Stochastic Modelling of GPS Phase Observations for Improved Quality Estimation

Transcription

1 Stochatic Modelling of GPS Phae Obevation fo Impoved Quality Etimation Neil Bown 1, Allion Kealy 2 and Ian Williamon 3 1 PhD Candidate neb@unie.li.unimelb.edu.au 2 Lectue akealy@unimelb.edu.au 3 Pofeo and Head of Depatment ianpw@unimelb.edu.au Depatment of Geomatic The Univeity of Melboune, Autalia Tel: / Fax: ABSTRACT Data quality infomation ha been ecognied a eential in aeing the fitne fo ue of any patial dataet, and fundamental to enabling efficient and effective data integation though patial data infatuctue (SDI). Miing o inaccuate data quality infomation can eult in inappopiate ue of the data with aociated conequence of poo deciion making, educed utility and deceaed maket value. The inceaing ue of the Global Poitioning Sytem (GPS) a a pimay data acquiition ouce fo patial databae highlight the ignificance of thi poblem. At peent the meaue of quality fo GPS deived coodinate given by commecial oftwae package tend to be unealitic and ae moe often than not optimitic. Thi i becaue not all of the ytematic and andom eo peent in the obevation ae fully modelled though the tandad functional o tochatic model ued. Thi pape peent ome of the cuent poblem in identifying the quality of GPS data a deived fom commecial poceing oftwae. Common GPS poceing tategie ae eviewed in the context of eo modelling and data quality. Finally, cuent eeach activitie into tategie fo maximizing GPS data quality ae peented.

2 INTRODUCTION Recognition of patial data a a valuable eouce fo deciion making and aet management i diving the development of patial data infatuctue (SDI) at global, egional, national and local cale. In geneal the pupoe of SDI i to enable efficient collection, management, acce, delivey and utiliation of patial data (Coleman and McLaughlin, 1998, Rajabifad et al., 2000, GI2000, 1996). SDI ae initiative that aim to hae conitent data et in an eay and ecue manne with a vaiety of ue and typically conit of an intitutional famewok, technical tandad, fundamental data et, acce netwok and human eouce (Rajabifad et al., 2000, Coleman & McLaughlin, 1998). The potential application of SDI ae unlimited, howeve they ae geneally mot ecognied fo thei benefit in eouce maximization and deciion making. At the coe of SDI i the deie to integate patial data et fom a ange of ouce into a GIS in ode to manage aet o aid deciion-making. The geodetic famewok i one of the fundamental data et in SDI becaue it i neceay to efeence patial data and facilitate the integation of data fom a vaiety of ouce and egion. Without a common efeence famewok data et will be inconitent and not match. Theefoe, in ode to integate two data et conideation mut be given to the efeence fame (geodetic datum) ued and the tanfomation between them. Unmodelled ytematic eo in the datum definition can eult in lo of data quality if the tanfomation doe not account fo them. The quality of individual ecod within a dataet alo effect data integation, a eal-wold elationhip may not be epeented within the data. Without undetanding of the data quality uch miepeentation have the potential to adveely affect deciion made baed on the data. Spatial data quality i expeed in tem of accuacy and peciion and i a function of the geodetic infatuctue, equipment, field pactice and poceing methodology ued to gathe the data. Often accuacy i difficult to meaue and peciion i ued intead. Thi ha the potential to give mileading etimate of the accuacy and i a majo focu of thi pape. The eade i efeed to Hunte (1999) fo infomation on the handling of patial data quality in GIS. Peciion, o epeatability, i a tatitical tem that decibe the andom eo in a olution and i epeented by a tandad deviation o RMS (oot-mean-quae). A ytem in which the calculated peciion etimate of the paamete i epeentative of the tue eo i aid to have high fidelity. If a meauement ytem ha high fidelity, the ue i bette able to enue that meauement ae within toleance. The difficultie in detemining good (high fidelity) data quality etimate hall be dicued with efeence to GPS. The accuacy equiement of data collected fo ue within SDI depend on the intended application of the data. Regadle of how coae the data ae thee i a equiement to have a meaue of the data quality. Knowledge of data quality i eential to aeing data fitne fo pupoe and inceaing it potential ueability within a SDI. It i ecognied that fo patial data to be ued coectly and wiely, metadata that decibe data quality, in addition to othe attibute, hould accompany the patial data (Nebet, 2000, GI2000, 1996). Depending on the paticula data and it poible ue thi may mean that metadata down to the individual featue, object o ecod level i neceay (Nebet, 2000). Data quality fo poitional infomation i geneally given in tem of a tandad deviation and eult fom the data captue poce. Mipecification of thi quality paamete may eult in inappopiate ue and educed utility and

