COORDINATE TRANSFORMATION TOOL FOR ANDROID MOBILE DEVICES

Transcription

1 Ceylon Journl of Science (Physicl Sciences) 18 (2014) Computer Science COORDINATE TRANSFORMATION TOOL FOR ANDROID MOBILE DEVICES A. A. D. C. Alhkoon, S. R. Kodituwkku, J. Gunthilke Postgrdute Institute of Science, University of Perdeniy, Sri Lnk. (*Corresponding uthor s emil: slukk@pdn.c.lk). (Received: 28 June 2013 / Accepted fter revision: 04 Mrch 2014) ABSTRACT Android is becoming successful mobile operting system (OS) with growing populrity. Most ndroid devices hve inbuilt GPS receivers. Although it is very populr in Sri Lnk, coordinte system comes with it is not suited becuse pproprite coordinte trnsformtion tools tilored to Sri Lnk re not vilble. This pper presents the development of such tool for Android pltform with the cpbility of ccessing GPS or network derived loction dt from device nd performs Molodensky dtum trnsformtion with Trnsverse Merctor projection to derive Ntionl Grid coordintes. The proposed method ws tested within Sri Lnk nd it is found tht it is efficient nd relible. The softwre product nmed CTDroid with mny cpbilities including coordinte trnsformtion ws mde vilble to Android community s free tool vi Google Ply. University of Perdeniy 2014 INTRODUCTION Globl positioning system (GPS) is United Sttes (US) owned system trgeting position, nvigtion nd timing services. The bsic ide is to build constelltion of stellites (spce segment) hving the cpbility of trnsmitting one wy signl which cn be picked up by ground receivers (user segment) to derive loction nd timing. At present, GPS constelltion holds 31 opertionl GPS stellites nd 3 or 4 residul stellites which cn be ctivted if needed. Control segment mnges the entire spce segment opertions (USG, 2012). Currently, GPS plys vitl rolls relting to our dy tody ctivities even without us noticing them. For exmple, simple tsk of withdrwing money from n Automted Teller Mchine (ATM) my involve GPS technology to mesure timing of trnsctions. Vehicle nvigtion systems re nother well-known instnce tht is closer to generl public (USG, 2012b). These systems re lredy gining populrity in Sri Lnk s some telecommuniction providers providing such nvigtion service to their users. These devices including smrt phones hving GPS receivers help users to nvigte, find friends nd even for running ugmented relity pplictions. GPS devices found inside smrt phones mostly operte with ssisted University of Perdeniy 2014 GPS (A-GPS) technology where the GPS sensor cquires ephemeris nd lmnc through mobile dt network (Wikimedi, 2012). However, when it comes to professionl GPS users working in res of Nvigtion, Surveying, Mp mking, Disster relief, Reconstruction, Militry nd mny more (USG, 2012b), they tends to prefer professionl GPS receivers. Their choices my be from compnies like Mgelln, Gmin, DeLorme, nd Lowrnce etc., who provide GPS receivers with Coordinte Trnsformtion fcility nd mny dditionl fetures like point to point nvigtion, cpbilities to plot loctions, keeping trck of user trcks, heding nd bring indictions, compss, mps nd mny more. Smrtphone GPS devices usully work with WGS84 dtum. The defult pplictions support very few projections such s Merctor projection found on Google nd Bing mps. This pper presents n ppliction tht cn perform coordinte trnsformtion tilored to Sri Lnk. The ppliction is cpble of performing Molodensky dtum trnsformtion nd Trnsverse Merctor projection to derive Sri Lnk ntionl grid coordintes. Additionlly, the tool is cpble of storing, visulizing loctions on Google mps nd lso cpble of crrying out bck

