AAS MOPS: Practical Examples Todd alter Staford Uiversity ABSTRACT The AAS MOPS describes the method by which a ide Area Augmetatio System (AAS) trasmits its differetial GPS correctios ad itegrity iformatio to users i 5 bit messages. These messages must be decoded ad iterpreted every secod. The correctios eve for a sigle satellite are distributed across several idividual messages. The correctios for idividual satellites must be combied with receiver measuremets ad other local iformatio to form the avigatio solutio ad protectio bouds. The user must recostruct ad apply all of this iformatio correctly to achieve the required itegrity level of 1-7. hile the rules for coordiatig these messages are defied i the Miimum Operatioal Performace Stadards (MOPS), it is still helpful to provide some backgroud, describe the itet, ad show some examples. This paper provides examples of what the message order might look like ad how the iformatio should be iterpreted. Both omial ad alarm situatios are preseted. Particular attetio is paid to situatios i which the user has missed some of the broadcast messages, but still has eough iformatio to cotiue the procedure. Better uderstadig the itet of the authors will further assist the user implemetatio of the MOPS. The MOPS is a large ad fairly ivolved documet. To ew users i the process of implemetig this stadard, its rules may seem arbitrary. By showig how the differet messages iteract ad work to protect itegrity, the ew user may more readily uderstad how to implemet the MOPS compliat messages. INTRODUCTION The ide Area Augmetatio System (AAS) Miimum Operatioal Performace Stadards (MOPS) [1] is a large documet writte by committee to describe a complicated system. It has evolved slowly over time ad some of the omeclature ad writig reflects a history of ideas ad approaches. As such, it ca be a itimidatig documet to the ew iitiate. This paper is iteded to provide some cocrete examples to assist the reader i uderstadig how the differet message types coect together to form a differetial GPS correctio. Oly the iterpretatio ad applicatio of the messages themselves is ivestigated here. The MOPS cover umerous other issues which will ot be addressed. This paper caot substitute for the MOPS, ad will be of little value to a reader ot already familiar with Appedix A of the MOPS. Ay discrepacy betwee the MOPS ad this paper must be resolved i favor of the MOPS. The examples are iteded to aid i the iterpretatio of the applicatio of the correctios ad ot to take credit/blame for the cotets of the MOPS. The MOPS had several restrictios imposed o it for the defiitio of the messages, may of which apply specifically to precisio approach []. These iclude: A severe badwidth limitatio of 5 bits per secod. Striget user itegrity: < 1-7 chace of receivig Hazardously Misleadig Iformatio (HMI). 6 secod time to alarm for ay failure that could lead to HMI. High availability, the system should be usable > 99.9% of the time. Support for global or ear global coverage. Flexibility to support differet service providers. The MOPS was produced by a collaborative effort; may people cotributed to its cotets. It is remarkable that agreemet could be achieved o a format that met all of these restrictios, especially whe much of the framework of the MOPS was created before there was sigificat supportig data from the Natioal Satellite Test Bed (NSTB) [3] [4] [5]. However, as with ay joit veture o oe perso is etirely satisfied with the outcome. There is o doubt that these goals could be achieved i differet ways. This author is ot iterested i debatig the merits of oe method versus aother. Results have bee put ito the MOPS after laborious debate i which
authors have satisfied themselves that the methods meet the striget requiremets. The correctios are broke ito two categories: clockephemeris correctios ad ioospheric correctios. The most cofusig aspect of the clock ad ephemeris correctios is that the iformatio is distributed amog may message types all of which must be tied together correctly. The most difficult aspect of the ioospheric correctios is that the user must determie the correct pieces to use ad how to traslate them to the specific user coditios. MESSAGE FORMAT The messages come oce per secod ad cotai 1 bits of correctio data. Eight additioal bits are used for acquisitio ad sychroizatio, 6 more bits to idetify the message type ad the remaiig 4 bits desigated for parity to protect agaist the use of corrupted data (see [] ad A.4.3 of [1]). Complemetary message types must be stored ad coected to the other idividual compoets to form i a sigle correctio ad cofidece boud per satellite. Because of the costraits, the bits must be used as efficietly as possible. Thus they are sometimes used for more tha oe purpose. Ofte, meetig badwidth requiremets took precedece over ease of implemetatio or clarity. The overridig cosideratio is itegrity. However, itegrity must be cosidered together with availability [6]. I order to maitai itegrity ad provide availability, some extra actios are required [7] [8]. Some of the correctios require additioal effort to