ANNUAL OF NAVIGATION 1/99

Transcription

1 ANNUAL OF NAVIGATION /99 Arzej Felsi, Fracisze Grabsi, Cezary Secht Polish Naval Acaemy Gyia AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL AVAILABILITY PREDICTION ABSTRACT The most oular metho of etermiig availability of DGPS as a comlex raioawigatio system is the ratio of Mea Time Betwee Failures to total (i.e. sum MTBF a Mea Time To Reair). This simle metho ca be use oly as a ost rocesse metho. The aalytical metho of availability reictio of the DGPS raio sigals trasmitte by the Marie Raiobeacos is iscusse i the aer. Authors roose to etermie it o the basis of such iformatio lie: tye of RTCM message, sigal to oise ratio, rate of correctios etc. To moel the availability zoes of each DGPS Referece Statio these calculatios ca be use. The short versio of this article was resete o the GNSS 99 Coferece i Geoa. Now, the full versio is resete. Some results of the imlemetatio i ractice for Polish DGPS Referece Statio Rozewie are ae. ESSENCE OF AVAILABILITY PROBLEM Availability of a raioavigatio system is efie as the robability with which the service rovie by the system is available for a user locate withi its coverage area (service access robability). It is oe of the most imortat criteria for comariso of raioavigatio systems because it secifies the real status of the service rovie. I ricile, availability ca oly be referre to its coverage area. It is ecessary to emhasize that such efie cocet of availability alies toa comlete raioavigatio service rovie by the system. Therefore it meas the guaratee to ee the, secifie by rovier, arameters of system erformace. The efiitio of availability ca ot be limite oly to guaratee the trasfer of raio sigals but it also shoul tae ito cosieratio such features as reuire or assume fix accuracy, reliability of fuctioig of techical euimet a sigal trasmissio, itegrity, fix rate a may more. It shoul also iclue the techical characteristics of raio sigal i.e. sigal level or sigal to oise ratio. 9

2 Arzej Felsi, Fracisze Grabsi, Cezary Secht Each raioavigatio system is usually cosiere as a comlex serial structure, where a failure of eve oe elemet causes major fault of the whole system. System fault ca be etermie as a state cause by ay factor, which maes the system fuctioig uroerly. It meas that the system fault may be cosiere a state cause by failure of ay iteral elemet as well as a failure of raio li (for istace excessive oise level). These causes lea to aearace of secifie time erio calle Time to Reair (TTR). Durig that erio, the user assumes that if system oes ot fuctio roerly, it is ecessary to wait util the oerator removes all causes of system fault. Techical reair of ay mechaism, chagig of weather coitios or ecreasig of atmosheric iterferece ca be regare as the malfuctio correctio. So, for a average user, Time to Reair meas the time from the momet of aearace of ay factor, which maes the system faile util the momet of its roer fuctioig. Mea value of TTR may be use for estimatio of availability. Moreover, availability ca be calculate as the ratio of total time urig which the system was available to the total erio of time uer cosieratio. Thus, we are able to figure it out by iviig the value of Mea Time Betwee Failure (MTBF) by the sum of Mea Time Betwee Failure (MTBF) a Mea Time To Reair (MTTR) calle missio time. MTBF A () MTBF MTTR The otio of availability use i coverage area ca be ietifie with the same term erive from uiversal theory of eeability, which meas the robability of beig i articular momet t>0 i state of ossibility for fix calculatig usig acet of receive raio sigals: Where: λ - failure rate υ - reair rate υ λ K( t ) ex[ ( λ υ ) t] () λ υ λ υ From the viewoit of uiversal theory of eeability, formula () is euivalet to availability coefficiet (G), which is use, i coverage area, as a alterative measure of system availability: υ G lim K( t ) t λ υ Therefore, we ca tal about availability with referece to ay create fuctioal form beig both simle elemet of techical structure a very comlex system icluig comoets, whose techical character may be ebatable (i.e. uct of raio wave roagatio i atmoshere). () 0 Aual of Navigatio

