An Investigation of Performance Difference of Regional Atmospheric Models for Network RTK– A Case Study in Victoria Suqin Wu, Kefei Zhang, David Silcock RMIT University,GPO Box 2476V, Melbourn , Australia
[email protected] ABSTRACT The main advantage of the network RTK technique (NRTK) over the conventional RTK is that NRTK allows for a long distance between the reference station and the rover station without degradation in the accuracy of RTK positioning. Various regional GPS continuously operating reference stations (CORS) networks have been established and widely used to facilitate better positioning services, specifically for high-precision real-time applications in the world. GPSnet is the first state-wide and most dense CORS network in Australia incepted in early 1990s for the state of Victoria. To maximize the benefits of technology developments and the expensive CORS geospatial infrastructure, the state of Victoria in collaboration with a research consortium led by RMIT University, embarked on research of regional atmospheric modeling via an Australian Research Council project in early 2005. It is known that the core of the NRTK technique is the modelling of spatially-correlated errors for the network coverage area so that the error correction for the rover location can be determined to reduce the systematic bias in the rover’s measurements. This can lead to effective ambiguity resolutions for the rover’s positioning. The accuracy of the error models is a determinant factor for the performance of NRTK positioning. There are several error models (or interpolation methods) proposed for NRTK positioning in the past decades. Three of these methods including 1) Linear Interpolation Method (LIM); 2) Distance-Based interpolation method (DIM); and 3) Low-order surface model (LSM), are examined and tested in this paper. Three different baselines (named baseline1, baseline2, and baseline3) with various network configurations and different times of observations from GPSnet sites are chosen for the tests. Based on all the test results, the following conclusions can be made: 1) for all the test cases, LIM and DIM can be used to reduce the DD residual significantly, and LIM outperforms DIM slightly as most the differences in the interpolation accuracy of the two models are at mm level, in the (DD) observation domain. However this does not hold for LSM as in some cases LSM performs very poor. 2) for the five-station configuration, the performance of the three models are very similar since there is at least one redundant station that can average out the station specific error, if any; to some extend by least square adjustment, for all the three model. 3) for four-station configurations, in some cases, the performance of LSM is similarly to that of LIM and DIM, however in other cases, LSM’s results are significantly worse than LIM and DIM, and even much worse than residuals without correction applied. The test results indicate that LIM and DIM are more reliable and consistent than LSM, and LSM may not be suitable for the error modeling for NRTK in some cases, especially in the cases that double differencing approaches are used and only four (or less of) reference stations are used in the error modeling. Since in this case, any station specific error may totally contaminate the resolved model’s parameters. 4) the test results also suggest that it has no any advantages of using LSM over LIM and DIM for NRTK, for GPSnet.
INTRODUCTION GPSnet is a regional GPS CORS network in the state of Victoria, Australia. Currently it consists of more than 30 reference stations covering Melbourne metropolitan area and rural area of Victoria. The inter-station distances of GPSnet range from several tens of kilometres up to 200 km, a typical medium-to-long-range reference network. For real-time high accuracy GPS positioning applications, only some selected GPSnet stations provide single base RTK services (baseline length up to 20 km) at centimeter
level positioning accuracy. To extend the RTK service coverage area so that real-time, high accuracy RTK services can be provided for the whole area of the state, the Network RTK technique (NRTK) has been under intensive development and testing since early 2005. This research is funded by Australia Research Council and three universities and two state government organisations are involved (i.e. RMIT University, University of New South Wales, University of Melbourne, Department of Sustainability and Environment, State of Victoria and the Department of Lands, State of New South Wales).
It is well known that the accuracy of the regional error model is a determinant factor for the accuracy of network RTK positioning and the variability of the atmospheric errors in different regions may behave differently. Therefore, it is important that the performance of the error model for the region of Victoria is assessed, and improved if possible, for the enhancement of NRTK performance of GPSnet (Zhang, Wu et al. 2006). In the past several years, various error models (or interpolation methods) for multiple reference stations have been proposed. The typical methods include: 1) Linear Interpolation Method (LIM) (Wanninger 1995; Wübbena, Bagge et al. 1996); 2) Linear Combination Method (LCM) (Han 1997; Rizos, HAN et al. 1999); 3) Distance-Based Linear Interpolation Method (DIM) (Gao, Li et al. 1997); 4) Low-Order Surface Model (LSM) (Wübbena, Bagge et al. 1996; Fotopoulos 2000; Varner 2000; Fotopoulos and Cannon 2001); 5) Least Squares Collocation Method (LSCM) (Raquet 1998). Since model 2) and model 1) are more similar to each other compared to all the rest models in both formula and the way to be implemented (for the case of three reference stations their interpolation results are exactly the same (Dai, Han et al. 2001)), so model 2) is not discussed in this paper. More over, since model 5) is a stochastic model that requires a tremendous amount of observations from many reference stations with various lengths of baselines between the reference stations, for the purpose of obtaining the covariance functions. This requirement can be hardly met in our test due to the fact that the network ambiguity may not be able to be resolved simultaneously for all (so many) the baselines, especially for long baselines. In addition, it is very difficult to implement this method in real-time scenario, therefore this method is not tested in this paper. Model 1), model 3), model 4) are selected for the tests for this paper. In this paper, firstly, the algorithm for the three selected error models, i.e., LIM, DIM, and LSM, are briefly introduced. Secondly, test results on the performance of the three models for two different baselines with different network configurations using GPSnet observation data are presented and analyzed. Through the comparison of the performance difference of the three models based on the test results for the two selected baselines, some conclusions are given.
ALGORITHMS FOR THREE ERROR MODELS
Linear Interpolation Model (LIM)
Distance-based Linear Interpolation Model (DIM)
Low-Order surface model (LSM) SELECTED BASELINES AND THEIR NETWORK CONFIGURATIONS FOR TESTS
THREE MODELS PERFORMANCE BASELINE1–BACC-PARK
FOR
THREE MODELS PERFORMANCE BASELINE2–MORN-PARK
FOR
TWO MODELS PERFORMANCE BASELINE3–COLA-GEEL
FOR
CONCLUSIONS
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