3 maket value of the data. At peent, the meaue of GPS quality given by common oftwae package ae eithe ove-optimitic, o conveely, ae ovely conevative and theefoe have low fidelity (Keenan and Co, 2001, Bane et al., 1998, Wang, 1999). Thi lack of fidelity can potentially impact SDI development tating with the geodetic infatuctue and at evey juidictional level and i an active aea of eeach woldwide. The Global Poitioning Sytem (GPS) ha etablihed itelf a the pimay mean fo patial data captue and i inceaingly being ued in a wide ange of application fom peonal navigation to geodey. In ecent yea thee ha been a lot of dicuion egading GPS data quality. Much of the eeach in thi aea ha focued on the tochatic model ued in GPS poceing and thei impotance to ambiguity eolution (eg Han, 1997, Teunien, 1997, Wang, 1999). Thi pape outline the fundamental theoy of GPS and the methodology behind cuent poceing algoithm and model in ode to illutate the quality concen in GPS poitioning. GPS POSITIONING Each atellite in the GPS contellation tanmit ignal on two inuoidal caie wave with fequencie of MHz and MHz, deignated L 1 and L 2. Modulated onto L 1 ae two peudo-andom noie (PRN) code, C 1 and P 1 in RINEX (Gutne, 2000) notation. A econd P-code (P 2 ) i modulated onto the L 2 fequency. The C 1 (o civilian/acce o C/A) code epeat evey milliecond and i unique fo evey atellite. A GPS eceive geneate intenal copie of the PRN code. Auming the clock in the atellite and eceive ae both ynchonied to GPS time, the ignal tavel time can be detemined by meauing the hift between the intenal and incoming veion of the code. The PRN code ae deigned o that they have a low auto coelation allowing the hift to be meaued peciely and unambiguouly. Multiplication of the tanmition time by the peed of light give the ange between the atellite and eceive. Howeve, becaue the atellite and eceive clock ae not pefectly ynchonied with GPS time and the influence of othe eo ouce thee ange ae called peudoange. It i poible to meaue the caie beat phae ued to tanmit the code moe peciely than the code themelve, howeve the o-called intege ambiguitie mut be eolved fo centimete and bette poitioning (Hoffman-Wellenhof et al., 1994). Both phae and code meauement can be witten in the fom of peudoange. A phae peuodoange a (van de Mael, 1998) Φ between eceive and atellite (in mete) can then be expeed Φ = x (t) x (t) + cδt (t) cδt (t) + I (t) + T (t) + M (t) + D (t) + λn + e (t) (1) whee: x, x δ t, δt ae the vecto of atellite and eceive coodinate at time of tanmiion (t); ae the atellite and eceive clock offet fom GPS time;

4 I T M D e λ c i the appaent eo in the ange caued by the ionophee; i the appaent eo in the ange caued by the topophee; i the multipath eo; i the antenna phae cente offet and vaiation; i the meauement noie; i the wave length of the ignal; and i the peed of light. Peudoange ae imultaneouly meaued fom a numbe of atellite. Meauement to at leat fou atellite ae equied to calculate a thee-dimenional poition becaue the eceive clock mut alo be etimated. Thi educe to thee if Dopple meauement ae available (Hoffman-Wellenhof et al., 1994). Data ceening i pefomed to emove outlie and (fo phae data) detect and epai cycle lip. The leat quae algoithm i ued to etimate the unknown coodinate of the eceive and (optionally) othe paamete of inteet along with thei peciion. Conequently an obevation equation of the fom: Φ = f (X, Y, Z, Δδt ) (2) can be contucted whee Φ peudoange meauement X, Y, Z coodinate of the eceive δ eceive clock offet t Thi mut be lineaied uing a Taylo Seie expanion fo ue in the leat quae algoithm. On lineaiing the equation become: ' ' ' ' f f f f Φ f (X,Y, Z, Δδt ) = ΔX + ΔY + ΔZ + Δδt (3) X Y Z Z ' ' ' ' whee X, Y, Z, Δδt ae appoximate value (a pioi etimate) of the eceive poition and clock offet and ΔX, ΔY, ΔZ, Δδt ae coection to the appoximate value and ae the unknown being ought. The m meauement and u paamete ae then epeented in the linea fom uing the indiect method a: v = A x + w (4) mx1 mxu ux1 mx1 whee v i a vecto leat-quae eidual, A i the deign matix eulting fom the mathematical (functional) model which elate the obevation to the unknown paamete being ought, x i the vecto of unknown paamete (coection to the a pioi etimate) and w i a vecto of computed minu obeved meauement. A m by m vaiance-covaiance matix i C l

