25 Years of wrong GPS Campaign Planning

13 25 Years of wrong GPS Campaign Planning Wunderlich, T., Fischell, M. and Schäfer, T. Chair of Geodesy, Technische Universität München, Arcisstraße 21, D-80290 Munich, Germany, Web site: www.geo.bv.tum.de E-mail: th.wunderlich@bv.tum.de, michele.fischell@mytum.de, th.schaefer@bv.tum.de Abstract There is no denying the fact that absolute positioning (single point determination) and relative positioning (baseline determination) follow completely different mathematical algorithms corresponding to different geometrical coherences. In spite of this, quality predictions for GPS networks still make only use of DOP quality parameters exclusively valid for the navigation solution which proves wrong. Beginning with Goad, 1988 several authors made efforts to derive appropriate quality measures for baseline quality estimation prior to geodetic GPS observation campaigns, in particular concerning engineering networks. All of them have been turned down by practitioners because of tedious computation processes and missing off-the-shelf software. With exception of a comprehensive scientific approach by Kahmen et al., 1998 based on the Bernese Software and simulated signals no rigorous campaign planning has been reported. Nevertheless, many requests for tender prescribe the improper use of the familiar navigation DOP values for a priori accuracy evidence. The paper will provide insight into the problems related to baseline quality prediction and attempts to take advantage of a simplified procedure suggested by Merminod and Rizos, 1994 and realized by Rossetti, 1996. A software upgrade by Fischell, 2011 based on a tool by Richter, 1999 now grants a convenient access to both the approximate means of BPDOP and the rigorous ones as BDOP and RDOP. Thus 25 years of wrong GPS campaign planning should be enough! Key words: baseline quality prediction, relative dilution of precision, mission planning 1 PRACTICAL NEED AND MARKET GAP When surveying engineers attempt to set up an observation schedule for a local high precision GPS network, they need to meet strict quality demands combined with logistics and economy. Unfortunately, providing sound quality proofs in advance for baselines derived from relative positioning turns out rather difficult. Though geodetic science disposes of probable baseline quality measures, their application for prediction purposes proves sophisticated and moreover suffers from a lack of software. Moreover, common textbooks, above all Wells, 1986, give no hint at baseline quality parameters, but only at navigational DOPs which are not applicable to baselines. What are the practitioners needs? Subject to baseline length and accuracy requirement there are two fundamental questions to be answered: how long do they need to observe and TS 1 Data Processing INGEO 2011 5 th International Conference on Engineering Surveying Brijuni, Croatia, September 22-24, 2011

14 INGEO 2011 what is the optimum start time for a particular baseline, i.e. to locate and to dimension an optimum observation window. Clearly, the problem has to be solved including the obstruction masks of the baseline s end points. For a network of baselines the findings are concurrent and have to be mutually adapted until an overall optimum for a predefined number of receivers is found that is compatible with reasonable transfer times, staff effort and project cost limits. 2 RIGOROUS QUALITY PREDICTION Concerning absolute positioning by pseudoranges, a well known set of quality factors exists: dilution of precision. The most prominent is represented by GDOP (geometric dilution of precision), which, multiplied by the pseudoranges r.m.s, delivers the general metric accuracy of the navigation solution for a certain instant of time. It is exclusively dependent on the instantaneous configuration of the satellites (Wunderlich, 1992) with respect to the (single) receiver position. Using almanac data it can be easily used to predict favorable observation times (low GDOP) and to avoid rare critical configurations (GDOP growing to infinity). For baseline determination (Hofmann-Wellenhof et al., 2008) several fundamental differences exist, which prevent the familiar application of DOPs from navigation and call for a completely different quality prediction concept in GPS-surveying: Carrier phase data is used instead of code-pseudorange observations, The carrier phases have to be collected simultaneously by two receivers, To eliminate common error components double differences are computed, A number of unknown ambiguities has to be resolved due to the phase observables, A successful ambiguity fixing needs several epochs of data; one is not sufficient, The complete solution (3d components) can be contaminated by cycle-slips. For short baselines observed in rapid static or kinematic mode the manufacturers provide individual messages and key figures for real-time quality control. Besides, such scenarios have no requirement for quality prediction and detailed planning. In contrast to that there is no software support for baseline quality estimation prior to measurement, if optimum observation windows for longer baselines with challenging accuracy demands are to be determined in course of a GPS network campaign planning. As a result the common navigation DOPs are applied blindly and invalid instead; often even prescriptions of imperative use are reported. At the same time we can state that there are at least a few proper concepts available for years. Their theoretical layout and practical drawbacks will be described in the following. 2.1 THE CONCEPTS OF RDOP AND BDOP 2.1.1 Relative dilution of precision (RDOP) At first Goad, 1988 created the characteristic quality factor RDOP to compare the results of GPS relative positioning experiments in kinematic mode. Similar to the GDOP calculation the root of the least squares covariance matrix trace of the double differenced phase observations is determined, but scaled by the double difference standard deviation. The product of RDOP with the actual uncertainty of the double difference measurement renders the baseline error. However, the numerical computation of RDOP values proves tedious, because setting up the covariance matrix in advance is complex: on one hand the derivatives of the double difference with respect to the unknown baseline elements have to consider