costruct so as to guaratee itegrity to all users. Time-Out Periods Most messages have a associated time-out period. These time-out periods prevet old data from beig used beyod the time which it is valid. Some of these timeout periods are costat values (see Table A-4 of [1]) ad some are broadcast to the user i the messages (see Table A-8 of [1]). For Category I precisio approach, the timeout itervals are set so that users may miss oe of ay idividual message, ad still form a avigatio solutio usig older messages. For No-Precisio Approach (NPA) ad E Route (ER) phases of flight, i may cases, a user ca miss two i a row of ay idividual messages. Thus users ca cotiue to operate eve if they do ot have the latest correctios. The service provider caot kow if a particular user has received each of the most recet messages ad if ot, which oes were lost. Therefore the format must protect these users without pealizig users who have ot missed ay messages. Hece differet rules gover the implemetatio of correctios ad cofideces whe oe is missig data. This ca potetially lead to cofusio. The time of applicability of each message is defied to be coicidet with the first bit of the message. However, the time-out period begis with the last bit of the message. Sice, the message is oe secod i legth, the time-out periods must be icreased by oe secod whe they are beig compared to the time of applicability. Issue Of Data (IOD) Because iformatio must be coordiated across differet messages ad with the iformatio broadcast from the GPS satellites, there must be a way to idetify which data may be used i combiatio. Issue umbers, termed Issue Of Data (IOD), must match betwee messages splittig iformatio. he the IODs do ot agree, the user kows that they are missig crucial pieces of iformatio. This maitais the high level of itegrity madated by the system. There are at least five defied types of IOD. O the uaugmeted GPS system there are IODs to coordiate clock (IODC) ad ephemeris (IODE) iformatio. Each satellite has its ow idividual values [9]. The IODE represets the 8 least sigificat bits of the IODC. The IODE also eables the AAS service provider to uiquely idetify which ephemeris iformatio is beig corrected. The user must esure that the IODE i the AAS correctio matches that i the GPS satellite broadcast. ithi the MOPS messages there is a IODP which allows the user to uiquely match the PRN umber of the satellite beig corrected to the locatio of the correctios ad bouds i the messages. The IODF allows the itegrity iformatio i Type 6 to be traced back to a specific fast correctio. The IODF also serves aother purpose. It icremets by oe from oe fast correctio to the ext, modulo 3. Thus, a user ca detect whe they have missed a message because the IODFs will ot be sequetial for the received messages. By determiig that they are missig iformatio the user ca the take the prescribed steps to esure that their itegrity boud sufficietly covers the error. This will be discussed i further detail below. Fially, the IODF is used to sigal a alarm coditio. If the service provider should discover that iformatio already broadcast would fail to protect all users, they must alert everyoe to this fact. This situatio is idicated by havig IODF = 3. The IODI allows latitude ad logitude to be mapped oto the ioospheric correctio iformatio. If the iformatio were ot divided i this maer, it would be impossible to fit the data ito the 5 bps badwidth.
Nor could the iformatio be recombied with sufficiet itegrity. CLOCK AND EPHEMERIS CORRECTIONS The satellite clock ad ephemeris errors are corrected ad bouded by iformatio i Types 1-7, 9, 1, 17, 4, 5, ad 7. The correctios are split ito two types: fast correctios, which are scalar values commo to all users; ad slow correctios which are i the form of a four dimesioal vector ad affect users differetly depedig o their locatio. Most of the commo errors, particularly Selective Availability (SA), are removed by the fast correctio. The slow correctios primarily remove the satellite ephemeris errors. I additio they model the satellite s slowly varyig clock compoet. Ay discotiuities betwee oe set of ephemeris parameters broadcast from a GPS satellite ad the ext set are also icorporated ito the slow correctios. This is doe for two reasos: to keep the fast correctios cotiuous, ad to match specific ephemeris parameters, sice oly the slow correctios iclude the IODE. The cofidece boud o the clock ad ephemeris correctios is called the User Differetial Rage Error (UDRE) ad is broadcast to the user i the form of a boudig variace. Although it is called a error ad has the form of a variace, it should be viewed as a statistical cofidece boud [6]. Fast Correctio Calculatio Types - 5 ad 4 cotai fast correctios. These correctios primarily remove the error caused by SA. The pseudorage correctio for oly a idividual epoch is broadcast. Users update these correctios over time by applyig a rage rate correctio term formed from recet correctios. The rage rate correctio, RRC, is determied by differecig a ewer fast clock correctio with a older oe (see A.4.4.3 of [1]) ad dividig by the