5 contucted baed on the tochatic model which decibe the tatitical behaviou of the obevation in context of the mathematical model. The diagonal element of C l ae the vaiance (σ 2 ) of the meauement. The leat-quae optimied etimate fo the paamete i then obtained by iteating (Mikhail, 1976) xˆ T 1 T = (A PA) A Pw (5) whee P i the weight matix, defined a the invee of the vaiance-covaiance matix C l. The vaiance-covaiance matix of the leat quae etimate i obtained via (Mikhail, 1976) C 2 T 1 xˆ = σ0 (A PA) whee v T 2 Pv σ 0 = (6) (m u) Obviouly, the mathematical and tochatic model ae citical to paamete etimation. It i the tak of the mathematical model to account fo ytematic eo in the obevation whilt the tochatic model decibe thei andom natue. Failue to coectly model the ytematic biae will eult in inaccuate coodinate. Inadequately modelled andom eo, which ae geneally mall, have only a mino effect on the paamete but caue low fidelity quality etimate and can make ambiguity eolution moe difficult. Unfotunately many of the eo ouce lited above ae difficult to model, epecially if the GPS antenna i moving. A uch eveal poceing algoithm ae commonly adopted when tying to obtain poition accuate to between the decimete and millimete level fom GPS, all of which impoe etiction on the equipment and meauement pocedue that i ued. The mot widely known of thee method i diffeential poitioning (o DGPS). Note the tem DGPS i nomally only ued fo poitioning baed on the PRN code. Anothe technique employ linea combination of the code and/o phae meauement on one o moe fequencie to eliminate o etimate ome ouce of eo. Linea Combination If both code and phae meauement ae available on one o moe fequencie linea combination of the meauement may be fomed. A numbe of linea combination ae widely ued to etimate o eliminate eo in the GPS ignal. Fo intance, a linea combination of code and phae meauement on a ingle fequency can be ued to etimate the code multipath (Etey and Meeten, 1999). Othe linea combination ae ued to fom new obevation equation a pat of the mathematical model. Two uch linea combination (in Benee notation) ae the L 3 ionophee-fee and the L 5 wide-lane linea combination. The L 3 combination i calculated a (Hugentoble et al., 2001) 1 L = (f1 L1 f2 L2) 2 2 f1 f (7) 2

6 and i vey ueful fo ambiguity eolution becaue it eliminate almot all of the ionopheic delay. Howeve, the noie on L 3 i appoximately thee time geate than that of L 1. Alo the ambiguitie loe thei intege natue when L 3 i fomed meaning that L 3 cannot be diectly ued to eolve L 1 and L 2 ambiguitie. Intead L 3 i ued in conjunction with anothe combination uch a L 5. Calculated a (Hugentoble et al., 2001) 1 L5 (f1l1 f2l2) f1 f2 = (8) the wide-lane linea combination i named becaue of it long (~86cm compaed with 19cm fo L 1 ) wavelength. Whilt the noie i geatly magnified the influence of the ionophee i elatively mall in elation to the wavelength and the ambiguitie etain thei intege natue. If the widelane ambiguitie ae eolved the detemination of the L 1 (and hence L 2 ) ambiguitie i geatly implified. Diffeencing Whilt the peviouly mentioned eo ae unique to a paticula eceive-atellite combination, eo between anothe eceive and the ame atellite will be imila if the eceive ae cloe to one anothe (ee Figue 1). The ame i tue fo one eceive and two atellite, o between one eceive and one atellite at diffeent time. Thee patial and tempoal coelation in the obevation ae a function of baeline length and aie fom eo caued by the atellite and eceive clock, topophee, ionophee and obit. The patial coelation between the meauement i the bai fo the double-diffeencing pocedue, wheeby one eceive i poitioned elative to anothe eceive with known coodinate. A typical example i the cae of a oving eceive being poitioned elative to eceive fom a pemanent aay of efeence tation (uch a the Autalia-wide Autalia Regional GPS Netwok (ARGN) opeated by AUSLIG o Land Victoia GPSnet in Victoia). The double diffeence fo obevation taken imultaneouly with two eceive (i and j) fom two atellite (m and n) i given by: mn m m n n Δϕ = ( ϕ ϕ ) ( ϕ ϕ ) (9) ij i j i j whee Δ i the double diffeence opeato and ϕ i the code o phae obevation. Thi can be pefomed a a matix opeation: Δ ϕ = D.ϕ (10) whee ϕ i a vecto of code o phae meauement and D i the double diffeencing matix. Diffeencing ha the effect of eliminating the patially coelated eo and i mot effective with hot baeline. Double-diffeencing effectively emove eo eulting fom the atellite and eceive clock and ignificantly educe eo caued by the ionophee, topophee and