2 projection to obtin Geogrphic coordintes when presented with Sri Lnk ntionl grid coordintes. METHODOLOGY The overll trnsformtion is performed in severl steps described below. Coordinte Trnsformtion Coordinte trnsformtion is simply, trnsforming from one coordinte system to nother. For exmple, one 2D coordinte System to nother 2D coordinte system. The process my involve dtum trnsformtion nd projection. The ppliction presented through this pper pplies coordinte trnsformtion to convert mobile GPS sensor obtined ltitude, longitude in reference to WGS84 dtum in to Sri Lnk ntionl grid coordintes in the form of x nd y. Dtum trnsformtion is crried out using Molodensky lgorithem while Trnsverse Merctor projection lgorithum is utilized for projection (Knippers, 2012). Dtum Trnsformtion The erth is not perfect sphere nor is perfect ellipsoid. This is due to the erth s rottion nd the grvity differences in its surfce. This shpe, more clerly the shpe of the men se surfce under the influence of vrying grvity is clled the Geoid. Geoid cn be modelled by complex mthemticl equtions. To simplify the complexity, ellipsoids re used to represent erth s shpe. Ellipsoid with the prmeters used to fit the ellipsoid in to specific region collectively is clled the dtum. WGS84 is such dtum defined to use with entire erth surfce nd is used in GPS receivers when clculting initil loction. Since WGS84 is not perfect for mny regions including Sri Lnk, dtum trnsformtion is necessry. In the cse of Sri Lnk, Kndwl or SLD99 dtum should be used. In this study, WGS84 to Kndwl dtum trnsformtion is considered. Molodensky Dtum Trnsformtion Molodensky trnsformtion is three prmeter dtum trnsformtion. However more complex trnsformtions re vilble with Helmet, Abridged Molodensky nd Molodensky-Bdeks. Molodensky formule enbles ltitudes, longitudes nd heights (φ, λ, h) with reference to one dtum to be trnsferred in to (φ, λ, h) relted to nother dtum. During the conversion, three implicit ssumptions re mde tht is: the X, Y, Z Crtesin xes of both ellipsoids re prllel, the coordinte differences δx, δy, δz between the origins of the two reference ellipsoids re known nd the defining geometric prmeters of both reference ellipsoids re known. The lgorithm ccepts φ, λ, h s input nd clcultes nd output δx, δy, δz vlues. Due to these chrcteristics, Molodensky trnsformtion formule re known s curviliner trnsformtion formule. Stndrd Molodensky coordinte trnsformtion formule re given below (NGIA, 2012). 1 δφ = { δx sin φ cos λ R m + h δy sin φ sin λ + δz cos φ + R Ne 2 sin φ cos φ δ + sin φ cos φ (R M b b + R N ) δf} δλ = [(R N + h ) cos φ] 1 ( δx sin λ + δy cos λ) δh = δx cos φ cos λ + δy cos φ sin λ + δz sin φ δ R N b + R N sin2 φ δf Where R N =, R M = (1 e 2 sin 2 1 φ) 2 (1 e 2 ) (1 e 2 sin 2 φ) 3 2, h = N + H In the bove equtions, φ is Geodetic ltitude, λ is Geodetic longitude, h is geodetic height (height reltive to the ellipsoid), N is geoid height, H is orthometric height (height reltive to the geoid), δφ, δλ, δh re Corrections needed to trnsform the dtum, δx, δy, δz re sifts between centers of the from nd to dtum, is semi mjor xis of the from dtum ellipsoid, b is semi minor xis of the from dtum ellipsoid, f is flttening of the from geodetic dtum ellipsoid, e is first eccentricity, R N is rdius of curvture in

