Assessment of commercial network RTK user positioning performance over long inter-station distances

The paper provides an assessment of the performance of commercial Real Time Kinematic (RTK) systems over longer than recommended inter-station distances. The experiments were set up to test and analyse solutions from the i-MAX, MAX and VRS systems being operated with three triangle shaped network cells, each having an average inter-station distance of 69km, 118km and 166km. The performance characteristics appraised included initialization success rate, initialization time, RTK position accuracy and availability, ambiguity resolution risk and RTK integrity risk in order to provide a wider perspective of the performance of the testing systems. ----- ----- The results showed that the performances of all network RTK solutions assessed were affected by the increase in the inter-station distances to similar degrees. The MAX solution achieved the highest initialization success rate of 96.6% on average, albeit with a longer initialisation time. Two VRS approaches achieved lower initialization success rate of 80% over the large triangle. In terms of RTK positioning accuracy after successful initialisation, the results indicated a good agreement between the actual error growth in both horizontal and vertical components and the accuracy specified in the RMS and part per million (ppm) values by the manufacturers. ----- ----- Additionally, the VRS approaches performed better than the MAX and i-MAX when being tested under the standard triangle network with a mean inter-station distance of 69km. However as the inter-station distance increases, the network RTK software may fail to generate VRS correction and then may turn to operate in the nearest single-base RTK (or RAW) mode. The position uncertainty reached beyond 2 meters occasionally, showing that the RTK rover software was using an incorrect ambiguity fixed solution to estimate the rover position rather than automatically dropping back to using an ambiguity float solution. Results identified that the risk of incorrectly resolving ambiguities reached 18%, 20%, 13% and 25% for i-MAX, MAX, Leica VRS and Trimble VRS respectively when operating over the large triangle network. Additionally, the Coordinate Quality indicator values given by the Leica GX1230 GG rover receiver tended to be over-optimistic and not functioning well with the identification of incorrectly fixed integer ambiguity solutions. In summary, this independent assessment has identified some problems and failures that can occur in all of the systems tested, especially when being pushed beyond the recommended limits. While such failures are expected, they can offer useful insights into where users should be wary and how manufacturers might improve their products. The results also demonstrate that integrity monitoring of RTK solutions is indeed necessary for precision applications, thus deserving serious attention from researchers and system providers.

Geometry‐specified troposphere decorrelation for subcentimeter real‐time kinematic solutions over long baselines

Real‐time kinematic (RTK) GPS techniques have been extensively developed for applications including surveying, structural monitoring, and machine automation. Limitations of the existing RTK techniques that hinder their applications for geodynamics purposes are twofold: (1) the achievable RTK accuracy is on the level of a few centimeters and the uncertainty of vertical component is 1.5–2 times worse than those of horizontal components and (2) the RTK position uncertainty grows in proportional to the base‐torover distances. The key limiting factor behind the problems is the significant effect of residual tropospheric errors on the positioning solutions, especially on the highly correlated height component. This paper develops the geometry‐specified troposphere decorrelation strategy to achieve the subcentimeter kinematic positioning accuracy in all three components. The key is to set up a relative zenith tropospheric delay (RZTD) parameter to absorb the residual tropospheric effects and to solve the established model as an ill‐posed problem using the regularization method. In order to compute a reasonable regularization parameter to obtain an optimal regularized solution, the covariance matrix of positional parameters estimated without the RZTD parameter, which is characterized by observation geometry, is used to replace the quadratic matrix of their “true” values. As a result, the regularization parameter is adaptively computed with variation of observation geometry. The experiment results show that new method can efficiently alleviate the model’s ill condition and stabilize the solution from a single data epoch. Compared to the results from the conventional least squares method, the new method can improve the longrange RTK solution precision from several centimeters to the subcentimeter in all components. More significantly, the precision of the height component is even higher. Several geosciences applications that require subcentimeter real‐time solutions can largely benefit from the proposed approach, such as monitoring of earthquakes and large dams in real‐time, high‐precision GPS leveling and refinement of the vertical datum. In addition, the high‐resolution RZTD solutions can contribute to effective recovery of tropospheric slant path delays in order to establish a 4‐D troposphere tomography.

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed the for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newlydeveloped e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.