Wunderlich, Th. et al.: 25 Years of wrong GPS Campaign Planning 15 alternating reference satellites carefully; on the other hand mathematical correlations have to be taken fully into account. 2.1.2 Bias dilution of precision (BDOP) While Goad tried his RDOP computations only a posteriori using solved ambiguities Merminod, 1988 started a series of individual and joint attempts to find a suitable solution. He started with the design of a couple of BDOPs to be derived prior to the actual observations. Merminod designed his BDOPs for use in a pure relative manner to get rid of the double difference r.m.s. that can hardly be specified exactly in advance. The BDOPs differ in investigating the complete covariance matrix, consisting of the baseline components and the double difference ambiguities as unknowns (fixed solution) or the submatrix of the baseline components without fixing the ambiguities (float solution). The most important profit can be taken from comparing different time spans of observation; it shows convincingly how increasing observation time improves the solution and reciprocally reduces the influence of the start time. Customary testing intervals are 20, 30 or 60 minutes, corresponding to BDOP or RDOP with indices of 20 to 60 or sometimes more. An algorithm for systematic investigation of optimum observation time and interval according to the RDOP concept has been created and patented by Yang, 2000 in the United States. Nevertheless, all these approaches cannot involve possible worsening effects of cycle-slips. 2.2 SIMULATION BY PROCESSING ARTIFICIAL OBSERVATIONS To even cope with the latter problem, Kahmen et al., 1998, invented a completely different approach. The idea was to enable a realistic simulation by processing artificial observations. Such observations can be produced by the Bernese Software (Rothacher and Mervart, 1996) for approximate receiver locations and forecast almanac parameters. A specific switch allows setting an arbitrary number of cycle-slips to contaminate the data. Subsequent processing of the data by the same software delivers a very realistic covariance matrix that can be used for simulating a network adjustment. Testing observation windows of different interval and start time, an optimum solution can be found and proved. Then logistics can follow. 3 AN ALTERNATE APPROACH (BPDOP) During his investigations Merminod found out that favorable conditions for baseline solutions are densely correlated with the change of the satellite configuration during the observation time span and successfully created a simplified approach based on the satellites velocities and track directions. He employed an imaginative perception of paired satellites which opened the opportunity to use the familiar design of the navigational GDOP as a BPDOP. Although one of Merminod s diploma students, Rossetti, 1996, wrote and implemented a splendid plug-in to be used within the Leica SKI software suite, it was only scarcely used. Richter, 1999 collected all concepts presented here and wrote a Matlab toolbox APRIRDOP at Vienna Technical University which was at its time extensively used both for teaching and for professional mission planning. In fact, the GPS week number rollover as well as advanced Matlab versions let it expire far too soon. It took more than a decade until the authors of this paper were able to initiate the next attempt to establish an efficient baseline