7 atellite obit. The downide of thi pocedue i that each double diffeence equie fou oneway meauement. Figue 1. Coelation in the GPS ignal (Bane and Co, 1998) LIMITATIONS IN ERROR HANDLING Uing the diffeencing and linea combination algoithm outlined above mot of the ytematic eo can be eliminated fom the obevation. Thi eult in geatly implified obevation equation and, hence, a implified mathematical model. The functional model ued in GPS poitioning ae well defined and documented and ae geneally accepted (Bock et al., 1986, Hoffman-Wellenhof et al., 1994, Stang and Boe, 1997). Howeve, ome ytematic eo (uch a multipath) ae not emoved by thee method and eidual eo emain fom othe ouce. Empiically deived mathematical model fo the topophee and antenna phae cente vaiation can help in educing thi eo. The magnitude of the emaining eo depend on: multipath, the poceing algoithm ued (eg L 3 ued to eliminate the ionophee), baeline length, antenna phae cente model and topopheic model ued, ephemei type (boadcat o pecie), and the paamete etimated explicitly by the mathematical model (eg topopheic etimate). In addition to the ytematic eo, coelation and noie exit in the data and hould be accounted fo in the tochatic model. Moden eceive ae able to meaue the caie phae to

8 bette than 0.01 cycle, which coepond to millimete peciion (Hoffman-Wellenhof et al., 1994). Thi noie i amplified when ome linea combination ae fomed (eg L 3 mentioned peviouly). Coelation eult fom a numbe of pocee. The elatively low vaiation in the atmophee compaed to the GPS obevation inteval intoduce a time coelation in the eo. When antipoofing i enabled, eceive mut apply econtuction technique to enable meauement of the P-code and caie phae on L 2. Thi can eult in a coelation between the obevable on the two fequencie (Bona, 2000). Some eceive alo filte the meauement in an effot to educe noie intoducing a time coelation (Bona, 2000). Receive have alo been een to have inte-channel biae and L 1 /L 2 diffeential delay (Gao et al., 1999, Lin and Rizo, 1996). CURRENT STOCHASTIC MODELS The leat quae algoithm elie on coect weighting of the meauement to povide unbiaed etimate of the paamete. Reidual and unmodelled ytematic eo in the functional model and coelation between the GPS obevable mean that detemination of the vaiance-covaiance matix (and hence the weight matix) i difficult (Bane et al., 1998, Wang, 1999, Keenan and Co, 2001). It i common pactice (Hoffman-Wellenhof et al., 1994, Stang and Boe, 1997) to aume that the obevation fom evey atellite have equal vaiance and ae uncoelated. I.e. [ e (t)] 0 [ e () t.e j() t ] 0 [ e () t.e i ( v) ] 0 2 [ () t ] = E[ e () t e () t ] = σ E i = (11a) E i = ( i j) (11b) E i = ( t v) (11c) V ε (11d) i i i 2 The tochatic model fo the one-way obevation i theefoe Cl = σ I. The mathematical coelation that aie fom the fomation of the double diffeence obevation can be modelled T uing Cll = D ClD whee Cll i the vaiance-covaiance matix of the double diffeenced obevation and D i the diffeencing matix fom Equation (10). Such an appoach ignoe diffeence in the noie chaacteitic that eult fom ignal popagation and adio fequency (RF) intefeence and diffeence in the atellite antenna. It alo ignoe the coelation between the meauement that wee mentioned peviouly. Some oftwae ue a lightly moe ophiticated poce that calculate individual weight fo each atellite baed on it elevation, ignal to noie atio (SNR) o the baeline length, but which alo ignoe coelation between the meauement (Bane et al., 1998, Bock et al., 1986). Even high-end oftwae ue thee tochatic model, though they may alo have the option to etimate a tochatic model by pot-fitting the eidual fom the poceing (MIT and Scipp, 2000). Whilt atellite elevation and SNR can be ued a quality indicato, they do not alway eflect eality becaue of ignal diffaction and othe influence (Satiapod and Wang, 2000, Bunne et al., 1999, Gedan, 1995). Bane et al. (1998) demontate the inadequacie of thee appoache

