PRECISE GPS POSITIONING IMPROVEMENTS BY REDUCING ANTENNA AND SITE DEPENDENT EFFECTS

Transcription

1 PRECISE GPS POSITIONING IMPROVEMENTS BY REDUCING ANTENNA AND SITE DEPENDENT EFFECTS Günter Seeber, Falko Menge, Chrstof Völksen Insttut für Erdmessung, Unverstät Hannover, D-3167 Hannover, Germany Gerhard Wübbena, Martn Schmtz Geo++, D-387 Garbsen, Germany ABSTRACT In order to estmate the characterstcs of GPS antennas ths paper descrbes a new approach for the estmaton of absolute phase center varatons (PCV) n a feld calbraton. The man obectve of ths approach s the elmnaton of multpath from the GPS observable and the elmnaton of any nfluence of the reference antenna. Ths s acheved by formng the so called mean sdereal day tme dfference between observatons of successve days. Snce the satellte geometry of GPS satelltes repeats every mean sdereal day multpath does as well. Therefore, by dfferentatng observatons of two dfferent days multpath can be elmnated. To gan nformaton about the PCV specal rotatons have to be appled to the antenna of nterest. The paper shows the results for three dfferent antenna types. A second applcaton of the mean sdereal day tme dfference shows the estmaton of small poston changes between consecutve days. The mean sdereal day tme dfference s formed n the same manner as for antenna calbraton, however, wthout any rotaton. Therefore multpath and PCV are elmnated from the observable. We acheved wth observaton perods of 1 mnutes a horzontal poston resoluton of only 1. mm whch s better than results from standard data processng. INTRODUCTION Precse postonng wth GPS has now reached a level of accuracy where the remanng error sources are dentfed as effects caused by phase center varatons (PCV) of the antenna and ste effects lke multpath. Phase center correctons are generally mportant for GPS observatons wth mxed antenna desgn to take nto account the dfferent phase patterns of each antenna type. In addton t s not easy to separate between tropospherc errors and phase center bases. Multpath can have a sgnfcant nfluence on precse postonng dependng on the ste. Therefore the mpact of multpath on the poston estmaton should be consdered carefully.

2 So far the PCV are estmated by two dfferent methods. In an absolute sense t s possble to determne the PCV n an anechoc chamber [1] and n a relatve sense by a feld procedure [] wth a known antenna as a reference, whose PCV are estmated based on the frst method. The man dsadvantage of the relatve feld calbraton s the nfluence of the used stes. One can never assume that the feld calbraton s free of multpath. Therefore t s very lkely that the determned PCV hghly depend on the multpath effects and are correlated wth the selected ste. Wth a new method [3] we have shown a feld procedure for the calbraton of antennas n an absolute sense. Ths new method s based on the elmnaton of multpath by usng observaton data of dfferent days. ELIMINATION OF MULTIPATH A ste whch s totally unaffected by multpath does not exst. Thus, feld procedures for an antenna calbraton as well as short tme GPS observatons are dsturbed by ths effect. The results are ncorrectly estmated PCV values whch are ste dependent and a decreased resoluton for the pont postonng wth short observaton tmes. A short summary of the basc concept for the method to elmnate multpath s gven n ths paragraph. It s based on the repeatablty of the satellte geometry and therefore of the multpath sgnals after one mean sdereal day [4, 5]. New nvestgatons concernng the exact perod for the repeatablty of the satellte constellaton durng a four days test n 1997 revealed slghtly dfferent values for each satellte n a range between 4 s and 56 s nstead of the generally assumed value of 3 mn 56 s (36 s). The perod for the constellaton repeatablty was estmated by three methods. Frst of all, double dfferences of two successve days were cross-correlated n the tme doman. The maxma show the tme lags and clearly ndcate the sgnfcant perodcal appearance of multpath after a mean sdereal day (see [3]). Furthermore the perods are calculated from the correlaton of elevaton/azmuth tme seres and from ndvdual ephemers. The results of these three methods are n good agreement. Fgure1 shows the orbtng tmes for dfferent satelltes computed from the ephemers of four days. The perodcal appearance s used to greatly reduce the effect of multpath by subtractng the undfferenced GPS observable Fgure 1: The orbtng tmes for dfferent satelltes. of two successve days, takng nto account the evaluated tme lag for the dfference between a mean solar and a mean sdereal day, whch should be calculated from the data sets. The followng s a smplfed lnearzed notaton of the phase observaton equatons l Φ