3 AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL... The coitios ecessary to estimate the availability are the followig: a) Defiig the structure of elemets or system, b) Defiig u state a ow state, c) Assigig their umerical reresetatio. Whe relatig the above cosieratios to DGPS we ca coclue that, ue to the cosierable umber of etermiig factors, estimatio of availability is ossible oly i a emirical way, usig log term research a observatio. Fuctioal structure of DGPS has both serial a arallel character. It iclues two arallel chaels: GPS a LDAS (Local Differetial Augmete GPS Service). At the same time, both of these moules have to fuctio roerly i orer that DGPS might be regare as a correctly worig uit. Cosierig relatioshi betwee DGPS availability, LDAS availability a sace segmet of GPS it ca be show as: A (4) DGPS A GPS A LDAS where: A DGPS Availability of DGPS A GPS Availability of sace segmet of GPS A LDAS Availability of LDAS Reliable show (Fig.) structure of LDAS causes its availability to simultaeously cosist of availability of four elemets: a) Referece Statio, b) Moitorig Statio, c) Cotrol Statio, ) User s segmet. Oly their simultaeous availability may esure the comlete availability of the ifferetial system: A LDAS A A A (5) RS IM CS A US where: A RS Availability of a referece statio, A IM Availability of a moitorig statio, A CS Availability of a cotrol statio, A US Availability of user segmet. /99

4 Arzej Felsi, Fracisze Grabsi, Cezary Secht Cotrol Segmet Sace Segmet Atmoshere User s Receiver Local Referece Statio Trooshere Beaco Receiver Cotrol Statio Itegrity Moitor Fig.. Simlifie scheme of DGPS Withi some cofies of availability of a Referece Statio A RS we ca cosier availability of a techical structure cocerig the referece statio as well as trasmittig system. Besies it we shoul ot igore the roblem of raio sigal availability coecte with local raio characteristic of a give area, the tye of use emissio a the techology of trasmissio of ifferetial correctios referre to relate trasfer format (i. e. RTCM SC-04). A RS A A A (6) DTA DTN where: A DTA Availability of a techical structure, A IM Availability of a trasmittig system, A CS Availability of a raio sigal, A US Availability of the trasmissio chael. I eeecies (4) (6) most of variables costitute arameters of such techical evices as receiver, satellite or moitorig statio. DS A DT Aual of Navigatio

5 AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL... Oly oe elemet of that very comlex structure of LDAS is cosiere i this aer. It is availability of trasmissio, which is efie as user s availability to receive GPS ifferetial correctios trasmitte i MF/LF ba accorig to RTCM SC-04 staar. I the case of ata trasmissio with MSK moulatio broacaste by DGPS Referece Statio, its sigal is iterfere by various atural or ma-mae iterfereces. If the egative ifluece is strog eough, eformatio of receive sigal may be so weighty that ecisio cocerig the selectio of imulse level (0 or ) is wore out icorrectly. Statistical measuremet of such occurrece is efie as a Bit Error Ratio (BER), i.e. mea umber of errors isie their seueces of recise legth. This uatity is irectly correlate with the ratio of sigal ower (S) to iterfereces ower (N) isie the raio li. I secific coitio of Gauss white oise iterfereces, the above uatity ca be estimate as follows [Rusi, 990]: BER erf S N ef π S N x e x (7) O the basis of the above formula a its relatio with S/N (Sigal to Noise Ratio) we ca wor out the aalytical relatioshi [Secht, 997] betwee BER a the availability of trasmissio for PRC trasmissio methos, both recommee by RTCM staar. THE AVAILABILITY OF SIGNAL FROM DGPS REFERENCE STATION Discussio o RTCM massage, the tye DGPS LF/LM caability for trasmissio we ca efie as a state i which miimum oe RTCM massage, tye is correctly trasmitte to user s receiver urig time erio eual to T secos. Freuetly the uatity of T is etermie as 0 secos. By aalogy the fault of DGPS LF/LM trasmissio ca be iterrete as a state i which o RTCM massage is correctly trasmitte to user s receiver urig time erio eual to T secos. Correct trasfer of RTCM message meas that oe of its bits is amage urig trasmissio. The legth of RTCM message, tye (L ), as a fuctio of trace satellites umber ca be resete as follows: For N S {, 6, 9, } L 6050N S (8) For N S {4, 7, 0} L 7050N S (9) For N S {, 5, 8, } L 8050N S (0) where: N S umber of satellites for which a Referece Statio trasmits seuorage correctios. /99

