http://www.tnsnv.eu the Intentionl Jounl on Mine Nvigtion nd Sfet of Se Tnspottion Volume 9 Nume Mch 5 DOI:.76/.9..9 lgoithms fo Ship Movement Pediction fo Loction Dt Compession. Czpiewsk & J. Sdowski Fcult of Electonics, Telecommunictions nd Infomtics, Gdnsk Univesit of Technolog, Polnd BSTRCT: Due to sfet esons, the movement of ships on the se, especill ne the cost should e tcked, ecoded nd stoed. Howeve, the mount of vessels which tjectoies should e tcked uthoized institutions, often in el time, is usull huge. Wht is moe, mn souces of vessels position dt (ds, IS) poduces thousnds of ecods desciing oute of ech tcked oject, ut lots of tht ecods e coelted due to limited dnmic of motion of ships which cnnot chnge thei speed nd diection ve quickl. In this sitution it must e consideed how mn points of ecoded tjectoies ell hve to e ememeed to ecll the pth of pticul oject. In this ppe, uthos popose thee diffeent methods fo ship movement pediction, which eplicitl decese the mount of stoed dt. The lso popose pocedues which enle to educe the nume of tnsmitted dt fom osevto points to dtse, wht m significntl educe equied ndwidth of dio communiction in cse of moile osevto points, fo emple onod ds. INTRODUCTION Fo sfet esons, movement of ships on the se must e monitoed. Wht is moe, the el time vessel tcking is not enough. Those dt should e stoed nd ville fo futue use uthoized institutions. Unfotuntel, the nume of vessels seen ne the cost is huge. Futhemoe, the souces fom which the infomtion out vessels tjectoies cn e possessed e lso few IS, ds, moile osevto points nd ech of them gives thousnds of ecods desciing oute of ech tcked oject. Howeve, one must sk if ll those dt e ell impotnt nd povide significnt updte in the knowledge of position, speed o stte of vessels. Most of ships which e moving on Bltic Se e following known outs. In ddition, ecuse of thei dimensions thei dnmic is limited. The cnnot chnge thei speed nd diection ve quickl. Tht mkes possiilit to pedict some pts of the outs on the sis of cuent pmetes of motion to educe the mount of dt stoed in dtses. In this ppe uthos popose thee diffeent methods fo ship movement pediction. Pefomnce of these methods ws tested on the sis of el vessels tcks gtheed fom IS eceive. uthos lso popose pocedues esponsile fo selection of dt ecods which must e stoed ecuse the povide significnt updte of position o velocit pmetes. Those pocedues m lso e used in osevto points such s uos o ode gud vessels which send infomtion dio links with limited ndwidth. Descied pocedues will significntl educe the nume of tnsmitted dt fom those ojects. Which in tun will educe the time of tnsmission nd m sve dio communiction esouces. 75
This ppe is divided into two pts. In the fist one poposed lgoithms e pesented. In the second pt the esults of compison nlsis e shown. (utomtic Identifiction Sstem) nd infomtion fom this sstem wee used to conduct comptive nlsis. LGORITHMS FOR SHIP MOVEMENT PREDICTION In litetue thee e mn methods used fo pediction nd sstem modelling, to mention few: n utoegessive model R, moving vege model M o n utoegessive moving vege model RM. The e descied i.e. in Kshp (98), Genie (98) o l Smdi (9). In those methods pmetes of models must e estlished. Mn pulictions e devoted to the polem of settlement of those pmetes s it is unique polem fo diffeent models nd sstems. Theefoe, in this ppe uthos popose to use the simplest desciptions of ship movement: line nd cicul. The compe the pefomnce of those two movement desciptions with well known howeve comple Klmn filteing estimtion method. In the ppe uthos poves tht fo ship movement pediction the simplest model desciption is efficient nd sufficient. Thus, thee diffeent lgoithms designed fo movement pediction of vessels tcks e discussed in this ppe. Becuse most of the ships e moving the shotest oute we m ssume tht the e moving long the line pth. Tht is wh, fist lgoithm is sed on the monotonous, line movement desciption nd it will e lte clled line lgoithm. Second lgoithm ssumes tht, while vessels cnnot do shp tuns, the must follow cs. So thei