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The global BeiDou navigation satellite system (BDS-3) has been in operation recently and many related applications have been already compatible with BDS-3 satellites. Most applications still use th...

With the rapid development of BeiDou satellite navigation system (BDS), high-quality service has been provided in the Asia-Pacific region currently, which will be extended to the whole world very soon. BDS is the first Global Navigation Satellite System that all satellites broadcast the triple-frequency signals. The triple-frequency signals in theory can improve the cycle slip detection that is one of the preconditions in precise positioning by making use of carrier phase. This paper discusses the development of a cycle slip detection method for undifferenced BDS triple-frequency observations in kinematic scenario. In this method, two geometry-free extra-wide-lane combinations and one geometry-free narrow-lane (NL) combinations are employed. The key is to mitigate the between-epoch ionospheric biases in the geometry-free NL combinations. We propose to predict the ionospheric biases of current epoch by using those from its consecutive foregoing epochs. The method is tested with extensive experiment...

Affine transformation that allows the axis-specific rotations and scalars to capture the more transformation details has been extensively applied in a variety of geospatial fields. In tradition, the computation of affine parameters and the transformation of non-common points are individually implemented, in which the coordinate errors only of the target system are taken into account although the coordinates in both target and source systems are inevitably contaminated by random errors. In this article, we propose the seamless affine error-in-variables EIV transformation model that computes the affine parameters and transforms the non-common points simultaneously, importantly taking into account the errors of all coordinates in both datum systems. Since the errors in coefficient matrix are involved, the seamless affine EIV model is nonlinear. We then derive its least squares iterative solution based on the Euler–Lagrange minimization method. As a case study, we apply the proposed seamless affine EIV model to the map rectification. The transformation accuracy is improved by up to 40%, compared with the traditional affine method. Naturally, the presented seamless affine EIV model can be applied to any application where the transformation estimation of points fields in the different systems is involved, for instance, the geodetic datum transformation, the remote sensing image matching, and the LiDAR point registration.

Sampling design plays an important role in spatial modeling. Existing methods often require a large amount of samples to achieve desired mapping accuracy, but imply considerable cost. When there are not enough resources for collecting a large set of samples at once, stepwise sampling approach is often the only option for collecting the needed large sample set, especially in the case of field surveying over large areas. This article proposes an integrative hierarchical stepwise sampling strategy which makes the samples collected at different stages an integrative one. The strategy is based on samples' representativeness of the geographic feature at different scales. The basic idea is to sample at locations that are representative of large-scale spatial patterns first and then add samples that represent more local patterns in a stepwise fashion. Based on the relationships between a geographic feature and its environmental covariates, the proposed sampling method approximates a hierarchy of spatial variations of the geographic feature under concern by delineating natural aggregates clusters of its relevant environmental covariates at different scales. The natural occurrence of such aggregates is modeled using a fuzzy c -means clustering method. We iterate through different numbers of clusters from only a few to many more to be able to reveal clusters at different spatial scales. At a particular iteration, locations that bear high similarity to the cluster prototypes are identified. If a location is consistently identified at multiple iterations, it is then considered to be more representative of the general or large-scale spatial patterns. Locations that are identified less during the iterations are representative of local patterns. The integrative stepwise sampling design then gives higher sampling priority to the locations that are more representative of the large-scale patterns than local ones. We applied this sampling design in a digital soil mapping case study. Different representative samples were obtained and used for soil inference. We started with samples that are the most representative of the large-scale patterns and then gradually included the samples representative of local patterns. Field evaluation indicated that the additions of more samples with lower representativeness lead to improvements of accuracy with a decreasing marginal gain. When cost-effectiveness is considered, the representative grade could provide essential information on the number and order of samples to be sampled for an effective sampling design.

This paper presents a regional scale network‐based real time kinematic (RTK) positioning strategy based on the use of three carrier GNSS signals, in which the inter‐station distances of the network could be doubled, that is, around 140 to 180 km instead of the current 70 to 90 km with the use of dual‐frequency GPS receivers. The paper outlines the most efficient virtual observables and models that allow for resolving ambiguities of three carriers with observation of above 7 minutes for baselines of a few hundreds of kilometres. As a result, the remaining key limiting factor for implementation of the regional scale network RTK is the distance‐dependent residual tropospheric bias. A reference station placement scheme of doubling the inter‐station distances is then suggested based on the interpolation accuracy of the tropospheric errors within the network. A semi‐simulation procedure is introduced for generation of the third GPS signal from the real GPS L1 and L2 data to allow for more realistic assessment o...

Most multiple-flow-direction algorithms (MFDs) use a flow-partition coefficient (exponent) to determine the fractions draining to all downslope neighbours. The commonly used MFD often employs a fixed exponent over an entire watershed. The fixed coefficient strategy cannot effectively model the impact of local terrain conditions on the dispersion of local flow. This paper addresses this problem based on the idea that dispersion of local flow varies over space due to the spatial variation of local terrain conditions. Thus, the flow-partition exponent of an MFD should also vary over space. We present an adaptive approach for determining the flow-partition exponent based on local topographic attribute which controls local flow partitioning. In our approach, the influence of local terrain on flow partition is modelled by a flow-partition function which is based on local maximum downslope gradient (we refer to this approach as MFD based on maximum downslope gradient, MFD-md for short). With this new approach, a steep terrain which induces a convergent flow condition can be modelled using a large value for the flow-partition exponent. Similarly, a gentle terrain can be modelled using a small value for the flow-partition exponent. MFD-md is quantitatively evaluated using four types of mathematical surfaces and their theoretical 'true' value of Specific Catchment Area (SCA). The Root Mean Square Error (RMSE) shows that the error of SCA computed by MFD-md is lower than that of SCA computed by the widely used SFD and MFD algorithms. Application of the new approach using a real DEM of a watershed in Northeast China shows that the flow accumulation computed by MFD-md is better adapted to terrain conditions based on visual judgement.