6 Arzej Felsi, Fracisze Grabsi, Cezary Secht Number () of trasmitte RTCM messages urig time erio eual to T max is fuctio of biary flow of telemetric li omiate by bau rate (R) a legth of massage (L ). Tmax R () L where: R bau rate, T max age of correctio limit. Probability of correct recetio of RTCM message, L bits log as a fuctio of BER value ca be escribe by meas of the followig formula: ) L ( BER () Cosierig T max iterval (usually 0 secos) characterizig DGPS trasmissio availability ( s ) we ca eclare that system is faulty i the case of all RTCM massages, whe all trasmitte urig time erio eual to T max, were faile. Hece the robability of system availability loss ( s ), which meas icorrect recetio all messages urig time erio eual to T max : the: ( s ) () (4) s Discussio o RTCM massage, the tye 9-. For this tye of message, the DGPS LF/LM caability for trasmissio ca be efie as a state i which miimum two ifferet RTCM messages, tye 9- were correctly trasmitte to user s receiver urig time erio eual to T secos. They shoul refer to two ifferet sets of three satellites. This tye of trasmissio has a costat message legth (L 9- ) eual to 0 bits. Hece the robability of correct recetio RTCM messages is ietical for each of sets of three satellites: 9 ( BER) L (5) A the oosite is: s (6) Deeig o a umber of satellites trace by Referece Statio there are two cases: a) Correctios are trasmitte for two sets of three satellites < N s < 6 b) Correctios are trasmitte for three sets of three satellites 6 < N s < 9 Variat a) Let us cosier two sets of three seuo-rage correctios (PRC) relate aeuately to satellites:,, a 4, 5, 6. Mea umber () of RTCM massages, tye 9- (for each of two sets of three satellites) urig the time erio T max is efie as follows: 4 Aual of Navigatio

7 AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL... L 9 R T max (7) For the coitios etermie i this way the state of fault (lac of availability) will be a failure to receive correctly, urig erio Tmax, at least oe of two sets of three PRC relate to ifferet satellites. This situatio will tae lace if, urig assige time erio, all correctios relate to both or oly to oe of two sets of three satellites fail. Probability of such evet - s we ca escribe as follows: s 0 (8) Usig the ext ietity: 0 (9) Fially we ca write: ( ) s (0) Variat b) Let us cosier three sets of three seuo-rage correctios relate aeuately to satellites:, 4 6 a 7-9. Mea umber () of RTCM messages, tye 9- (for each of three sets of three satellites) urig time erio eual to T max is efie as follows: L 9 R T max ( ) () For the coitios etermie i this way the state of fault (lac of availability) will be a failure to receive correctly, urig time erio eual to Tmax, at least two sets of three PRC relate to ifferet satellites. This situatio taes lace if, urig assige time erio, all PRC relate to miimum two sets of three satellites are faile. Probability of such evet - s we ca escribe as follows: ( ) ( ) ( ) s 0 () /99 5