differece betwee the time of arrival, t, of the ewer pseudorage correctio, PRC, ad the time of arrival of the older oe, t o : RRC PRC = t PRC t The pseudorage correctio as a fuctio of time is give by o o (1) PRC() t = PRC + RRC ( t t ) () This correctio is added to the user s measured pseudorage to remove the fast clock error. For precisio approach, this correctio is valid from time t + 1, whe the message is fully decoded, util the message times out, as specified by the fast correctio time-out iterval, I fc, i Type 7, at time t + I fc +1 (see A.4.4.5 of [1]). UDRE Degradatio The fast correctio was estimated by the master statio at some previous time, t t, where t l l is the system latecy time provided i Type 7. The boudig variace i the pseudorage correctio icludes estimatio errors for fast clock, slow clock, ad the projectio of the ephemeris offset, quatizatio errors i those terms ad some of the errors from propagatig the correctio forward i time, ad is give by the boudig variace, σ UDRE, which is broadcast i Types - 6 ad 4. To be applicable for the preset time, the ucertaity of the pseudorage correctio must be updated by the remaiig errors resultig from propagatig the correctios forward i time. Ay error i the user s estimate of the rage error rate will affect the cofidece i the forward propagatio of the correctio. Calculatio of the rage rate correctio i (1) has two primary error sources: quickly varyig errors i the fast correctios estimates, such as quatizatio, ad eglected higher order terms such as SA acceleratio. The first error source is described by: Brrc t t where B rrc is a value greater or equal to the quatizatio error. The service provider estimates this term ad broadcasts it to the user via Type 1 [1] [8]. The secod error source ca be described by the first eglected term i the liear model of the rage error. The boudig acceleratio estimate is called the Fast correctio degradatio factor, a, ad is broadcast i Type 7. The rage rate correctio estimate formed i (1) is the best estimate for a time midway betwee the ewer ad older correctios, ( t + t )/. Thus, eve at t o, the rate calculated i (1) is already out of date. I additio, the system latecy, t l, also adds to the ucertaity i the estimated rage rate correctio. Thus this secod error source takes the form of: t + t o a t o + tl Both (3) ad (4) are ucertaities o rage rate. Their respective cotributios to ucertaity o pseudorage correctio are: (3) (4)
ad Brrc t t o ( t t ) (5) a t t t t t t l o l ( + ) ( + ) (6) The MOPS specifies the degradatio o the fast correctio to be modeled as a ( t t + t ) (7) l which is very similar to (6). he the true SA acceleratio is very large, the broadcast value of σ UDRE must be icreased to accout for the discrepacy betwee (6) ad (7) at the message time-out period. The derivatio above assumes that o data is missig. he the user fails to receive a fast correctio, they will cotiue to apply the above correctios util a ew fast correctio is received or the old iformatio times out. Upo receipt of the ew fast correctio there will be a break i the sequece of the IODFs idicatig a missed message. The user cotiues to use (1) ad () to geerate the correctio. he missig the previous fast correctio, oe must add a extra term to accout for additioal latecy ad quatizatio errors i the RRC. Provided either of the messages idicate a alarm coditio, this term is a Ifc Brrc ε rrc + 4 t t o ( t t) Alarm coditios are idicated whe the IODF of either message is set to 3. I this case, ε rrc has a slightly differet form as give by (A-47) of [1]. Uder alarm coditios, fast clock correctios may be as closely spaced as 1 secod apart. A user who differeces adjacet or closely spaced fast clock errors will suffer greater σ UDRE degradatio (ad cosequetly lower availability ad higher risk of lost cotiuity) tha a user who differeces fast clock error terms with omial or close to omial spacig [8]. User algorithms will have better performace takig this latter approach, although it is ot madated. I additio the message may ot be forward propagated more tha eight times the time differece used to form the RRC. Thus two messages oe secod apart may oly be used eight secods ito the future before the ucertaity grows too large to cotiue. (8) Type 6 The above discussio assumed that the service provider was broadcastig i a mode where the fast correctios ad the σ UDRE always arrive i the same messages. This is the expected case for whe SA is tured o. However, i the future, whe SA is tured off, it will ot be ecessary to sed the fast correctios as ofte as they are set curretly. Sigificat badwidth ca be gaied by sedig these messages less frequetly. The extra badwidth ca be used to improve performace by sedig other messages more ofte or by defiig future message types. It will still be ecessary to update the itegrity status at the high rate. Thus, it is desirable to sed the σ UDRE values every six secods. Type 6 allows these values to be set without also retrasmittig the fast correctios. Type 6 cotais σ UDRE values for all satellites that are beig corrected (up to 51). Thus, oe could receive a subset