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The accuracies of TEC models derived from ground-based GPS data are affected by several factors including assumed ionospheric shell height, satellites geometry, the chosen satellite cut off angles, the quantity of the GPS measurement data and etc.. Potential outliers within the measurements can have a significant impact on the quality of the estimated TEC models. However, there have been no any discussions on the outlier detection procedures in the literature on TEC modelling.This paper for the first time extends the commonly used Truncated Singular Value Decomposition (TSVD)-based TEC modelling method with an outlier detection and exclusion procedure. Furthermore, the retrieved TEC is transferred as vertical electron density (VED) profiles using the Shape Function model for the outlier impact analysis. In the paper, the biases from the outlier and the Shape Function model error can be separated and evaluated with the use of ionosonde data. To test the performance of this proposed quality control procedure, a day-time data set was used to produce the VED profiles at 3 different locations in Australia where both GPS and ionosonde data are available. The real-data tests have shown that the proposed outlier detection and exclusion procedure can numerically evaluate the impact of outliers and the Shape Function model errors, which are time and location dependent, in terms of the relative RMS measure commonly used in the ionospheric modelling studies. For example, the above two influences are 17.95% and 45.95% at Townsville, and 13.13% and 13.31% at Canberra, respectively. Besides, the simulated data were also used in the analysis. The result has demonstrated that as the magnitude of the outlier increases, the estimated VED can be biased by over 50%. Therefore, it is necessary to include a quality control procedure in retrieving an accurate and reliable TEC distribution.

The paper discusses GNSS statistical-testing methods for detection and identifications of observation outliers at the estimation “current” epoch, defined here as local testing. First, detection methods are discussed including testing the probability distribution (likelihood) of the residuals, testing using dynamic control limits of the range, the mean and standard deviation of the residuals. A method is proposed examining the difference between the mean and the median of the residuals. To identify the satellites with faulty measurements, several methods were investigated, including checking the likelihood of the residuals at the present epoch, and in a time series. A test is presented utilizing the control limits of the residuals' moving range for each satellite. Testing of the proposed methods was carried out using only GPS phase measurements in the kinematic mode. Results show that the proposed methods are efficient for detection and identification of large errors/outliers. However, the performance degrades with error values less than 5 cycles and when using small significance levels.

The conventional ionosphere total electron content (TEC) models based on geodetic coordinates have asynchronous dimensional resolution, especially in the area close to the pole. This paper presents a novel spherical cap harmonic model for mapping the arctic regional ionospheric TEC in a spherical cap coordinate system. Utilizing a series of IGS (International GNSS Service) products, a set of dual-frequency GPS (Global Positioning System) data from IGS stations in high latitudes is processed and used to map the arctic regional TEC values with the spherical cap harmonic model and the conventional regional TEC models. Together with the global ionosphere mapping (GIM) model from IGS, the TEC mapping accuracies from these models are compared. The comparison results show that the spherical cap harmonic model has a better TEC mapping performance with more homogeneous accuracy distributions in both temporal and spatial domains for the arctic region. In addition, the spectrum components of the coefficient series of the spherical cap harmonic models are demonstrated in this paper.

One of the most important tasks in integration ofGPS/INS is to choose the realistic dynamic modelcovariance matrix Q and measurement noise covariancematrix R for use in the Kalman filter. The performanceof the methods to estimate both of these matricesdepends entirely on the minimization of dynamic andmeasurement update errors that lead the filter toconverge. This paper evaluates the performances ofadaptive Kalman filter methods with differentadaptations. Innovation and residual based adaptiveKalman filters were employed for adapting R and Q.These methods were implemented in a loose GPS/INSintegration system and tested using real data sets. Theirperformances have been evaluated and compared. Theirlimitations in real-life engineering applications arediscussed.

Use of inter-loop aiding for improving tracking performance has been widely researched in recent years. However, most of the previously proposed aiding schemes rely on the assumption that the aiding loop remains unaffected by received interference. This paper argues that this may not always be the case. It is likely that the performance of the aiding loop may also degrade in the case where interference is received at the aiding carrier’s frequency resulting in performance degradation of both aiding and aided loops. This paper proposes an aiding scheme that offers performance improvements in case interference corrupts both frequencies. Also, an algorithm is proposed that continuously updates the aided loop bandwidth to keep its jitter at a minimum. A relationship between the quality of the aiding signal and its effects on the performance of the aided loop is analysed. An adaptive Kalman filter-based implementation of the aiding architecture is proposed to improve the quality of aiding estimates. This implementation offers an improved margin against received interference. Simulation and real data results are presented that show improvements of 7 and 5 dB-Hz in this margin by employing the proposed aiding scheme with and without an adaptive Kalman filter.

One of the main factors that lead to better performance of a Network RTK (NRTK) system is to predict/generate and transmit high accuracy error corrections from the central server for the rover’s location without much latency. The corrections are mainly for the atmospheric errors i.e. the tropospheric and ionospheric errors. These two types of atmospheric errors can be calculated and transmitted either separately or together, depending on the way the NRTK system is implemented. It is commonly thought that the magnitudes and temporal variations of the two types of atmospheric errors are quite different. For example, it is often emphasized that the ionospheric errors vary more quickly with time and so more difficult to be modeled than the tropospheric errors.In this paper, comparisons of the differences in the magnitudes and temporal variations between the double differenced (DD) tropospheric and ionospheric errors were conducted using GPS observations from GPSnet, the Victorian CORS network. Test results indicated that both types of the DD atmospheric errors significantly contaminate GPS measurements regardless whether it was day time or nighttime. Test results also showed that the temporal variation amplitudes of the DD tropospheric residuals in a fixed time span was not always significantly less than that of ionospheric residuals. In some cases, the DD tropospheric residuals reached several centimetres in a one-minute time span. These results can be instructive in the determination of the way a NRTK system is implemented, e.g. the rates or frequencies for generating and transmitting both types of atmospheric corrections.

As shown in a companion paper devoted to GNSS networks in algebraic graph theory, any (real- or) integer-valued function taking its values on the edges of the GNSS graph can be regarded as the sum of three (real- or) integer-valued functions: a function taking its values on the receiver vertices of this graph, another one on the satellite vertices, and the last one, the closure-delay (CD) function, taking its values on the loop-closure edges. For a given spanning tree, this decomposition is unique. The notion of closure delay generalizes that of double difference (DD). In this framework, particular satellite biases can be estimated and broadcasted to the network users for their precise point positioning (PPP). For example, in the case of large networks, each of these biases includes three (or four) terms: a satellite-clock term, a satellite time-group term, a satellite ionospheric term, and (for the phase) a satellite integer ambiguity mulitplied by the corresponding wavelength. the form of the PPP equations to be solved by the network user is then the same as that of the traditional PPP equations. As soon as the CD ambiguities are fixed and validated, estimates of these float biases can be obtained. the main result of this paper is that no other ambiguity is then to be fixed, hence a better efficiency. In particular, in this approach, it is not necessary to fix the carrier-phase ambiguities, a problem which cannot be easily solved. Indeed, as shown in this paper, when the CD ambiguities are fixed (or when a maximum set of DD ambiguities is fixed), the remaining float problem is not of full rank.

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 triangle shaped network cells, each having 70km, 140km or 210km inter-station distances. 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 the 70km inter-station distance. 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 tends to be over-optimistic and not functioning well with 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 demonstrate that integrity monitoring of RTK solutions is indeed necessary for precision applications.