The Global Positioning System (GPS) is widely used for positioning in the airborne mode such as in navigation as a supplementary system and for geo-referencing of cameras in mapping and surveillance by aircrafts and Unmanned Aerial Vehicles (UAV). The Precise Point Positioning (PPP) approach is an attractive positioning approach based on processing of un-differenced observations from a single GPS receiver. It employs precise satellite orbits and satellite clock corrections. These data can be obtained via the internet from several sources, e.g. the International GNSS Service (IGS). The data can also broadcast from satellites, such as via the LEX signal of the new Japanese satellite system QZSS. The PPP can achieve positioning precision and accuracy at the sub-decimetre level.
In this paper, the functional and stochastic mathematical modelling used in PPP is discussed. Results of applying the PPP method in an airborne test using a small fixed-wing aircraft are presented. To evaluate the performance of the PPP approach, a reference trajectory was established by differential positioning of the same GPS observations with data from a ground reference station. The coordinate results from the two approaches, PPP and differential positioning, were compared and statistically evaluated. For the test at hand, positioning accuracy at the cm-to-decimetre was achieved for latitude and longitude coordinates and doubles that value for height estimation.
In this pilot study, availability of the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) when integrating various combinations of satellite constellations including; Galileo, GLONASS and BeiDou with GPS is investigated. The Multiple Hypothesis Solution Separation method was applied using one month of real data. The data was collected at stations of known positions, located in regions that have different coverage levels by the tested constellations. While most previous studies used simulated data, the importance of using real data is twofold. It allows for the use of actual User Range Accuracy (URA) received within the satellite navigation message, which is a fundamental component for computation of the integrity protection level; and the computation of vertical position errors to validate the integrity approach. Results show that the vertical position error was always bounded by the protection level during the test period and the ARAIM availability can reach 100% of the time when using all constellations even though some constellations are yet incomplete.
Real-time Precise Point Positioning (RT PPP) is a primary positioning method used in natural hazard warning systems (NHWS) such as monitoring tsunami and earthquakes. The method relays on precise orbit and clock corrections to eliminate satellite-related errors and its performance can be significantly improved by using measurements from multi-GNSS constellations compared with using only one system, such as GPS. The Japanese Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis (MADOCA) provides these corrections for GPS, GLONASS and QZSS satellites enabling a multi-GNSS RT-PPP. However, the accuracy of RT PPP will suffer a major decline in case of presence of an outage in receiving these corrections, for instance due to a temporary failure of the user modem. For that reason, a method is proposed to maintain RT PPP when such a break takes place. For short outages less than 30 minutes we predict MADOCA orbits using a Holt-Winters’ auto-regressive model, and for longer outages up to 1 hr, the most recent International GNSS Service (IGS) ultra-rapid orbits can be used, but only for GPS. In addition, the clock corrections are predicted as a time series using a linear model with sinusoidal terms. The best regression period to estimate the required model parameters is discussed based on analysis of the autocorrelation of the corrections. The prediction model parameters are estimated using a sliding time window. Evaluation of the proposed method showed that positioning accuracy of 15 cm was maintained during the prediction period, which is twice better than using IGS ultra-rapid predicted products. For NHSW, the displacement errors due to prediction errors were generally within ±6 cm with one min interval and ±10 cm with five min interval.
The wet delay is one of the most difficult sources of error to quantify in global navigation satellite systems (GNSS) due to its spatial and temporal variability. However, its estimation is vital in some applications, such as in Precise Point Positioning (PPP), network real-time kinematic and weather forecast. Such estimation is usually carried out for its projected component along the zenith, defined as the zenith wet delay (ZWD). Prediction of the ZWD is important if there is a break in its estimation, and in providing initial values for future processing. In this paper, prediction modeling for the ZWD is investigated. An autocorrelation study was first performed on ZWD data over three different days at the international GNSS service station ONSALA to provide an insight into the temporal correlations among ZWDs. The choice of this station was based on the availability of reliable ZWD data measured by water vapor radiometers, which provide a reference for assessment of the accuracy of predicted values. Results have shown that successive ZWD estimates are significantly correlated for up to 1.7 hours. Different trend and smoothing prediction models were then investigated. Since prediction of ZWD requires continuous data sequence, interpolation methods of possible missing ZWD values are discussed. The use of linear interpolation or a cubic Hermite polynomial was found to be sufficient for interpolation of ZWD. Test results of prediction models show that the single-exponential smoothing model was the best performer where ZWD estimates were forecasted with a root mean square error of less than 1 cm for up to two hours.
Proper dynamic modelling of the troposphere wet delay using the Global Navigation Satellite Systems (GNSS) measurements is important in precise point positioning and in estimation of the PrecipitableWater Vapour (PWV) for weather forecast. The random walk (RW) and the first-order Gauss-Markov (GM) autocorrelation models are commonly used for this purpose. However, it was found that these models consistently underestimate the temporal correlations that exist among the troposphere wet delay. Therefore, a new dynamic model is proposed. The performance of the proposed model in following the autocorrelation of actual data is demonstrated and its impact on the near-real time estimation of the wet delay was tested and compared to that of the GMand RWmodels. Results showed that the proposed model outperformed these models. When the computed wet delays were used to compute PWV, their estimated valueswere very close to actual PWV data measured by radiosonde with differences less than 1 mm.