A Modified inverse integer Cholesky decorrelation method and the performance on ambiguity resolution

One of the research focuses in the integer least squares problem is the decorrelation technique to reduce the number of integer parameter search candidates and improve the efficiency of the integer parameter search method. It remains as a challenging issue for determining carrier phase ambiguities and plays a critical role in the future of GNSS high precise positioning area. Currently, there are three main decorrelation techniques being employed: the integer Gaussian decorrelation, the Lenstra–Lenstra–Lovász (LLL) algorithm and the inverse integer Cholesky decorrelation (IICD) method. Although the performance of these three state-of-the-art methods have been proved and demonstrated, there is still a potential for further improvements. To measure the performance of decorrelation techniques, the condition number is usually used as the criterion. Additionally, the number of grid points in the search space can be directly utilized as a performance measure as it denotes the size of search space. However, a smaller initial volume of the search ellipsoid does not always represent a smaller number of candidates. This research has proposed a modified inverse integer Cholesky decorrelation (MIICD) method which improves the decorrelation performance over the other three techniques. The decorrelation performance of these methods was evaluated based on the condition number of the decorrelation matrix, the number of search candidates and the initial volume of search space. Additionally, the success rate of decorrelated ambiguities was calculated for all different methods to investigate the performance of ambiguity validation. The performance of different decorrelation methods was tested and compared using both simulation and real data. The simulation experiment scenarios employ the isotropic probabilistic model using a predetermined eigenvalue and without any geometry or weighting system constraints. MIICD method outperformed other three methods with conditioning improvements over LAMBDA method by 78.33% and 81.67% without and with eigenvalue constraint respectively. The real data experiment scenarios involve both the single constellation system case and dual constellations system case. Experimental results demonstrate that by comparing with LAMBDA, MIICD method can significantly improve the efficiency of reducing the condition number by 78.65% and 97.78% in the case of single constellation and dual constellations respectively. It also shows improvements in the number of search candidate points by 98.92% and 100% in single constellation case and dual constellations case.

Computed success rates of various carrier phase integer estimation solutions and their comparison with statistical success rates

The success rate of carrier phase ambiguity resolution (AR) is the probability that the ambiguities are successfully fixed to their correct integer values. In existing works, an exact success rate formula for integer bootstrapping estimator has been used as a sharp lower bound for the integer least squares (ILS) success rate. Rigorous computation of success rate for the more general ILS solutions has been considered difficult, because of complexity of the ILS ambiguity pull-in region and computational load of the integration of the multivariate probability density function. Contributions of this work are twofold. First, the pull-in region mathematically expressed as the vertices of a polyhedron is represented by a multi-dimensional grid, at which the cumulative probability can be integrated with the multivariate normal cumulative density function (mvncdf) available in Matlab. The bivariate case is studied where the pull-region is usually defined as a hexagon and the probability is easily obtained using mvncdf at all the grid points within the convex polygon. Second, the paper compares the computed integer rounding and integer bootstrapping success rates, lower and upper bounds of the ILS success rates to the actual ILS AR success rates obtained from a 24 h GPS data set for a 21 km baseline. The results demonstrate that the upper bound probability of the ILS AR probability given in the existing literatures agrees with the actual ILS success rate well, although the success rate computed with integer bootstrapping method is a quite sharp approximation to the actual ILS success rate. The results also show that variations or uncertainty of the unit–weight variance estimates from epoch to epoch will affect the computed success rates from different methods significantly, thus deserving more attentions in order to obtain useful success probability predictions.

Preparation of porous calcium phosphate ceramic scaffold in bone tissue engineering

Calcium Phosphate ceramic has been widely used in bone tissue engineering due to its excellent biocompatibility and biodegradability. However, low mechanical properties and biodegradability limit their potential applications. In this project, hydroxyapatite (HA) and calcium phosphate bioglass were used to produce porous tri-calcium phosphate (TCP) bio-ceramic scaffolds. It was found that porous TCP bioceramic could be obtained when 20wt percent bioglass addition and sintered in 1400 degrees celsius for 3 h. Significantly higher compressive strength (9.98 MPa) was achieved in the scaffolds as compared to those produced from tCP power (<3 MPa). The biocompatibility of the scaffold was also estimated.

Preparation of mesoporous bioglass coated zirconia scaffold for bone tissue engineering

Porous yttria-stabilized zirconia (YSZ) has been regarded as a potential candidate for bone substitute due to its high mechanical strength. However, porous YSZ is biologically inert to bone tissue. It is therefore necessary to introduce bioactive coatings onto the walls of the porous structures to enhance its bioactivity. In this study, porous YSZ scaffolds were prepared using a replication technique and then coated with mesoporous bioglass due to its excellent bioactivity. The microstructures were examined using scanning electron microscopy and the mechanical strength was evaluated via compression test. The biocompatibility and bioactivity were also evaluated using bone marrow stromal cell (BMSC) proliferation test and simulated body fluid test.