3 n meters contanng the desgn matrx subvector a; the recever coordnate correctons x; the recever and satellte clock error dt and dt, respectvely, scaled to meters by the speed of lght c ; the ambguty N scaled to meters by the wavelength λ; the error terms d for onosphere (ION), troposphere (TROP), multpath (MP), and phase center varatons (PCV); and the nose of the phase ε φ : lφ = a x + c ( dt dt ) λ N d + d + d + d + εφ. (1) ION The subscrpt and superscrpt stand for recevers and satelltes, respectvely. Buldng a mean sdereal day tme dfference δ elmnates the multpath, phase center varaton and the complete geometrc nformaton. The followng observaton equaton does not contan any nformaton about geometry, snce the desgn elements a are almost dentcal on two successve days: δ lφ = c ( δ dt δ dt ) λ δ N δ d + δ d + δ εφ. () TROP ION MP PCV TROP The remanng terms comprse the mean sdereal tme dfferences of every component, whch are small for a short baselne (.e. atmospherc errors) and/or are correctly modeled n the GPS processng package GEONAP [6] (.e. clock errors). The nose level of the observable changed due to error propagaton to δ ε φ. In our paper [3] we demonstrated the elmnaton of multpath applyng the mean sdereal day tme dfference δ. Together wth the dramatcally reduced multpath the resoluton of the phase measurements mproved by a factor of 1.5. MODELLING AND ESTIMATION OF ABSOLUTE PHASE CENTER VARIATIONS (PCV) Although the mean sdereal day tme dfference elmnates ste dependent errors, ths approach can be used for the determnaton of absolute phase center varatons. Observatons are carred out on two days. One antenna s dentcally orentated on both days, whereas the antenna to be calbrated performs vertcal and horzontal rotatons on the second day only. Now, n extenson to equaton (), the lnearzed observaton equaton (3) for the tme dfference δ of the rotated antenna contans PCV of two dfferent orentatons: δ l = c ( δ dt δ dt ) λ δ N δ d + δ d Φ ( α, z) ( α+ α, z+ z) + d d + δ PCV PCV ε Φ. ION TROP (3) The observable for the estmaton of the absolute PCV s the dfference n the PCV of two antenna orentatons to an dentcal satellte: d ( α, z, α, z) = d ( α, z ) d ( α + α, z + z). (4) PCV PCV PCV

4 9 Elevaton [ o ] Azmuth [ o ] -1-8 a) 9 Elevaton [ o ] Azmuth [ o ] b) 9 6 Elevaton [ o ] Azmuth [ o ] c) Fg. : L1-PCV [mm], a) Ashtech 78 Rev. B, b) Trmble 4 ST L1/ Geod, c) Trmble Dorne Margoln Choke Rng.

5 In equaton (4) α und z are the orentaton parameter of the frst day, whle α and z represent the appled orentaton changes on the second day. As noted before, relatve observables are used for the generaton of the absolute phase pattern. Thus, only the topology of the pattern can be descrbed. The absolute sze s not known, but wll be treated as a constant clock error or a hardware delay n the GPS poston soluton. The term "absolute antenna calbraton", however, s stll vald for the approach, because the phase center varatons are determned ndependently from the phase pattern of a reference antenna. For the estmaton of the elevaton (and azmuth) dependent PCV serves a sphercal harmonc functon [3]: d ( α, z) = ( A cos mα + B sn mα) P (cos z). PCV nmax n n= m= nm nm nm (5) P nm are normalzed assocated Legendre functons. Azmuth α and zenth angle z refer to the poston of a partcular satellte n the antenna coordnate system. To enable horzontal rotatons and vertcal tlts of the GPS antenna, a specal mount must be used. Through the tlts a recepton of undsturbed satellte sgnals from hgher elevatons contrbute to a relable PCV determnaton at low elevatons n the antenna coordnate system, even at elevaton zero. Usng ths approach three dfferent antenna types have been calbrated so far (Ashtech 78 Rev. B Notches, Trmble 4 ST L1/L Geod, Trmble Dorne Margoln Choke Rng). The L1- and L-PCV are determned by a sphercal harmonc functon of degree 1 and order 5. Only the L1-PCV of these antenna types are shown n fgure. The calbraton for the Ashtech and the Trmble Choke Rng antenna was verfed n a second ndependent experment showng good agreement. Clearly, elevaton and azmuth dependent varatons are vsble. All antennas have very large varatons at low elevatons n common, especally for the Trmble Choke Rng reachng up to several cm. The performance of the antennas seems to be rather poor at very low elevatons. DETECTION OF SMALL DEFORMATIONS Another applcaton of the proposed observable δ s feasble for the determnaton of small poston changes. A baselne s observed on two dfferent days. The lnearsaton, dentcal on both days for each staton, s performed n the same manner as shown n equaton (1). Usng the reduced observable,.e. the mean sdereal day tme dfference, one should yeld the baselne components wth a hgher precson due to the mproved phase measurement resoluton. In an experment for the verfcaton of ths approach a short baselne was observed on two dfferent days. One of the antennas was mounted to a specal mechancal sledge (fgure 3) whch allows shfts n two horzontal drectons normal to each other. These can be performed wth hgh precson (better than.1 mm). The observatons on the frst day were carred out wthout changng the poston of the sledge. Small poston changes at a rate of mm were appled durng the second day. The sledge was shfted every 1 mnutes, frst to the north and then to the east. Ths procedure was repeated several tmes. The dashed lnes n fgure 4 and 5 show the performed shfts.