8 Arzej Felsi, Fracisze Grabsi, Cezary Secht PRACTICAL IMPLEMENTATION DGPS LF/MF Systems are commoly use for sea-surveyig alicatios, esecially i maritime hyrograhy, regig etc. The high accuracy a the high availability are referable for this i of measuremet. The metho resete ca be use for availability calculatios before a surveyig camaig for a secifie regio of coverage a/or secifie time. Fig.. Coverage zoe of the RS Rozewie Coverage of DGPS referece statio ees to be etermie urig the test trials base o measure sigal stregth a sigal to oise ratio for the worst time bloc. As a examle let s cosier Polish DGPS RS Rozewie, whose electric fiel stregth is resete i fig.. 6 Aual of Navigatio

9 AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL... Fig.. Availability zoe of the RS Rozewie The SNR value was collecte urig a secial camaig of the sigal stregth measuremets mae by authors. Next stee shoul be GPS sace segmet surveyig esig base o a staar software lie: Trimble - Quicla, Leica Si, Ashtech Evaluate. The umber of available satellites is ecessary for trasmissio calculatios urig the survey. The availability zoe calculate o the basis of the metho roose is resete i fig.. The followig ata: N S 8, RTCM tye, bou rate 00 are use for the calculatio. It is clear, that the same calculatios ca be oe for ifferet RTCM messages, trasmissio rate a umber of visible satellites. CONCLUSIONS The availability of DGPS regare as a robability of correctly receive satellite sigals a PRC emitte by a Referece Statio is efie as a rouct of robabilities of roer fuctioig of system iiviual elemets. The availability of system techical elemets a robability of roer trasmissio from satellites to users are very high. Thus availability of DGPS system is maily etermie by PRC trasmissio li betwee the Referece Statio a the user. The aer resets a aalytical metho of calculatio of the robability of the roer PRC trasmissio as a fuctio of message tye, rate a coitio of trasmissio. /99 7

10 Arzej Felsi, Fracisze Grabsi, Cezary Secht O this basis we are able to reict the availability of the secific statio i ay area. It is also ossible to carry out may aalyses relate to the comlete system or to a articular elemet imact o service uality. I fig. 4 we ca see a examle of such theoretical aalysis. It resets the availability of PRC trasmissio as a fuctio of BER, use message tye (RTCM 9- a RTCM ) a biary flow of telemetric li (bau rate) - 00 or 00, for 9 visible satellites. High values of BER, taig lace ear coverage borer were assume o urose. It is clear from the figure that the RTCM message tye 9- icreases the system coverage because i site of lower value of S/N (a corresoig with it BER value) eables achievig higher theoretic availability of DGPS trasmissio P M9-00 M9-00 M-00 M BER Fig. 4. Availability of DGPS trasmissio BIBLIOGRAPHY. Acrou N., Quality Cotrol Cosieratios for Real Time Differetial GPS, The Iteratioal Coferece of the Royal Istitute of Navigatio, Loo 99.. CCIR, Reort, Worl Distributio a Characteristics of Atmosheric Raio Noise, ITU, Geeve Farrell J., Graas F., Statistical Valiatio for GPS Itegrity Test. Navigatio vol.9 o., Summer Felsi A., Secht C., Trials of DGPS i the Area of Norther Pola. EURNAV 96, Vehicle Navigatio Locatio a Cotrol, Loo Aual of Navigatio

11 AN ANALYTICAL METHOD OF THE DGPS RADIOBEACON SIGNAL Huuha E., Lehtorata V., Stuy of Night-time Coverage of DGPS Raiobeacos i Fila, ocumet reare for Fiish Maritime Amiistratio, Joela, December Pole ositio Sercel Positioig News No 8, Aril Poe D., Last J. D., DGPS Raio-Beaco Coverage Preictio i the Euroea Eviromet. Thir Iteratioal Coferece o Differetial Satellite Navigatio Systems, Loo, Rusi M., Trasmissio Systems Televisio. Wyawictwo Komuiacji i Łączości, Warsaw 990 (i Polish). 9. Secht C., Multicriterial aalyses of DGPS i cotext of raioavigatio service o the South Baltic. Doctoral Thesis. Polish Naval Acaemy, Gyia 997 (i Polish). /99 9