of Types -5 ad 4 at oe miute itervals ad Type 6 every six secods i betwee. Equatios (1) ad () remai valid. However, (7) will have to be updated as follows to allow for this possibility. The receipt of Type 6 has the effect of retrasmittig the last broadcast fast correctio messages. It tells the user that the last fast correctio broadcasts are still valid ad ca be used for aother twelve secods. This is the other ad more importat role of the IODF which icremets for every ew fast correctio. Every Type 6 message set i betwee successive fast correctios will have IODFs correspodig to the value i the last fast correctio broadcast. Thus users will kow uambiguously which fast correctios the Type 6 is updatig. The ew equatio for updatig σ UDRE is uchaged i form from (7) but has oe crucial differece. The degradatio starts from the time of applicability, t UDRE, of the last received σ UDRE with matchig IODF < 3. If Types -5 or 4 are the most recet source of σ UDRE the t = t UDRE. If the most recet source is from Type 6 with matchig IODF < 3 the t = t UDRE 6 where t 6 is the time of applicability of that message. Fially, if the IODF i either message is set to three the t = t UDRE ad is ot updated to the time of the Type 6 message. Because the receipt of Type 6 with matchig IODF < 3 is equivalet to aother receptio of the last fast correctio, the Fast correctio degradatio term ca be reset ad t i (7) ca be replaced with t UDRE resultig i ε fc a ( t t + t ) (9) UDRE l
6 4 5 3 4 1 Error (m) 3 Error (m) -1 1 AAS Correctios Missig AAS Correctio - PRC AAS Measuremet True Error 5 1 15 5 3 35 4 Time (sec) Figure 1. True clock error, the error as measured by the service provider, ad the resultig correctios are show for a extreme case with maximum acceleratio. where ε fc is the degradatio parameter for fast correctio data (see A.4.5.1.1 of [1]). Thus eve though fast correctios are comig at a slower rate, the Fast correctio degradatio is still reset every six secods provided the user has ot lost ay messages ad the IODFs are ot equal to 3. Fast Correctio ad UDRE Time-Outs A user must verify that the ewer fast clock error used i Equatios (1) ad () to geerate the pseudorage correctio be o older tha the broadcast time-out period, I fc, for that satellite. Thus, oe must verify t t I +1, before applyig the correctio (). If this fc time differece is greater tha I fc + 1, the user must ot apply the correctio ad the satellite is flagged as ot havig a differetial correctio. Similarly, if the old fast clock error is too outdated, t t > I, the the user also o fc caot use (). A user must have both a valid fast clock correctio ad rage rate correctio to differetially correct the satellite. I additio, they caot project fast clock correctios beyod eight times the time differece used to form the rage rate correctio, t t > 8 ( t t ). o The time-out for σ UDRE values is 1 secods from the ed of the message (or 13 secods from the time of applicability of the σ UDRE iformatio). Thus it also must be true that t t UDRE 13sec for a user to apply differetial correctios to that satellite. he the user is missig a fast correctio ad the Type 6 IODF does ot match, it is sufficiet to use t t 13sec i place of the 6 above equatio. I all cases σ UDRE values set to Do Not Use or Not Moitored take precedece over ay pseudorage correctio calculatios. Upo receipt of such iformatio, a user must remove all other kowledge of the satellite ad wait for the master statio to declare it - -3 σ flt 5.33 σ flt Boud Error i PRC -4 5 1 15 5 3 35 4 Time (sec) Figure. The error i the correctio ad the resultig 1-σ ad 1-7 bouds are show for the data i Figure 1. safe ad the fill i correctio iformatio for it oce agai. A user also caot form a rage rate correctio (1) across fast clock errors if the σ UDRE iformatio has bee set to Do Not Use or Not Moitored i betwee receptio of those fast clock errors (Types -5 ad 4). After the receptio of a itegrity alarm with either of those two coditios, a user must receive two fast clock correctio messages before applyig correctios to that satellite. If there is a chage of itegrity status from safe to usafe, that itegrity message is broadcast four times i a row. A user who misses four messages i a row must assume that every σ UDRE has bee set to Not Moitored. The error terms ε rrc ad ε fc are added to the broadcast UDRE differetly depedig o the value of the RSS UDRE bit. If the bit is set to zero, the cotributios are summed as sigmas ad the squared to form a variace. If the RSS UDRE bit is set to oe, the cotributios are squared ad the summed as variaces. There are other cotributios from log term correctios ad extra missig messages that will be discussed later. The AAS system will iitially use the RSS UDRE set to [8]. However, i this paper, we will set RSS UDRE to 1 [7]. I this case, the variace of the correctios described so far is give by σ = σ + ε + ε (1) flt UDRE fc rrc where σ flt is the boudig variace of all the error terms discussed. Equatio (A-44) i [1] describes the equatio ad terms i full. To see how these cocepts coect together we will look at some examples.