This study presents validation of BeiDou measurements in un-differenced standalone mode and experimental results of its application for real data. A reparameterized form of the unknowns in a geometry-free observation model was used. Observations from each satellite are independently screened using a local modeling approach. Main advantages include that there is no need for computation of inter-system biases and no satellite navigation information are needed. Validation of the triple-frequency BeiDou data was performed in static and kinematic modes, the former at two continuously operating reference stations in Australia using data that span two consecutive days and the later in a walking mode for three hours. The use of the validation method parameters for numerical and graphical diagnostics of the multi-frequency BeiDou observations are discussed. The precision of the system’s observations was estimated using an empirical method that utilizes the characteristics of the validation statistics. The capability of the proposed method is demonstrated in detection and identification of artificial errors inserted in the static BeiDou data and when implemented in a single point positioning processing of the kinematic test.
Fault detection and exclusion (FDE) is the main task for pre-processing of global navigation satellite system (GNSS) positions and is a fundamental process in integrity monitoring that is needed to achieve reliable positioning for applications such as in intelligent transport systems. A widely used method is the solution separation (SS) algorithm. The FDE in SS traditionally builds the models assuming positioning errors are normally distributed. However, in urban environments, this traditional assumption may no longer be valid. The objective of this study is to investigate this and further examine the performance of alternative distributions, which can be useful for FDE modelling and thus improved navigation. In particular, it investigates characterization of positioning errors using GNSS when the Australian satellite-based augmentation system (SBAS) test bed is used, which comprised different positioning modes, including single-point positioning (SPP) using the L1 global positioning system (GPS) legacy SBAS, the second-generation dual-frequency multi-constellation (DFMC) SBAS service for GPS and Galileo, and, finally, precise point positioning (PPP) using GPS and Galileo observations. Statistical analyses are carried out to study the position error distributions over different possible operational environments, including open sky, low-density urban environment, and high-density urban environment. Significant autocorrelation values are also found over all areas. This, however, is more evident for PPP solution. Furthermore, the applied distribution analyses applied suggest that in addition to the normal distribution, logistic, Weibull, and gamma distribution functions can fit the error data in various cases. This information can be used in building more representative FDE models according to the work environment.
This paper proposes precise point positioning (PPP) methods that offer an accuracy of a few decimetres (dm) with triple frequency GNSS data. Firstly, an enhanced triple frequency linear combination is presented for rapid fixing of the extra wide-lane (EWL) and wide-lane (WL) ambiguities for GPS, Beidou-2 and Galileo. This has improved performance compared to the Melbourne-Wübbena (MW) linear combination, and has 6.7 % lower measurement noise for the GPS L1/L2 signals, 12.7 % for L1/L5 and 0.7 % for L2/L5. Analysis with tested data showed a 5–6 % reduction in time required to fix the and ambiguities.
Once the EWL/WL ambiguities are fixed with the proposed linear combinations, three methods are presented that aim to provide positioning accuracy of a few dm. In the first approach, the three EWL/WL ambiguities in their respective phase equations are used to derive a low-noise ionosphere-free (IF) linear combination. The second method uses a low noise IF combination with two carrier-phase EWL/WL equations and a single pseudorange measurement. The third method uses a low noise IF combination with a single carrier phase EWL equation and two pseudorange measurements. These proposed methods can provide dm level positioning accuracy if carrier phase measurements with mm precision is tracked by the receiver. When comparing these combinations with a combination proposed in , it is found that superior performance is achieved with the third method when carrier phase noise is >5–6 mm for GPS and Beidou-2 and >2–3 mm for Galileo. This model only requires the EWL ambiguity to be fixed which typically takes just one epoch of data. Thus, the user achieves instant decimetre level PPP accuracy.
The propagation of dust ion acoustic waves (DIAWs) in a weakly inhomogeneous, weakly coupled, collisionless, and unmagnetized four components dusty plasma are examined. The fluid system considered in this work consists of cold positive ions, cold negatively and positively charged dust particles associated with isothermal electrons. For nonlinear (DIAW) waves, a reductive perturbation method was employed to obtain the variable coefficients Kortewege-de Vries (KdV) equation for the first-order potential. For local inhomogenity, the present system admits the coexistence of rarefactive and compressive solitons. As a matter of fact, when the wave amplitude enlarged, the width and velocity of the wave deviate from the prediction of the KdV equation. It means that we have to extend our analysis to obtain the variable coefficients Kortewege-de Vries (KdV) equation with fifth-order dispersion term. For locally constant parameters, the higher-order solution for the resulting equation has been achieved via what is called perturbation technique. The effects of positive and negative dust charge fluctuations on the higher-order soliton amplitude and width of electrostatic solitary structures are outlined.