9 and the inceaed peciion and fidelity obtained by uing the coect tochatic model which they calculate uing a evee engineeing appoach. In geneal, an incoect tochatic model will eult in uneliable eult, ove-optimitic meaue of peciion and a educed ability to detect eo (Nicolai, 1988). Impoving the tochatic model alo ha benefit in fate and moe eliable intege ambiguity detemination (Eule, 2000, Han, 1997). DEVELOPMENTS IN STOCHASTIC MODELLING A numbe of technique ae available to etimate vaiance-covaiance infomation of geodetic data, including Minimum Nom Quadatic Unbiaed Etimation (MINQUE) developed by Rao (1971) and the Genealized Maximum-Likelihood Etimation (GML) in Godecki (2001). Unfotunately, thee appoache ae not ideal becaue they aume the covaiance matix i block diagonal, theeby making it difficult if not impoible to etimate tempoal coelation uing thee method. Wang (1998) ue the MINQUE algoithm and adapt the double-diffeence functional model to include time coelation. An initial olution fo the paamete i made uing the tandad double-diffeence mathematical and tochatic model, fom which the coelation coefficient ae etimated. Reult peented by Wang (1998) how a conideable impovement of thi method ove nomal poceing algoithm. Howeve, thi methodology aume the baeline ae hot and i computationally intenive. A genealied yet epeentative tochatic model i yet to be developed. One facto inhibiting the geneation of uch a model i multipath. Phae multipath on L 1 can be a high a 4.7cm, which i well above the noie level (Wanninge and May, 2000). Calculation of the multipath eo equie that the poition, oientation and eflectance of all eflective uface in the vicinity of the antenna be known. Tet by Moa-Cato et al. (1998) how that, if thi infomation i available, multipath can be modelled quite well. Poviding thee i no change in the eflectance of the eflecting uface (a might be caued by ain o now) the multipath at a fixed ite will epeat each 23h 56min when the configuation of the atellite contellation i the ame. Radovanovic (2000) how that multipath coelation between conecutive day i highet within 12 econd of 23h 56min. Modelling of multipath by it day to day epeatability can how impovement of 25% to 40% but equie well known eceive coodinate, a fixed antenna and table eflecto and eflectance (Radovanovic, 2000). The autho plan to analye lage amount of data fom the Victoian GPSnet efeence netwok (GPSnet) in ode to ty and etablih tend in the eidual and impove undetanding of eceive behaviou. If the tochatic model i coect and ytematic eo (uch a multipath) have been emoved the eidual may be expected to have a contant (zeo) mean and vaiance. If not a modification i equied to the tochatic model, pehap equiing the addition of one o moe vaiable. Due to modelling etiction the one-way obevation ae unuitable fo analyi at the noie level, while the double diffeence obevation have a moe complicated tuctue with the noie being a function of eight individual meauement. Analyi of zeobaeline data (two eceive connected to a ingle antenna) how that, in the abence of eidual ytematic eo, the double diffeence meauement ae uncoelated and Gauian (whitenoie) in natue. The vaiance vay widely between diffeent atellite pai howing elevation dependence. Plotting the empiical covaiance function of non-zeo baeline how that thee i a tong time coelation in the double diffeence. The aim i to epaate out each eo ouce,