Time (s) Time(s) PRC (m) IODF -1.5.83 -.83.39 3-1.5-1.167.5.338 6 5 -.15 1 -.563.55.39 9 5 -.15 1-3.875 1.45.338 1 11-3.15-3.9 -.14.39 15 11-3.15-3.79 -.71.338 18 17-4. -4.146.38.39 1 17-4. -4.583.373.338 4 17-4. -5.1.893.41 7 17-4. -5.458 1.584.544 3 9-3.5-3.458.8.311 33 9-3.5-3.333.479.354 36 35 -.75 -.65.537.39 39 35 -.75 -.5 1.1.338 Table 1. Values of Pseudorage Correctio (PRC), true error ad boudig variace, σ flt, are listed for various times alog with the correspodig message times, broadcast correctios, ad IODFs. PRC (m) Error (m) σ flt (m) Example 1: No Type 6 messages are broadcast ad a user is ot aware of ay missig messages from Types -5 or 4. This correspods to the data i Figures 1 ad ad Table 1 from times to just before 3, ad 36 to 4. Example : Same as Example 1 except ow the user has o-cosecutive IODFs so they kow they have missed a fast correctio. This correspods to the data i Figures 1 ad ad Table 1 from times 3 to 36. These examples are illustrated i Figures 1 ad ad i Table 1. Figure 1 shows a simulatio of true clock error. There is a uderlyig quadratic represetig the Parameter σ UDRE Examples 1 & Examples 3, 4, & 5.94 m.5 m.94 m a 4.6 mm/s.3 mm/s I fc 1 sec 66 sec FC update rate 6 sec 3 sec t l 4 sec 4 sec B rrc.15 m.15 m Table. The parameter values used to calculate the error bouds for examples 1-5. The upper value was broadcast three times per 3 secod fast correctio update iterval (with the fast correctios, 6 secods after ad 1 secods after), ad the lower value twice (18 secods after the fast correctio ad 4 secods after). true SA over time (light solid lie). This is corrupted by measuremet oise ad biases to form the istataeous service provider estimates idicated by the x s. These measuremets are used to forward predict a estimate of the correctio four secods ahead which is broadcast oce every six secods as idicated by the circles. Fially the messages are extrapolated as described by (1) ad () to form a pseudorage correctio. The pseudorage correctio, or rather, its egative, is show as the dark solid lie. Also show i Figures 1 ad is the effect of the user ot receivig the correctio broadcast at time 3. Notice that the RRC from time 3 to 36 is less accurate due to the lost message. Figure ad Table 1 show the error remaiig after correctio ad the error boud as calculated accordig to the MOPS. Util time 3 the user calculates the boud as though they are missig o data. At time 3 they fiish decodig a fast correctio whose IODF is out of sequece ( istead of 1). At that poit they must add the additioal degradatio term (8) to accout for the additioal error i the RRC term. At time 36 they receive aother ew fast correctio ad the calculatio of the error boud resumes to its omial form as o data is missig. These examples represet a worst possible case, with the true pseudorage acceleratio matchig the specified ot to exceed value of 19 mm/s [9]. The vast majority of the time the actual acceleratio will be less tha half this value [1]. The additioal broadcast parameters ecessary to calculate σ flt are listed i Table.