tjectoies m descied pt of the cicle. This lgoithm is clled in this ppe cicle lgoithm. The lst lgoithm is the most comple one consideing those thee. It uses Klmn filteing. uthos mde lso some ssumptions out sstem tht might use those lgoithms. The pesumed tht vessels tjectoies dt would e gtheed some emote osevto points (sensos) connected to centl dtse vi dio links. To educe the mount of tnsmitted dt, one of the lgoithms mentioned ove will e used. Pediction of vessels tcks must e pefomed on the oth sides of dt communiction chnnel: centl dt se (centl seve) will clculte coodintes of vessels etween ecods of tue positions eceived fom emote sensos; emote sensos will pefom the sme pediction in ode to decide if the el coodintes of vessels diffe fom estimted/pedicted ones moe thn specified theshold. It is ovious, tht the mount of dt which will hve to e tnsmitted nd stoed in dtse will depend on the equied ccuc of oute estimtion (the estlished theshold). uthos lso ssumed tht the sic souce of infomtion out vessels would e utomtic Identifiction Sstem IS (IMO (998)) sstem. Line lgoithm Eve vessel though IS sstem sends infomtion out its movement: if it is moving o not, its speed ove gound (SOG), its diection of movement COG (Couse Ove Gound), nd cuent position. If the position of vessel is given in Ctesin coodinte sstem (not in WGS 84 coodintes) the net position might e estimted s follows. Fistl, the speed given in knots (SOG) should e conveted to m/s (sog) with eqution: sog,54444* SOG. () Then the ovell shift s in time t of the moving oject must e clculted: s sog t. () To clculte the shift in nd is (espectivel nd ) the couse COG of the vessel must e tken into ccount: s sin COG /8. () s cos COG /8 Finll, new coodintes of the oject e: '. (4) ' The nd e coodintes of the oject in pevious moment. Those vlues must e known fom IS sstem o fom pevious estimtions if the eos of those estimtion e smlle thn estlished theshold.. Cicle lgoithm Cicle lgoithm should e ette to descie movements of mneuveing vessel. In this lgoithm the min ssumption is tht ships hve huge ineti wht mkes them disle to pefom quick diection o speed chnges. The diection is usull chnged on c tjecto. To wite eqution of pticul cicle one must know the coodintes of cicle cente (,) nd its dius. To find those pmetes knowledge of coodintes of thee points ((, ), (, ) nd (, )) ling on the cicumfeence is needed. Thn sstem of equtions cn e witten: 76
77. (5) Fom ove equtions the pmetes of the cicle cn e found. t fist, those equtions must e ewitten to: d c, (6) whee c, d ; c e d, (7) whee e. Then to find vlue of cicle dius the cicul eqution might e used. When the speed of oject is known the length of the c s pssed the oject in time t cn e found fom eqution (). Smols used in following equtions e eplined in Figue. s we know the vlue of s nd, the ngle nd vlue of R cn e clculted fom: sin 6 R s. (8) Then two cicle equtions might e witten. One with cente in (, ) nd dius. The othe with cente in (, B) nd dius R: ) ( ) ( B R. (9) Modifing ove sstem of equtions nd using eneth smols: D D G C CD F C E B R D B C () one cn get: G E E D C. () s esult of ove clcultions two points ling on the cicle e found. To decide which one is the coect one the COG pmete might e used. While implementing this lgoithm one must e we tht not fo eve thee points sstem of equtions (5) is solvle. In tht cse it is ecommended to use line lgoithm fo such thee points. Figue. Eplntion of smols used in Eqution (8) ().. Klmn filteing Klmn filteing is n ecusive lgoithm which povides mens to estimte the stte of discete line dnmic pocess in such w tht it minimizes the men of the squed eo (Welch & Bishop 6). It mens tht Klmn filteing m e used fo ship movement estimtion. The following equtions wee witten sing on the theo found in mentioned Welch & Bishop (6) nd Gewl & ndews (8). The stte vecto is: v v, ()