10 tating with multipath, fom the eidual leaving the andom eo, which can then be modelled. Fom the empiical covaiance function it i poible to fit a covaiance model fo the ytematic and andom pat of the eo (the ignal and the noie). Leat quae collocation, which include a tochatic ignal in the paamete etimation poce, can then be ued to povide moe pecie etimate of the paamete of inteet. The difficulty lie in detemining the ouce and natue of the coelation in the data. Thi mean beaking down the eultant eo into it contituent pat, and i the focu of ongoing eeach. CONCLUSION Examination of cuent technique ued to handle the numeou eo ouce in GPS ha hown that mot eo can be effectively emoved given the ight cicumtance (equipment, baeline length, time etc). Howeve, ome ytematic eo ae till poblematic, epecially multipath. Additionally cuent tochatic modelling i not neceaily able to model the noie and coelation in the GPS meauement. Continuing eeach into tochatic modelling i expected to eult in highe fidelity quality etimate of GPS deived poition than ae poduced by cuent commecial oftwae package. Impoved quality etimation will have follow-on effect fo data utility and ue though SDI by allowing fo moe ound aement of the uitability of the data and deciion made uing the data. ACKNOWLEDGEMENTS The autho would like to gatefully acknowledge the uppot of Land Victoia and the Cente fo Spatial Data Infatuctue and Land Adminitation, The Univeity of Melboune in pepaing thi pape. REFERENCES Bane, J.B., Ackoyd, N., and Co, P.A., (1998), Stochatic Modelling fo Vey High Peciion Real-Time Kinematic GPS in an Engineeing Envionment, Poceeding of FIG XXI Intenational Confeence, July, Bighton, UK, Commiion 6, Bock, Y., Gouevitch, S.A., Counelman III, C.C., King, R.W. and Abbot, R.I., (1986), Intefeometic Analyi of GPS Phae Obevation, Manucipta Geodaetica, 11, Bona, P., (2000), Peciion, Co Coelation, and Time Coelation of GPS Phae and Code Obevation, GPS Solution, 4, 2, Bunne, F.K., Hatinge, H., and Toye, L., (1999), GPS Signal Diffaction Modelling: The Stochatic SIGMA-Δ Model, Jounal of Geodey, 73, Coleman, D.J., and McLaughlin, J., (1998), Defining Global Geopatial Data Infatuctue (GGDI): Component, Stakeholde and Inteface, Geomatica, 52, 2,

11 Etey, L.H., and Meeten, C.M., (1999), TEQC: The Multi-Pupoe Toolkit fo GPS/GLONASS Data, GPS Solution, 3, 1, pp Eule, H-J., (2000), Advance in Ambiguity Reolution fo Suveying Type Application, Poceeding of ION GPS-2000, Salt Lake City, Utah, Septembe 19-22, Gao, Y., Lahaye, F., Héoux, P, Liao, X., Beck, N., and Olynik, M., (1999), Invetigation of Meauement Inconitency in Dual-Fequency GPS Receive, Poceeding of the 12 th Intenational Technical Meeting of the Satellite Diviion of the Intitute of Navigation, Septembe 14-17, 1999, Nahville, Tenneee, Gedan, G.P., (1995), A Compaion of Fou Method of Weighting Double Diffeence Peudoange Meauement, Tan Taman Suveyo, 1, 1, GI2000, (1996), Towad a Euopean Policy Famewok fo Geogaphic Infomation, A woking document of GI2000 homepage, Acceed May 2001, < Godecki, J., (2001), Genealized Maximum-likelihood Etimation of Vaiance-covaiance Component with Non-infomative Pio, Jounal of Geodey, 75, Gutne, W., (2000), RINEX: The Receive Independent Exchange Fomat Veion 2, Atonomical Intitute, Univeity of Ben. Han, S., (1997), Quality-contol Iue Relating to Intantaneou Ambiguity Reolution fo Realtime GPS Kinematic Poitioning, Jounal of Geodey, 71, Hoffmann-Wellenhof, B., Lichtenegge, H., and Collin, J., (1994), GPS Theoy and Pactice, Spinge-Velag, New Yok. Hugentoble, U., Schae, S., and Fidez, P., (ed), (2001), Benee GPS Softwae Veion 4.2, Atonomical Intitute, Univeity of Bene. Hunte, G.J., (1999), New Tool fo Handling Spatial Data Quality: Moving fom Academic Concept to Pactical Reality, Poceeding of the URISA 99 Confeence, Chicago, Augut 1999, pp Keenan, C.R. and Co, P.A., (2001), Stochatic Modelling: The Cucial Element in High- Fidelity DGPS Quality Aement?, Poceeding of Hydo'2001, Confeence of The Hydogaphic Society, Univeity of Eat Anglia in Nowich, Mach 2001, 12 pp. Lin, L, and Rizo, C., (1996), An Algoithm to Etimate GPS Satellite and Receive L1/L2 Diffeential Delay and it Application to Regional Ionophee Modelling, Geomatic Reeach Autalaia, 65, Mikhail, E.M., (1976), Obevation and Leat Squae, IEP, New Yok.

