On the performance of equiangular mascon solution in GRACE-like missions

Mass concentration (mascon) solutions for GRACE (Gravity Recovery and Climate Experiment) data are widely used in various regional-to-global mass change studies. The current advances in the mascon solution have mainly concentrated on improving the spatial resolution of the solution, enhancing the applied least-squares regularization, and the characterization of the solution errors. Most of the mascon solutions are obtained on the equal-area grid, inducing complexities in creating the grid and its presentation. In this regard, estimation of the mascon solutions on equiangular grids can be appealing. Furthermore, in the equal-area methods, there is no global criterion to determine the size of the mascon areas. The mascon size is usually chosen in a subjective manner which hampers the objective application of different mascon solutions. In view of these challenges, two main questions are addressed in this study: i) what kind of modifications should be made in computation scheme of the mascon solution if equiangular grids are used to account for different areas of the grid patches, and ii) in case of non-equiangular solutions, how to define an objective criterion for the patch sizes based on the resolution of both the observation and the signal of interest. We investigate the performance of the high-resolution mascon-based approach, proposed by Abedini et al. [2021], which uses GRACE-like observations similar to level-1 data for a period of one month over the Greenland region. Two main practical issues are studied on the estimation of the surface density changes as follows. First, we show that for equiangular grids, the area of the patches should be accounted for in the regularization by introducing area-affected weights for the unknown parameters. We investigate the effect of three different area-affected weighting strategies on the derived solution. Secondly in order to obtain proper size for the patches, a novel approach is presented to investigate the performance of the mascon solution using the analysis of the resolution matrix entries. The proposed resolution analysis is used to obtain the optimal patch size for the discretization of the area of interest. Based on the results, it is demonstrated that the minimum legible patch size in the Greenland area for the current settings of the GRACE observations is 0.5 degree in the NS direction and a latitude-adaptive grid-size rather than equiangular grids at high latitude regions in the EW direction

Closed form ADOP expressions for single-frequency GNSS-based attitude determination

Integer ambiguity resolution is a prerequisite to high-precision real-time GNSS-based attitude determination. The ADOP is a well-known scalar measure to infer whether ambiguity resolution can be expected successful or not. To compute ADOP it is sufficient to have knowledge about the measurement setup and the measurements noise characteristics; hence it can be used as a planning tool. In this contribution we present closed-form expressions for the ADOP in case of attitude determination. Using these expressions one may infer the impact of GNSS design aspects such as number of satellites, choice of frequency and the precision of the phase and code observables. In addition, they are useful to quantify the influence of the number of antennas in the configuration and the use of geometric constraints, such as the lengths of the baselines and/or the angles between the baselines in the configuration. In this article the behavior of the ADOPs as function of these design aspects will be evaluated for several GPS attitude determination scenarios

Low-cost, high-precision, single-frequency GPS–BDS RTK positioning

The integration of the Chinese BDS with other systems, such as the American GPS, makes precise RTK positioning possible with low-cost receivers. We investigate the performance of low-cost ublox receivers, which cost a few hundred USDs, while making use of L1 GPS + B1 BDS data in Dunedin, New Zealand. Comparisons will be made to L1 + L2 GPS and survey-grade receivers which cost several thousand USDs. The least-squares variance component estimation procedure is used to determine the code and phase variances and covariances of the receivers and thus formulate a realistic stochastic model. Otherwise, the ambiguity resolution and hence positioning performance would deteriorate. For the same reasons, the existence of receiver-induced time correlation is also investigated. The low-cost RTK performance is then evaluated by formal and empirical ambiguity success rates and positioning precisions. It will be shown that the code and phase precision of the low-cost receivers can be significantly improved by using survey-grade antennas, since they have better signal reception and multipath suppression abilities in comparison with low-cost patch antennas. It will also be demonstrated that the low-cost receivers can achieve competitive ambiguity resolution and positioning performance to survey-grade dual-frequency GPS receivers

Sturdy Positioning with High Sensitivity GPS Sensors Under Adverse Conditions

High sensitivity GPS receivers have extended the use of GNSS navigation to environments which were previously deemed unsuitable for satellite signal reception. Under adverse conditions the signals become attenuated and reflected. High sensitivity receivers achieve signal reception by using a large number of correlators and an extended integration time. Processing the observation data in dynamic and rapidly changing conditions requires a careful and consistent treatment. Code-based autonomous solutions can cause major errors in the estimated position, due primarily to multipath effects. A custom procedure of autonomous GPS positioning has been developed, boosting the positioning performance through appropriate processing of code and Doppler observations. Besides the common positioning procedures, robust estimation methods have been used to minimise the effects of gross observation errors. In normal conditions, differential GNSS yields good results, however, under adverse conditions, it fails to improve significantly the receiver’s position. Therefore, a so-called conditional DGPS has been developed which determines the position differentially by using data from the strong signals only. These custom-developed procedures have been tested in different conditions in static and kinematic cases and the results have been compared to those processed by the receiver

ON THE REALISTIC STOCHASTIC MODEL OF GPS OBSERVABLES: IMPLEMENTATION AND PERFORMANCE

High-precision GPS positioning requires a realistic stochastic model of observables. A realistic GPS stochastic model of observables should take into account different variances for different observation types, correlations among different observables, the satellite elevation dependence of observables precision, and the temporal correlation of observables. Least-squares variance component estimation (LS-VCE) is applied to GPS observables using the geometry-based observation model (GBOM). To model the satellite elevation dependent of GPS observables precision, an exponential model depending on the elevation angles of the satellites are also employed. Temporal correlation of the GPS observables is modelled by using a first-order autoregressive noise model. An important step in the high-precision GPS positioning is double difference integer ambiguity resolution (IAR). The fraction or percentage of success among a number of integer ambiguity fixing is called the success rate. A realistic estimation of the GNSS observables covariance matrix plays an important role in the IAR. We consider the ambiguity resolution success rate for two cases, namely a nominal and a realistic stochastic model of the GPS observables using two GPS data sets collected by the Trimble R8 receiver. The results confirm that applying a more realistic stochastic model can significantly improve the IAR success rate on individual frequencies, either on L1 or on L2. An improvement of 20% was achieved to the empirical success rate results. The results also indicate that introducing the realistic stochastic model leads to a larger standard deviation for the baseline components by a factor of about 2.6 on the data sets considered

Variance component estimation uncertainty for unbalanced data: Application to a continent-wide vertical datum

Variance component estimation (VCE) is used to update the stochastic model in least-squares adjustments, but the uncertainty associated with the VCE-derived weights is rarely considered. Unbalanced data is where there is an unequal number of observations in each heterogeneous dataset comprising the variance component groups. As a case study using highly unbalanced data, we redefine a continent-wide vertical datum from a combined least-squares adjustment using iterative VCE and its uncertainties to update weights for each data set. These are: (1) a continent-wide levelling network, (2) a model of the ocean’s mean dynamic topography and mean sea level observations, and (3) GPS-derived ellipsoidal heights minus a gravimetric quasigeoid model. VCE uncertainty differs for each observation group in the highly unbalanced data, being dependent on the number of observations in each group. It also changes within each group after each VCE iteration, depending on the magnitude of change for each observation group’s variances. It is recommended that VCE uncertainty is computed for VCE updates to the weight matrix for unbalanced data so that the quality of the updates for each group can be properly assessed. This is particularly important if some groups contain relatively small numbers of observations. VCE uncertainty can also be used as a threshold for ceasing iterations, as it is shown—for this data set at least—that it is not necessary to continue time-consuming iterations to fully converge to unity