whee, epesents position coodintes of the oject nd v, v e vlues of line speed in nd is. Speed vlues depends fom SOG nd COG. The tnsition mti fo this stte vecto is: t t, () whee t is time diffeence etween cuent mesuement nd pevious one. The pocess noise covince mti is digonl one Q = Iq, whee I is identit mti nd q must e positive vlue. The mesuement noise covince mti is clculted in eve ecusion: R, (4) v v whee digonl vlues e vinces of lst thee mesuements of, nd v, v. Mti H tht eltes the stte to the mesuement vecto is n identit mti, s elements of stte vecto nd mesuement vecto e the sme. Pocedues of Klmn filteing e conducted in two phses. In fist one, pediction phse, the stte vecto nd pioi estimte eo covince is updted: P P T. (5) Q In second phse, coection one, Klmn gin K is clculted nd stte vecto s well s eo covince mti e coected: K P P H T K z H P I K H P H H T R. (6) Duing the following comptive nlsis, it ws ssumed tht the initil stte vecto of Klmn filte consists of the oldest mesuements (those with the smllest timestmp). While the fist mesuement vecto consists of mesuements with the second smllest timestmp. Becuse thee e needed thee mesuements to fill mesuement noise covince mti fist thee itetions of Klmn filteing do not etun n esult. Those thee mesuements must lws e ememeed nd send to dtse cente. When the distnce etween estimted position nd tue position is gete thn estlished theshold the tue position must e ememeed nd lso send to dtse cente. Wht is moe, in net filte ecusion, it is foidden to use the estimted stte vecto. s stte vecto must e used ememeed mesuement (tue position). COMPRTIVE NLYSIS To pefom comptive nlsis of pesented lgoithms dt fom IS sstem wee ecoded. eceiving IS ntenn ws plced on the oof of the uilding of Fcult of Electonics, Telecommunictions nd Infomtics of Gdnsk Univesit of Technolog. Loction of ntenn nd sensitivit of eceive llowed to ecod IS dt fom ll vessels in the B of Gdnsk. Dution time of ecoding ws ppoimtel one hou. Fo comptive nlsis wee used onl ecods of vessels tht wee moving. Infomtion out ship movement is send s nvigtionl sttus in IS sstem. ll lgoithms wee eecuted on dt conveted fom WGS84 coodinte sstem to PUWG coodinte sstem. Fo ech lgoithm wee detemined: estimted oute, nume of positions gtheed IS sstem (tue positions), nume of positions tht must e stoed in dtse, oot men sque eo fo ech tjecto. Results chieved fo thee vessels e discussed in pgphs... In pgph.4 thee is shown nlsis fo ll moving ships ecoded within n hou.. Vessel MMSI 45 This oject ws moving towds ho in Gdni. Its dimensions e 85 m nd its dught is.9 m. In Tles 4 e pesented esults fo diffeent thesholds. Thee e oot men sque eos fo pth clculted with utiliztion of ll positions (RMS of ll positions) nd clculted onl fo estimted positions (RMS of estimted positions). In the lst column is infomtion out the nume of ememeed points given in pecentge. The nume of ll points fo this vessel is 66 (length of tjecto is sevel kilometes). Tle. Results fo vessel MMSI 45 nd theshold equl to m. Line 4.8 5..8 Cicle 4.6 4.9.7 Klmn 4.8 5.. 78
Tle. Results fo vessel MMSI 45 nd theshold equl to 5 m. Line..7 4. Cicle.6 4. 5. Klmn..8 4.5 Tle. Results fo vessel MMSI 45 nd theshold equl to m. Line 47 48.4 Cicle 4 4.6 Klmn 46 46.6 Tle 4. Results fo vessel MMSI 45 nd theshold equl to m. Line 8 8. Cicle 9 94.6 Klmn 77 78. Fo this pticul vessel ll of the lgoithms gve simil esults. Nevetheless, the llowed to educe nume of stoed dt significntl. Tle 7. Results fo vessel MMSI 59 nd theshold equl to m. Line 4 46 5.6 Cicle 58 6 4. Klmn 6 6. s it cn e seen fo this pticul oject nd tjecto line lgoithm gives the wost esults, especill fo lge vlue of theshold. Howeve, onl fo this cse the line lgoithm pefoms so pool.. Vessel MMSI 4448 This oject ws lso moving towds ho in Gdnsk. Its dimensions e 8 m nd its dught is.6 m. This vessel, in spite of nvigtionl sttus suggesting tht it ws moving, ws mneuveing to moo in Kszuin Cnl, wht cn e seen in Figue. Nevetheless, ll of the discussed lgoithms wee eecuted fo this oject. Results e shown in Tles 8 nd 9 s in pevious cses. Fo this vessel lso ll of the lgoithms pefomed equll. The oot men sque eos e simil s well s the nume of dt tht must e ememeed in dtse. Howeve, s the ship ws mneuveing in spce of few metes with ve low speed, this is one of the esiest cses to estimte the oute.. Vessel MMSI 59 This vessel ws moving towds Gdnsk. Its dimensions e 8 m nd its dught is 6.6 m. Fo this oject onl 96 points wee ecoded tht llowed to ecll tjecto of length out 7 m. In Tles 5 7 e shown esults fo diffeent thesholds s it ws shown in pevious pgph. Tle 5. Results fo vessel MMSI 59 nd theshold equl to m. Line. 4.8 5. Cicle 4.4 5. 