3 the prime verticl nd R M is rdius of curvture in the meridin. During the implementtion, prmeters defined in the Tble 1 were used. Mp Projection Mp projection describes mthemticl trnsformtion of ny prt of erth s curved surfce in to flt pne. In other words, during mp projection, the curved horizontl reference surfce must be mpped onto the 2D mpping surfce. Trnsformtion of geogrphic coordintes (f, l) of point on the curved reference surfce to set of plnr Crtesin coordintes (x, y) is known s forwrd mpping eqution while the reverse process is clled inverse mpping eqution. These cn be illustrted s below (x, y) = f(f, l) nd (f, l) = f(x, y) Mp projections cn be clssified in the terms of their clss for exmple: cylindricl, conicl, zimuthl projections. In ddition, it cn be clssified in terms of their point of secncy for exmple: tngent nd secnt or else in terms of their spect for exmple: norml, trnsverse or oblique or finlly in terms of their distortion property for exmple: equivlent, equidistnt or conforml (Knippers, 2012). Trnsverse Merctor Projection Trnsverse Merctor (TM) lso known s Guss-Krüger or Guss conforml projection is trnsverse cylindricl conforml projection. The term Trnsverse is defined considering the spect of the projection nd it mens the min orienttion of the projection surfce is perpendiculr to erth s xis. Conforml mens tht the ngles between lines in the mp re identicl to the ngles between the originl lines on the curved reference surfce. This mens tht ngles nd shpes re shown correctly on the mp. TM projection is the best-suited projection for Sri Lnk. TM projection cn be mthemticlly described s follows (LINZ, 2012). - Semi-mjor xis of reference ellipsoid, f- Ellipsoidl flttening, 0 - Origin ltitude, λ 0 - Origin longitude, N 0 - Flse Northing, E 0 - Flse Esting, k 0 - Centrl meridin sclefctor, - Ltitude of computtion point, λ - Longitude of computtion point, N - Northing of, computtion point, E- Esting of computtion point. Severl dditionl prmeters need to be computed before trnsformtions cn be undertken. These prmeters re constnt for given projection. The prmeters re b, e 2 nd m 0 b = (1 f), e 2 = 2f f 2 m = (A 0 φ A 2 sin 2φ + A 4 sin 4φ A 6 sin 6φ) where: A 0 = 1 ( e2 ) 4 (3e4) 64 (5e6), A = 3 8 (e2 + e4 + 15e6 ), A = (e4 + 3e6 ), 4 A 6 = 35e m 0 Should be obtined by evluting m using φ 0. The conversion of geogrphic coordintes (, λ) to projection coordintes (N, E) is chieved in severl steps. First determine (m, ρ, ν) t the computtion point (, λ) ρ = (1 e2 ) (1 e 2 sin 2 3 φ) 2, ν = t = tn φ, ω = λ λ 0 1 e 2 sin 2 φ, ψ = ν ρ, The projection northing (N) of the computtion point is determined using: N = N 0 + k 0 (m m 0 + Term 1 + Term 2 + Term 3 + Term 4) Where: Term 1 = ω2 ν sin φ cos φ, Term 2 = ω ν sin φ cos3 φ(4ψ 2 + ψ t 2 ) Term 3 = ω6 720 ν sin φ cos5 φ[8ψ 4 (11 24t 2 ) 28ψ 3 (1 6t 2 ) + ψ 2 (1 32t 2 ) ψ(2t 2 ) + t 4 ] ω 8 Term 4 = ν sin φ cos7 φ ( t t 4 t 6 ) Finlly the projection esting (E) of the computtion point is determined using:

4 E = E 0 + k 0 νωcosφ(1 + Term 1 + Term 2 + Term 3) Where: Tble 1: Molodensky dtum trnsformtion prmeters used in the ppliction Prmeter Vlue The semi-mjor xis of the WGS84 ellipsoid () m Flttening of thewgs84 ellipsoid (f) Eccentricity-squred of thewgs84 ellipsoid (e 2 ) Chnge in semi-mjor xis (δ): "Everest 1830" - "WGS84" m Chnge in flttening (δf): "Everest 1830" - "WGS84" x 10E4 Chnge in x between WGS84" nd "Kndwl" dtum (δx) 97m Chnge in y between WGS84" nd "Kndwl" dtum (δy) -787m Chnge in z between WGS84" nd "Kndwl" dtum (δz) -86m Term 1 = ω2 6 cos2 φ (ψ t 2 ) Term 2 = ω4 120 cos4 φ [4ψ 3 (1 6t 2 ) + ψ 2 (1 + 8t 2 ) ψ2t 2 + t 4 ] ω 6 Term 3 = 5040 cos6 φ (61 479t t 4 t 6 ) The conversion from projection coordintes (N, E) to geogrphic coordintes (, λ) (Bck Projection) cn be chieved with severl steps. First N, m, n, G, σ nd φ should be determined using following equtions. N = N N 0, m = m 0 + N k 0, n = b +b, G = (1 n)(1 n 2 ) (1 + 9n n 4 ) ( π m π ), σ = G φ = σ + ( 3n 2 27n3 ) sin 2σ 32 + ( 21n n4 ) sin 4σ 32 + ( 151n3 ) sin 6σ 96 + ( 1097n4 ) sin 8σ 512 Next ρ, ν, ψ, t, E nd x is determined by the use of following equtions. ρ = (1 e2 ) (1 e 2 sin 2 3 φ ) 2, ν = 1 e 2 sin 2 φ, ψ = ν ρ, t = tnφ, E = E E 0, x = E k 0 ν The ltitude of the computtion point cn now computed using following equtions. φ = φ Term 1 + Term 2 Term 3 + Term 4 where: Term 1 = t E x 3 t k 0 ρ E x 2, Term 2 = k 0 ρ 24 [ 4ψ2 + 9ψ(1 t 2 ) + 12t 2 ] Term 3 = t E x 5 k 0 ρ 720 [8φ4 (11 24t 2 ) 12ψ 3 (21 7t 2 ) + 15ψ 2 (15 98t t 4 ) + 180φ(15t 2 3t 4 ) + 360t 4 ] Term 4 = t E x 7 [ t 2 k 0 ρ t t 2 ] Finlly, the longitude of the computtion point cn now computed using following equtions. λ = λ 0 + Term 1 Term 2 + Term 3 Term 4 where: Term 1 = xsecφ, Term 2 = x3 secφ (ψ + 6 2t 2 ) Term 3 = x5 secφ 120 [ 4ψ3 (1 6t 2 ) + ψ 2 (9168t 2 ) + 72ψt t 4 ] Term 4 = x7 secφ 5040 ( t t t 6 ) Projection prmeters used in the development re listed in Tble 2.

