD-based LS algorithm significantly outperforms the existing LS algorithm, with root mean square error (RMSE) reduced by more than 0.7m.
With the recent advances in the theory of fractional Brownian motion (fBm), this model is used to describe the position coordinate estimates of Global Navigation Satellite System (GNSS) receivers that have long-range dependencies. The... more
With the recent advances in the theory of fractional Brownian motion (fBm), this model is used to describe the position coordinate estimates of Global Navigation Satellite System (GNSS) receivers that have long-range dependencies. The Modified Leaky Least Mean Squares (ML-LMS) algorithms are proposed to filter the long time series of the position coordinate estimates, which uses the Hurst parameter estimates to update the filter tap weights. Simulation results using field measurements demonstrate that these proposed modified leaky least mean squares algorithms can outperform the classical LMS filter considerably in terms of accuracy (mean squared error) and convergence. We also deal with the case study where our proposed algorithms outperform the leaky LMS. The algorithms are tested on simulated and real measurements.
- by Jean-Philippe Montillet and +1
- •
Accuracy of ordinary sensor node localization in wireless sensor networks mainly depends on the signal parameter such as time-of-arrival and signal strength estimation errors and the accuracy of the anchor node locations. In this paper a... more
Accuracy of ordinary sensor node localization in wireless sensor networks mainly depends on the signal parameter such as time-of-arrival and signal strength estimation errors and the accuracy of the anchor node locations. In this paper a lowcomplexity but efficient algorithm is derived to improve anchor location accuracy in the presence of both anchor-to-anchor distance and AOA estimates and GPS measurements. Also, a Lenvenberg-Marquardt (LM) optimization based algorithm is developed for accuracy improvement when anchor-to-anchor distance estimates and GPS measurements are provided. Further, we derive the Cramer-Rao lower bound (CRLB) to benchmark the anchor position accuracy. To our knowledge, improving anchor node location accuracy and deriving the CRLB in the presence of both GPS and anchor-to-anchor measurements in 3-D scenarios are not reported in the literature. Simulation results demonstrate that the proposed approaches can improve the anchor position accuracy substantially and that the accuracy of the two developed algorithms approaches the corresponding CRLB.
This appendix provides an analytical analysis of the hyperbolic navigation problem for the 2D case with three base stations. The problem may be defined either as a navigation problem (receiver in the mobile device) or as a tracking... more
This appendix provides an analytical analysis of the hyperbolic navigation problem for the 2D case with three base stations. The problem may be defined either as a navigation problem (receiver in the mobile device) or as a tracking problem (transmitter in the mobile device). In either case, it is assumed that the receiver measures the pseudo-range to the three base stations and from these data the position of the mobile device is sought.
- by Kegen Yu
- •
In this study the focus is on ocean surface altimetry using the signals transmitted from GNSS (Global Navigation Satellite System) satellites. A low-altitude airborne experiment was recently conducted off the coast of Sydney. Both a LiDAR... more
In this study the focus is on ocean surface altimetry using the signals transmitted from GNSS (Global Navigation Satellite System) satellites. A low-altitude airborne experiment was recently conducted off the coast of Sydney. Both a LiDAR experiment and a GNSS reflectometry (GNSS-R) experiment were carried out in the same aircraft, at the same time, in the presence of strong wind and rather high wave height. The sea surface characteristics, including the surface height, were derived from processing the LiDAR data. A two-loop iterative method is proposed to calculate sea surface height using the relative delay between the direct and the reflected GNSS signals. The preliminary results indicate that the results obtained from the GNSS-based surface altimetry deviate from the LiDAR-based results significantly. Identification of the error sources and mitigation of the errors are needed to achieve better surface height estimation performance using GNSS signals.
- by Kegen Yu
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Global Navigation Satellite System reflectometry (GNSS-R) has recently drawn significant attention since it can be employed in a range of applications including sea state, ocean altimetry, soil moisture measurement, and disaster (e.g.... more
Global Navigation Satellite System reflectometry (GNSS-R) has recently drawn significant attention since it can be employed in a range of applications including sea state, ocean altimetry, soil moisture measurement, and disaster (e.g. flooding, bushfire, and earthquake) monitoring. Although research on GNSS-R in the past two decades has made advances, there are no (or few) real applications of the technique. This is mainly because GNSS-R is still not a mature technique, there are no satellite-borne missions, there are few systematic airborne experiments, and GNSS-R is not yet able to provide information with high enough resolution and reliability. The authors are investigating new approaches to improve the performance of the GNSSbased geophysical parameter estimation. This paper focuses on the sea surface roughness estimation through an analysis of the reflected signal power. In particular, the theoretical modelling of the sea wave and surface scattering is studied in detail. Solution-level and waveform-level combination techniques are proposed to improve the estimation accuracy through jointly processing the measurements of the reflected signals which are transmitted by multiple GNSS satellites. These combination methods also can be employed for other parameter estimation tasks. Airborne experiments were carried out by a UNSW-owned light aircraft over the sea off the coast of Sydney. The data were logged using the NordNav software receiver which has four front-ends so that the signals arriving at the LHCP (left hand circularly polarized) and RHCP (right hand circularly polarized) antennas could be recorded simultaneously. Both the delay waveforms and delay-Doppler waveforms were generated from the processing of the real data. Theoretical delay waveforms were also generated. The preliminary results confirm that the waveform-matching estimation method is not suited for scenarios where the flight height is below 500 m.
- by Kegen Yu
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