On the Method of Selecting Independent Baselines for ...

On the Method of Selecting Independent Baselines for GPS Control Network Erhu WEI

Xianan DENG

School of Geodesy and Geomatics Wuhan University 129 Luoyu Road ,Wuhan 430079,China [email protected]


Kun YANG

Qi ZHANG

Zhejiang Huadong Surveying and Mapping Co., Ltd 997 Gudun Road, Hangzhou, 310030, China [email protected]


Abstract—In this paper the concept of independent baseline was introduced and its impact on GPS observation network was analyzed. Then the principle of selecting independent baseline in the GPS network was given by an example. Keywords- GNSS; Independent baseline; Adjustment of network

GNSS (The Global Satellite Navigation System) has enormously promoted human beings’ life and developed the technology. Understanding and studying the principle for surveying and positioning of GNSS and its present situation and prospects for development is important[1]. In later period's data processing, the quality of the individual baseline and the selection situation of the individual baseline will have great impact on the precision and efficiency for balancing of GPS network through the processing research on the GPS data sets, and we also obtained the methods of selecting the individual baseline and so on. I.

THE CONCEPT OF INDEPENDENT BASELINE

If any of the baseline vector in a batch of baseline vectors can not be expressed by linear combination of the other baselines, The baselines are a batch of independent baseline. Vectors matching the following conditions are independent baseline vectors[2]. Firstly, a batch of baseline vectors can not constitute a closed loop. Secondly although the vectors constitute a closed loop, not all of them are from the same observing session. When using the N represents the number of GPS receivers in synchronize observing session, the number of the whole baseline vectors is N(N1)/2, but only (N-1) of them are independent baseline vectors. Methods of selecting independent baseline vectors various a lot. FIG.1 gives an example of selection of the independent baseline when N equals 4. This research is funded by the national ‘863 Project’ of China (No. 2008AA12Z308), and the National Natural Science Foundation of China(No. 40974003). 978-1-4577-0321-8/11/$26.00 ©2011 IEEE

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FIG.1 The selection of the independent baseline vectors (n = 4)

II. IMPACT OF THE SELECTION OF INDEPENDENT BASELINE VECTOR IN THE NETWORK ADJUSTMENT When N GPS receivers are used in a synchronize observing session, each two of the receivers can form one baseline vector. The total number of the simultaneous observation baseline is N(N-1)/2[3]. Among the vectors you can elect up to (N-1) synchronous baselines. But how to select the (n-1) independent baselines? We just need to ensure that the selected independent baselines can not constitute a closed loop. That means if all the synchronous baseline that can constitute a closed loop, they are function related. Though the independent baselines obtained in the simultaneous observation do not have function-related features, they are error-related. Actually all the simultaneous observation baseline are error- related. GPS control network is a Survey Control Network that constituted by the GPS baseline vectors. Baseline vectors is the basic unit that

constitutes the GPS network. Its quality will directly affect the efficiency and the precision of the results in the postprocessing of the network adjustment. According to the principle of adjustment, observations that participate in the adjustment process should be independent. If the dependent baselines are selected, the adjustment results are not consistent with the real situation[4][6]. For example, some points appears to have a few baseline connection and they only have single connection, some baselines form a closed loop, but they are actually simultaneous loop which are not really appropriate. Therefore baselines that participate in the GPS network adjustment process should be independent. III.

all the qualified baselines have been selected in the network adjustment. If the results of the network adjustment failed, re-selecte and process the baselines. Then choose the independent baselines for constrained adjustment of the network. The efficiency and accuracy (with emphasis on analysis of the observation residuals after adjustment) of these two methods were evaluated as below. Firstly, select the independent baselines for the constrained and unconstrained adjustment of the network. Unconstrained adjustment results (observations after adjustment) is showed in FIG.3. Secondly, all the qualified baselines in the network have been choosen for adjustment. If the results of the network adjustment failed, re-selecte and process the baselines. Then choose the independent baselines for the constrained adjustment of the network. Unconstrained adjustment results (observations after adjustment) is showed in FIG.4. Adjustment observations after the network adjustment was calculated as Fig.5 and 6.

EXPERIMENTS AND DATA PROCESSING

A. Experimental example We choose a D-GRADE GPS observing network of a small city for an example. The network is constituted of a total of eight points, and four GPS receivers were used to observe. The graph of the GPS observation network is under below as FIG.2. Each station was observed by GPS receiver 3 times. In accordance with previous theoretical part, we can calculate the observation sessions of 6, the whole network baseline vectors to a total of 36, in which the number of the independent baseline vector is 18. By testing the quality of collected data to eliminate the problem observations, We finally get the total number of 30 qualified baseline for data processing in which the total number of independent baseline is 14. We use this example to illustrate the impact of different method of selecting independent baselines on network adjustment results.

FIG.3 Method One-observations after unconstrained adjustment

FIG.2 GPS network graphics experiment

When the qualified baselines are processed and the misclosures of synchronous and asynchronous loop are within the limitation, two different methods was selected to deal with the following data processing. One is selecting the independent baseline, then the constrained and unconstrained adjustment have been applied to the network. The other is

FIG.4 Method Two observations after constrained adjustment

We found that some of the baseline did not pass the test. By removing or correlation processing the ill baselines, we can attain the adjustment observations of the unconstrained adjustment .

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Accordance with the standards of network adjustment of the "Global Positioning System (GPS) measurement norms", now these baselines have passed the unconstrained baseline adjustment[5]. Selecting the independent baseline from these passed baseline to conduct the constraint adjustment of the network, the adjustment results are obtained as FIG.7.

Fig.5 Method Two observations that failed the unconstrained adjustment

What to be noted is that in this example the total number of qualified independent baselines is 14, while the final number of the observations after the adjustment is 11. The reason is that the ill baselines were removed and were not in the adjustment of the network in the data processing. B. Experiment Result According to the result of analysis and the efficiency of data processing, we can conclude as follow: Firstly, after baseline calculating, due to the adjusted observation’s residual of selected individual baselines and analysis of network adjustment without constraint, we can find that the possibility of passing is high, and the precision is satisfied, but the time spend on selecting individual baseline is costly. Secondly, calculate all the qualified baselines with network adjustment without constraint first and only select baselines under the circumstance of not passing adjustment without constraint. Then analyze the residual of adjusted observation. After processing, some unsatisfied baselines can still pass. Afterwards, selecting individual baselines from them to network constraint adjustment. This method not only meets the precision but also takes less time. IV.

Fig.6 Method Two observations calculated after unconstrained adjustment processing

CONCLUSION

The selection of independent baselines affects the final results and accuracy of network adjustment in the GPS data processing. In this paper, an example was given to calculate and study the selecting method of independent baseline in the GPS observation network, one method is selecting the independent baselines, then conducting the unconstrained and constrained adjustment of the network. The other method is selecting all the qualified baselines for the network adjustment. If the network adjustment failed, re-selecting and processing the baselines. Then choosing the independent baselines for constrained adjustment of the network. By analyzing the results and efficiency of these two methods of processing, we conclude that selecting all the passed baselines as a whole for network adjustment and selecting the independent baselines to for the constrained adjustment of the network after they pass the unconstrained adjustment, This method of processing is not only of higher efficiency, but also of a higher accuracy that meets the requirements of the measurement specifications. About the first author: WEI Erhu, Professor, Ph. D, Ph.D supervisor, engaged in the research on spatial geodesy and geodynamics. E-mail: [email protected] REFERENCES [1] [2]

FIG.7 Method Two observations after constrained adjustment

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