5 Tble 2: Trnsverse Merctor prmeters used in the ppliction Prmeter Vlue Centrl meridin Ltitude of origin Scle fctor Flse esting m Flse northing m Proj4j Projection Librry Proj4j (Projections for Jv) is port of Proj4 C librry in to Jv nd is librry hving the cpbility to trnsform one geogrphic coordinte system to nother including dtum trnsformtion. It implements over ninety projections nd the source is vilble to downlod freely. The librry is prt of MetCRS group of projects hosted by OSGeo. Proj4J provides simple nd understndble ppliction progrmming interfces (API s) for developers (OSGeo, 2011). Figure 1: Design of the system Tble 3: Smple set of obtined results nd there comprison ginst Arc GIS nd GEOTRANS results Ltitude Longitude CTDroid x (m) Arc GIS x (m) GEOTRANS x(m) CTDroid y (m) Arc GIS y (m) GEOTRANS y(m)

6 Android Android is softwre stck for mobile devices. It is not only n Operting System (OS) it lso includes middle-wre nd key pplictions. Developers cn build ppliction with the help of Android Softwre Development Kit (SDK) which provides tools nd Appliction Progrmming Interfces (API) necessry to build pps using both Jv nd C lnguges (Hshimi nd Komtineni, Yer). SQLite SQLite offers free lightweight dtbse engine tht specilly trgets mobile devices. It is self-contined server-less nd trnsctionl Structured Query Lnguge dtbse engine tht do not need ny specil configurtion. It is very compct librry nd the size cn be less thn 350KB. It cn be mde to run in 4KB of stck spce nd 100KB of hep. The SQLite project is open source nd thus it is free to use for ny commercil or privte purposes (SQLite, 2011). Design of the system Figure 1 shows the bsic design of the developed ppliction. For the coordinte trnsformtion process, the first step is to ccess loction informtion mnully or through vrious sensors of the device: Minly from GPS sensor nd the mobile network. This informtion is vilble in geogrphic coordintes nd height tht references WGS84 dtum. Next, Molodensky nd Trnsverse Merctor projections methods re pplied to derive 2D Crtesin coordintes. In these steps, prmeters used in lgorithms cn be defined nd sve by the user or predefined prmeter sets cn be used. After successful projection the Crtesin coordintes is displyed in the disply unit with the height vlue. The ppliction lso provides the fcility to sve wypoints in SQLite dtbse nd the sved wypoints cn be lter export to personl computer s Comm Seprted Vlue (CSV) or Key Hole Mrk-up Lnguge (KML) formts for further nlysis. Another importnt feture of the ppliction is the cpbility to plot stored loction dt on Google Mps. The mp cn be either vector mp or rster imge. Current loction, GPS wypoints, wypoints obtined through network such s WiFi or through cell tower tringultion cn be plotted individully or ll in one in the mp view. Another minor feture of the ppliction is the cpbility of verging out the loction informtion computed to single point, leding to results tht re more ccurte. Also bck projection is supported vi mnul converter feture. RESULTS AND DISCUSSION In order to vlidte the system, comptibility of Android devices nd the ccurcy of the ppliction were tested. Comptible Android Devices The ppliction ws developed bsed on Android API set defined for ndroid OS (Gingerbred) version. After the development phse the ppliction ws tested with mny ndroid devices including Google Nexus 7 tblet, Google Nexus S, Smsung Glxy y, S, SII nd SIII models nd HTC Wildfire Smrtphone models. The tested devices were running Android OS versions (Gingerbred), 4.0 (Ice Crem Sndwich), nd (Jellyben) versions. According to Google Ply, As on April 2013 the ppliction is cpble of running in 2087 devices. Accurcy of the Appliction To ssets ccurcy of the coordinte trnsformtion lgorithm, two different reference pplictions were used nmely GEOTRANS nd Arc GIS. GEOTRANS is n ppliction progrm tht llows esy conversion of geogrphic coordintes mong wide vriety of coordinte systems, mp projections nd dtum. It runs on Microsoft Windows nd UNIX environments nd ws developed nd mintined by United Stte Ntionl Geosptil Intelligence gency. Arc GIS is well-known softwre product developed nd mintined by Esri. In both bove cses, it seems the developed lgorithm generted vlues re very close to both GEOTRANS nd Arc GIS generted vlues. In fct, in most of the occsions, vlues re correct up to first deciml plce. With these results, it cn be confirmed tht the lgorithm