6. Klmn. 4.7 54. Tle 6. Results fo vessel MMSI 59 nd theshold equl to 5 m. Line 5. 8.4.9 Cicle..7 7. Klmn 6.5 9.8.9 Figue. Points of oute of vessel MSSI 4448. Tle 8. Results fo vessel MMSI 4448 nd theshold equl to m. Line 5. 5.5 9. Cicle 5. 5.6 9.6 Klmn 5. 5.5 9.4 79
Tle 9. Results fo vessel MMSI 4448 nd theshold equl to 5 m. Line 7. 7.. Cicle 7. 7..4 Klmn 7.7 7.7..4 Compison fo ll ecoded vessels s it cn e seen in ove tles, the position pediction RMS eo vlue is the simil fo ll lgoithms nd stongl depends on estlished theshold of eo estimtion. Fo this eson, compison fo ll ecoded vessels ws mde onl on the ses of nume points tht must e stoed to fulfill the theshold condition. In Figues 6 e shown esults fo diffeent thesholds. The e shown s column plots. On is X e vlues of nume of positions tht must e ememeed (in [%]) in nges. Those nges depends, of couse, on the vlue of position pediction eo theshold. On is Y is the nume of cses (lso in [%]) in which the stoed nume of positions is within the pticul nge. s it cn e seen ll lgoithms enles to significntl educe the nume of dt tht must e stoed in memo to ecll the vessel tck. Even if the theshold is m the mount of stoed dt fo hlf of cses is less thn %. Fo gete vlues of theshold the mount of points tht must e ememeed deceses pidl to few pecent fo ove hlf of the cses. Fo theshold m thee is need to stoe onl 5% of positions fo 9% of cses. It poves the sttement mde in the intoduction tht the nume of ememeed points cn e getl educed. Figue 4. Stoed positions fo ll lgoithms fo theshold 5 m. Figue 5. Stoed positions fo ll lgoithms fo theshold m. Figue 6. Stoed positions fo ll lgoithms fo theshold m. Figue. Stoed positions fo ll lgoithms fo theshold m. ll of the lgoithms give simil esults. Howeve, slightl ette seem to e line lgoithm nd the one using Klmn filteing ove cicul lgoithm. s the line lgoithm is much less comple thn Klmn filteing uthos suggest using the line one. 4 CONCLUSIONS s it ws mentioned in the intoduction, due to sfet esons, movement of vessels ne the cost must e monitoed. It is not enough to oseve the sitution on the se in el time, ut it is lso impotnt to hve oppotunit to stoe those dt. Howeve, the mount of dt tht concens tjectoies fo ech vessel 8
gtheed onl fom IS sstem is huge. The nume of tcked ojects is lso significnt. Tht mens, thee is n ugent need to hve possiilit to educe this mount of dt. In this ppe uthos discuss lgoithms tht llows to educe stoed dt to onl few pecent of the oigin nume nd ecll lte the outes of the vessels with cceptle eo. Those lgoithms m e used not onl to educe stoed dt ut lso might e used to educe dt tht must e send to centl dtse fom emote sensos. In tht cse, mentioned lgoithms (o just one peviousl selected nd used lso on the eceive side) must e pefomed on the tnsmitte side. This fetue is ve impotnt if osevto points use dio communiction mens fo dt tnsmission. The eduction of dt will led to spe dio esouces shotening the time of tnsmission o educing the chnnel ndwidth. REFERENCES l Smdi. M. 9. Estimting utoegessive moving vege model odes of non Gussin pocesses, Poceedings of Intentionl Confeence on Electicl nd Electonics Engineeing ELECO 9, pges 6 Genie Y. 98. Estimtion of non sttion movingvege models, Poceedings of IEEE Intentionl Confeence on ICSSP 8, volume 8, pges 68 7 Gewl M. S., ndews. P. 8. Klmn Filteing Theo nd Pctice using MTLB IMO Resolution MSC.74(69). 998. Kshp R. L. 98. Optiml Choice of R nd M Pts in utoegessive Moving vege Models, IEEE Tnsctions on Ptten nlsis nd Mchine Intelligence, pges 99 4 Welch G., Bishop G. 6. n Intoduction to the Klmn Filte *** This wok ws finncill suppoted Polish Ntionl Cente fo Resech nd Development unde gnt no. O ROB///. 8