12 MIT and Scipp, (2000), Documentation fo the GAMIT GPS Analyi Softwae, Releae 10.0 Decembe Moa-Cato, E.J., Coacoa-Sanz, C., and Otega, G., (1998), Chaacteiation of the Multipath Effect on the GPS Peuodoange and Caie Phae Meauement, Poceeding of ION GPS 98, Nahville, Nebet, D.D., (ed), (2000), Developing Spatial Data Infatuctue: The SDI Cookbook, Global Spatial Data Infatuctue Technical Woking Goup, Daft 1.0 June Nicolai, I.R., (1990), Some pactical example of the ue of tandadied tatitical teting of poitioning fo eimic and engineeing uvey, FIG XIX Intenational Conge, Helinki, Finland, 17pp. Radovanovic, R.S., (2000), High Accuacy Defomation Monitoing Via Multipath Mitigation by Day-To-Day Coelation Analyi, Poceeding of ION GPS 2000, Salt Lake City, Rajabifad, A., Williamon, I.P., Holland, P., and Johntone, G., (2000), Fom Local to Global SDI Initiative: A Pyamid of Building Block, Poceeding of the 4 th GSDI Confeence, Cape Town, South Afica. Rao, C.R., (1971), Etimation of Vaiance and Covaiance Component MINQUE Theoy, Jounal of Multivaiate Analyi, 1, Satiapod, C. and Wang, J., (2000), Compaing the Quality Indicato of GPS Caie Phae, Geomatic Reeach Autalia, 73, Decembe 2000, Stang, G., and Boe, K., (1997), Linea Algeba, Geodey and GPS, Welleley-Cambidge Pe, Welleley. Teunnien, P.J.G., (1997), A Canonical Theoy fo Shot GPS Baeline Pat IV: Peciion and Reliability, Jounal of Geodey, 71, van de Mael, H., (1998), Vitual GPS Refeence Station in the Netheland, Poceeding of ION GPS 98, Nahville, Wang, J., (1999), Modelling and Quality Contol fo Pecie GPS and GLONASS Satellite Poitioning, PhD Thei, School of Spatial Science, Cutin Univeity of Technology. Wanninge, L., and May, M., (2000), Caie Phae Multipath Calibation of GPS Refeence Station, Poceeding of ION GPS 2000, Salt Lake City, Neil Bown BIOGRAPHICAL NOTES

13 Neil gaduated fom the Univeity of Melboune in 1999 with a Bachelo of At and a Bachelo of Geomatic (Honou). He i cuently undetaking a Docto of Philoophy degee in the Depatment of Geomatic, Univeity of Melboune on tochatic modelling of the GPS obevable. Allion Kealy Allion Kealy i cuently a lectue in the Depatment of Geomatic at the Univeity of Melboune, pecialiing in the eeach aea of GPS, GLONASS and integated ytem. Allion eceived he PhD in Geodey fom the Univeity of Newcatle upon Tyne, UK in 1996, afte which he pent 2 yea in induty poviding technical uppot fo GPS/GLONASS manufactue Ahtech Ltd. Pofeo Ian Williamon PhD (NSW), DHC (Olztyn), FTSE, FISAut, FIEAut, HonMFIG, HonFMSIAut, LS, CPEng Ian Williamon i Pofeo of Suveying and Land Infomation, Head, Depatment of Geomatic and Diecto, Cente fo Spatial Data Infatuctue and Land Adminitation at the Univeity of Melboune. Hi teaching and eeach i concened with deigning, building and managing land adminitation, cadatal, and land and geogaphic infomation ytem in both developed and developing countie. He i a Licened Land Suveyo and Chateed Pofeional Enginee. He ha undetaken eeach and conultancie woldwide including fo Autalian govenment, AuAID, many individual county govenment, the United Nation and the Wold Bank. He wa Chaipeon of Commiion 7 (Cadate and Land Management) of the Intenational Fedeation of Suveyo , and i cuently Diecto, FIG/UN Liaion He i an Honoay Membe of the FIG. At the Univeity of Melboune he ha been Peident of the Academic Boad and Po-Vice-Chancello. He i cuently Chaipeon of the Victoian Govenment Geopatial Infomation Refeence Goup and Chaipeon of Woking Goup 3 (Cadate) of the United Nation ponoed Pemanent Committee fo GIS Infatuctue fo Aia and the Pacific ( ).