7 is correct nd working s expected. When it comes to prcticl spects, the GPS sensor ccurcy in the mobile device lso will plys role towrds the finl result. b c d e f Figure 2: Bsic user interfces of the system: : Home Screen, b: GPS Screen, c: Loction Store, d: Mp view, e: Converter, f: Preferences Screen Tble 3 gives comprison of developed lgorithm computed vlues vs. Arc GIS nd GEOTRANCE computed vlues for smple set of loctions. Appliction Avilbility vi Google Ply Google ply is gret plce to distribute Android pplictions to intended users. The developed ppliction CTDroid is published in Google Ply s free tool for ny user to downlod. It lso fcilittes esy upgrde of published pplictions nd offers sttistics for them. According to google ply, s of April 2013, more thn 1000 users hve downloded the ppliction nd more thn 300 users re ctively using it. CTDroid first look

8 Some of the min user interfces of the ppliction re the home screen, GPS screen, loction store, mp view nd settings pge. Min user interfces of the ppliction re shown in figure 2.1. The home screen will provide esy nvigtion to other fetures of the ppliction, GPS screen fcilitte visulizing coordintes in WGS84, Kndwl nd the projected forms nd sving wypoints. The loction store enbles displying stored loctions, editing, deleting nd exporting them in comm seprted vlue (CSV) formt, Key hole mrk-up lnguge (KML) formt nd GPX formt. The mp view enbles visulizing stored loction overlid on top of rster or vector Google mps. Finlly, the preferences feture llows configuring coordinte trnsformtion prmeters nd vrious other settings for the ppliction. CONCLUSIONS Android is gret pltform for Mobile GIS solution development. Coordinte trnsformtion lgorithms cn be esily developed within Android frmework using Jv, nd librries such s Proj4J cn be ported to use with the pltform. The developed ppliction CTDroid cn be used within ny prt of Sri Lnk to perform coordinte trnsformtion with the cpbility to configure prmeters, perform Storing, visulizing loction dt on Google mps nd exporting them using KML nd CSV formts. REFERENCES United Stte Government (2012) The Globl Positioning System. [Online] Ntionl Coordintion Office for Spce-Bsed Positioning, Nvigtion, nd Timing nd the Civil GPS Service Interfce Committee, [Cited: April 23, 2012.] United Stte Government (2012b) GPS Applictions. [Online] Ntionl Coordintion Office for Spce-Bsed Positioning, Nvigtion, nd Timing nd the Civil GPS Service Interfce Committee, [Cited: April 23, 2012.] Wikimedi (2012)Assisted GPS. [Online] [Cited:_April_23,_2012.] PS. Knippers, R. (2012) Coordinte trnsformtions. Geomtic Aspects of Mpping. [Online] Interntionl Institute for Geo-Informtion Science nd Erth Observtion (ITC), [Cited: Mrch_16,_2012.]_http://plone.itc.nl/geo metrics/coordinte%20trnsformtions/ coordtrns.html. Ntionl Geosptil-Intelligence Agency (2012) Stndrd Molodensky Trnsformtions. [Online]_[Cited:_Mrch_20,_2012.]_http:// erthinfo.ng.mil/gndg/coordsys/dtums/ stndrdmolodensky.html. Knippers, R., Mp projections (2012) Geomtic Aspects of Mpping. [Online] Interntionl Institute for Geo- Informtion Science nd Erth Observtion (ITC), [Cited: April 23, 2012.] rojections/mppro.html. Lnd Informtion New Zelnd (2012) Trnsverse Merctor Trnsformtion Formule. [Online][Cited:_Jnury_20,_2012.]_http:/ / OSGeo (2011) Welcome to Proj4J. [Online] [Cited: 09 10, 2011.] Hshimi, S. Y., Komtineni, S. (YEAR) Pro Android. Springer-Verlg, New York, SQLite (2011) About SQLite. SQLite. [Online] The SQLite Consortium, [Cited: December 13, 2011.]