Porous zirconia scaffold modified with mesoporous bioglass coating

Porous yttria-stabilized zirconia (YSZ) has been regarded as a potential candidate for bone substitute as its high mechanical strength. However, porous YSZ bodies are biologically inert to bone tissue. It is therefore necessary to introduce bioactive coatings onto the walls of the porous structures to enhance the bioactivity. In this study, the porous zirconia scaffolds were prepared by infiltration of Acrylonitrile Butadiene Styrene (ABS) scaffolds with 3 mol% yttria stabilized zirconia slurry. After sintering, a method of sol-gel dip coating was involved to make coating layer of mesoporous bioglass (MBGs). The porous zirconia without the coating had high porosities of 60.1% to 63.8%, and most macropores were interconnected with pore sizes of 0.5-0.8mm. The porous zirconia had compressive strengths of 9.07-9.90MPa. Moreover, the average coating thickness was about 7μm. There is no significant change of compressive strength for the porous zirconia with mesoporous biogalss coating. The bone marrow stromal cell (BMSC) proliferation test showed both uncoated and coated zirconia scaffolds have good biocompatibility. The scanning electron microscope (SEM) micrographs and the compositional analysis graphs demonstrated that after testing in the simulated body fluid (SBF) for 7 days, the apatite formation occurred on the coating surface. Thus, porous zirconia-based ceramics were modified with bioactive coating of mesoporous bioglass for potential biomedical applications.

A restrike waveform predictive model for shunt capacitor bank switching with point-on-wave recommendation

Circuit-breakers (CBs) are subject to electrical stresses with restrikes during capacitor bank operation. Stresses are caused by the overvoltages across CBs, the interrupting currents and the rate of rise of recovery voltage (RRRV). Such electrical stresses also depend on the types of system grounding and the types of dielectric strength curves. The aim of this study is to demonstrate a restrike waveform predictive model for a SF6 CB that considered the types of system grounding: grounded and non-grounded and the computation accuracy comparison on the application of the cold withstand dielectric strength and the hot recovery dielectric strength curve including the POW (point-on-wave) recommendations to make an assessment of increasing the CB remaining life. The simulation of SF6 CB stresses in a typical 400 kV system was undertaken and the results in the applications are presented. The simulated restrike waveforms produced with the identified features using wavelet transform can be used for restrike diagnostic algorithm development with wavelet transform to locate a substation with breaker restrikes. This study found that the hot withstand dielectric strength curve has less magnitude than the cold withstand dielectric strength curve for restrike simulation results. Computation accuracy improved with the hot withstand dielectric strength and POW controlled switching can increase the life for a SF6 CB.

A circuit-breaker restrike diagnostic algorithm using ATP and wavelet transforms

Circuit breaker restrikes are unwanted occurrence, which can ultimately lead to breaker. Before 2008, there was little evidence in the literature of monitoring techniques based on restrike measurement and interpretation produced during switching of capacitor banks and shunt reactor banks. In 2008 a non-intrusive radiometric restrike measurement method, as well a restrike hardware detection algorithm was developed. The limitations of the radiometric measurement method are a band limited frequency response as well as limitations in amplitude determination. Current detection methods and algorithms required the use of wide bandwidth current transformers and voltage dividers. A novel non-intrusive restrike diagnostic algorithm using ATP (Alternative Transient Program) and wavelet transforms is proposed. Wavelet transforms are the most common use in signal processing, which is divided into two tests, i.e. restrike detection and energy level based on deteriorated waveforms in different types of restrike. A ‘db5’ wavelet was selected in the tests as it gave a 97% correct diagnostic rate evaluated using a database of diagnostic signatures. This was also tested using restrike waveforms simulated under different network parameters which gave a 92% correct diagnostic responses. The diagnostic technique and methodology developed in this research can be applied to any power monitoring system with slight modification for restrike detection.

Development of diagnostic and prognostic algorithms from vacuum circuit breaker restrike review and its validation proposal

The CIGRE WGs A3.20 and A3.24 identify the requirements of simulation tools to predict various stresses during the development and operational phases of medium voltage vacuum circuit breaker (VCB) testing. This paper reviews the modelling methodology [13], VCB models and tools to identify future research. It will include the application of the VCB model for the impending failure of a VCB using electro-magnetic-transient-program with diagnostic and prognostic algorithm development. The methodology developed for a VCB degradation model is to modify the dielectric equation to cover a restriking period of more than 1 millimetre.