6 Fg. 3: Sledge Fgure 4 shows the dsplacements computed from the observatons of the second day only. The postons were estmated wth a smultaneous adustment of L1 and L, called LX. It s clearly vsble that the agreement wth the known shfts s rather poor. In fgure 5 one can see the estmated postons after applyng the mean sdereal day tme dfference wth the GEONAP software module GNSDIF. The agreement between the computed dsplacements and the actual dsplacements s very good. Therefore the shfts of the sledge can easly be montored by the mean sderal day tme dfference. The accuracy of the horzontal poston estmaton s n the order of 1. mm for an observaton wndows of 1 mnutes only. Hence, wth ths method t s possble to montor rather small deformatons at the 1mm-level, even wth very short observaton tmes. Although observatons on two days wth an dentcal setup (mount, antenna etc.) are requred, a number of applcatons are concevable (e.g. dam montorng). CONCLUSIONS Multpath s stll the most lmtng factor for precse postonng. Wth the proposed approach, the mean sderal day tme dfference, t s possble to elmnate multpath from the GPS observables. Ths derved observable can be used to observe small poston changes from one day to another or estmate absolute PCV of an antenna.

7 The man advantages of the absolute antenna calbraton are that t s a feld procedure, free of multpath, and ndependent from a reference antenna's phase pattern. Through the rotatons and tlts of the antenna areas wthout any observatons are avoded,.e. northern hole or low elevatons, and the antenna s completely covered. Stll, further examnatons are requste, e.g. errors ntroduced by the mount (errors n the rotaton), nfluence of the Fg. 4: True postons (dashed lne) versus estmated postons (sold lne) wthout δ. Fg. 5: True postons (dashed lne) versus estmated postons (sold lne) usng δ.

8 mount on the multpath envronment, and comparson wth other sources by applyng the PCV n operatonal GPS evaluatons. A future goal s the automatc calbraton wth a very precse robot to avod nstrumental erros of the mount and save observaton tme. The frst experments wth the mechancal sledge for the determnaton of small deformatons are already promsng. The resoluton of the postonng s clearly mproved. Further experments have to be carred out n order to mprove ths method for dfferent applcatons, e.g. deformaton montorng n permanent GPS arrays. Acknowledgment: Parts of ths work are funded by the German Bundesmnsterum für Bldung, Wssenschaft, Forschung und Technologe (BMBF, No. 3PLB). REFERENCES 1. Schupler, B.R., T.A. Clark, R.L. Allshouse: Characterzatons of GPS User Antennas: Reanalyss and New Results, In: Beutler, G. et al. (Eds.). GPS Trends n Precse Terrestral, Arborne, and Spaceborne Applcatons. IAG Symposum, No. 113, Boulder, Colorado, USA, Rothacher, M., S. Schaer, L. Mervart, G. Beutler: Determnaton of Antenna Phase Center Varatons Usng GPS Data, Workshop Proceedngs, IGS Workshop Specal Topcs And New Drectons, May 15-18, Potsdam, Germany, Wübbena, G., F. Menge, M. Schmtz, G. Seeber, C. Völksen: A New Approach for Feld Calbraton of Absolute Antenna Phase Center Varatons, Proceedngs of ION GPS-96, 9th Internatonal Techncal Meetng, September 1-17, Kansas Cty, Mssour, USA, Bock, Y.: Contnuous Montorng of Crustal Deformaton, GPS World, June 1991, pp. 47, Genrch, J.F.,Y. Bock: Rapd Resoluton of Crustal Moton at Short Ranges Wth the Global Postonng System, Journal of Geophyscal Research, Vo. 97, No. B3, pp , Wübbena, G.: The GPS Adustment Software Package -GEONAP- Concepts and Models, Proceedngs of the Ffth Internatonal Symposum on Satellte Postonng, Las Cruces, New Mexco, pp. 4561, 1989.