16 INGEO 2011 quality prediction tool for theoretical studies as well as for practical use. It was urgently needed. 4 A COMPREHENSIVE PLANNING SOFTWARE Using smart algorithms and some APRIRDOP routines still working, Fischell, 2011, assembled the new software LIDOPRIO (baseline dilution of precision a priori) and improved the general possibilities and the performance remarkably. LIDOPRIO now is able to predict RDOP and BPDOP values for whole observation days or for specific windows of interest. The input consists of current almanac data, approximate station coordinates and obstruction masks and offers a choice of maps and diagrams to judge various start times and observation periods. So in theory campaign planning is feasible again. It should be mentioned yet that even with latest microprocessors the computational load still affords considerable time to determine rigorous RDOP values for longer observation intervals and dense epoch sequence. To examine the practical benefit and relevance of mission planning by LIDOPRIO, a profound test was executed. The complete GPS campaign to observe a monitoring network of a dam (Fig. 1) in a high alpine region of Austria was prepared by means of LIDOPRIO and all measurements were taken according to the computed optimum start times and intervals. Afterwards the accuracies of the processed baseline were checked and successfully approved. Figure 1: Monitoring network for the Kops dam, Vorarlberger Illwerke, Austria Figure 2 presents a characteristic example from this investigation in which from the comparison of three RDOP graphs (20, 30, 60 minutes session length) and the corresponding GDOP graph two facts can be clearly noticed: optimum observation times from RDOP do not coincide with those from GDOP and the relevance of a certain start time decreases with the session length.

Wunderlich, Th. et al.: 25 Years of wrong GPS Campaign Planning 17 Figure 2: LIDOPRIO results RDOPs versus GDOP for a baseline of the Kops GPS campaign Our ultimate target is to attain an automatic set-up of a GPS network s observation schedule. REFERENCES FISCHELL, M. 2011, Effizienzoptimierung bei der Planung von GNSS-Netzen für ingenieurgeodätische Aufgaben, Bachelor Thesis, Chair of Geodesy, TUM. GOAD, C. 1988, Investigation of an alternate Method of Processing Global Positioning Survey Data collected in Kinematic Mode, in: Lecture Notes in Earth Sciences, Springer Verlag, Berlin. HOFMANN-WELLENHOF, B., LICHTENEGGER, H., WASLE, E. 2008, GNSS, Springer Verlag, Berlin. KAHMEN. H. et al. 1998, Ein modulares Konzept zur Absteckung von Hochgeschwindigkeitstrassen, Zeitschrift für Vermessungswesen, Heft 4, Stuttgart. KAHMEN. H., WIESER, A., WUNDERLICH, Th. 1998, Technical Networks for High- Speed Railway Lines, in: Proc. of the IAG Symposium on Geodesy for Geotechnical and Structural Engineering, Congress Centre Eisenstadt. MERMINOD, B. 1988, Du bon usage des satellites GPS, Vermessung-Photogrammetrie- Kulturtechnik, No. 10, Solothurn. MERMINOD, B., Grant, D.B., Rizos, C. 1990, Planning GPS Surveys Using appropriate Precision Indicators, CISM Journal ACSGC, Vol. 44, No. 3, Ottawa.

18 INGEO 2011 MERMINOD, B., Rizos, C. 1994, Optimisation of Rapid Static Surveys, manuscripta geodaetica, Springer Verlag, Berlin. RICHTER, B. 1999, Konfigurationsabhängige Genauigkeitsfaktoren für GPS-Basislinien, Diploma Thesis, Dep. of Engineering Geodesy, Technische Universität Wien. ROSSETTI, M. 1996, Optimisation de l usage des récepteurs GPS, Vermessung- Photogrammetrie-Kulturtechnik, No. 4, Solothurn. ROTHACHER, M., MERVART, L. 1996, Bernese GPS Software Version 4.0 (Manual), Astronomical Institute, University of Berne. WELLS, D. et al. 1986, Guide to GPS Positioning, Canadian GPS Associates, New Brunswick. WUNDERLICH, Th. 1992, Die geometrischen Grundlagen der GPS- Einzelpunktbestimmung, in: Ingenieurvermessung 92, Dümmler Verlag, Bonn. WUNDERLICH, Th. 1993, How to Visualize Outages, in: Proc. of NAV93 Int. Conf. on Practical Navigation, London. YANG et al. 2000, RDOP Surface for GPS Relative Positioning, U.S. Patent, Albany, N.Y.