Error (m).5.4.3..1 -.1 -. AAS Correctios Missig AAS Correctio - PRC AAS Measuremet True Error Error (m).5 1.5 1.5 -.5-1 -.3 -.4 Type : IODF Type : IODF 1 Type : IODF Type 6: IODF Type 6: IODF Type 6: IODF Type 6: IODF Type 6: IODF -.5 5 1 15 Time (sec) Type : IODF Type : IODF 1 Figure 3. True clock error, the error as measured by the service provider, ad the resultig correctios are show for a case with o clock acceleratio. The times of the Type ad Type 6 messages are show ad the IODFs idicated. This simulatio is for illustrative purposes oly. Although the 1-7 cofidece boud (see Appedix J of [1]) was always larger tha the actual error, it did become larger tha 44. σ flt, which should occur less tha oe secod out of a day. I fact much of the time the error is outside of the oe sigma boud. If this situatio had really occurred, the service provider would have further icreased σ UDRE, or the broadcast degradatio parameter a. Merely boudig the errors i the pseudorage domai is ot sufficiet to protect the user i the positio domai. Large errors such as those i Figures 1 ad must also have a sufficietly low probability of occurrece [6]. Fast Correctio Degradatio Equatio Use with Type 6 At all times, each σ UDRE is updated at least every six secods, but if Type 6 is implemeted, the fast clock errors may be set out less frequetly. Type 6 performs a virtual update of the fast clock error if the IODF is ot equal to 3. A user who receives this message is effectively beig told that ay chages to fast clock error sice it was last broadcast are small, ad are covered by the ew σ UDRE icluded i that message. Example 3: The fast correctios are broadcast every 3 secods with four Type 6 messages i betwee. The user is ot aware of ay missig messages ad there are o alarm coditios. This correspods to the data i Figures 3 ad 4 ad Table from times to 9, ad 1 to 138. Example 4: The same as above except that the user is missig a fast correctio, but still o alarms. This Type : IODF -1.5 - σ flt 5.33 σ flt Boud Error i PRC -.5 5 1 15 Time (sec) Figure 4. The error i the correctio ad the resultig 1-σ ad 1-7 bouds are show for the data i Figure 3. Time (s) Time (s) Type IODF t UDRE (s) σ flt (m) -1-1.8 6 5 6 5.8 1 11 6 11.8 18 17 6 17.34 4 3 6 3.34 3 9 1 9.8 36 35 6 1 35.8 4 41 6 1 41.8 48 - - - 41.34 54 53 6 1 53.34 6 - - - 53.34 66 65 6 53.35 7 71 6 53.39 78 77 6 53.318 84 83 6 53.336 9 89 89.8 96 95 6 95.34 1 11 6 11.48 18 17 6 17.335 114 113 6 113.357 1 119 1 119.8 16 15 6 1 15.8 13 131 6 1 131.8 138 137 6 1 119.314 144 143 6 1 119.39 15 149 149.8 Table 3. Tabular values are listed for the message types, times, IODFs, t UDRE, ad the cofidece boud, σ flt, correspodig to Figures 3 ad 4. The - idicates a lost messages.
correspods to the data i Figures 3 ad 4 ad Table from times 9 to 1. Example 5: The same as Example 3 except that oe or more IODFs are set to 3. This correspods to the data i Figures 3 ad 4 ad Table from times 138 to 15. These examples are illustrated i Figures 3 ad 4 ad i Table 3. Figure 3 shows aother simulatio of true fast clock error. There are o acceleratio or velocity terms o the true pseudorage; it is costat ad zero (light solid lie). This is corrupted by measuremet oise ad biases to form the istataeous service provider estimates idicated by the x s. These measuremets are used to forward predict a estimate of the correctio four secods ahead which is the broadcast oce every thirty secods as idicated by the circles. I betwee these messages, every six secods, Type 6 is broadcast to update σ UDRE. The Type 6 messages i o way affect the extrapolatio of the pseudorage correctio. The pseudorage correctio (agai, actually the egative) is show as the dark solid lie. Also show is the effect of the user ot receivig the Type 6 at time 47, or the fast correctio broadcast at time 59. Additioally, at times 138 ad 144 the IODFs the Type 6 messages are set to 3. These examples represet a expected case with SA tured off. The parameters affectig the calculatio of σ flt are show i Table. Figure 4 shows the error remaiig after correctio ad the error boud as calculated accordig to the MOPS. Util time 9 the user calculates the boud as though they are missig o data. At time 66 they fiish decodig a Type 6 whose IODF is out of sequece ( istead of 1). The t UDRE remais at 53 s ad will remai there util the receipt of the ext fast correctio. Because the IODF was ot set to 3 ad the user has ot missed 4 messages i a row, they kow that the service provider is moitorig this ad other combiatios of old data ad it is safe for them to cotiue its use. Thus, t 6 is updated ad eve though t t UDRE >13sec, it is safe to cotiue operatio. he the ew fast correctio is decoded at time 9, the RRC is formed usig correctios with IODFs that are out of sequece, requirig the iclusio of the degradatio parameter ε rrc (8). At time 1 aother ew fast correctio is received ad the calculatio of the error boud resumes its omial form as o data is missig. At times 138 ad 144, the user decodes Type 6 messages with the IODF set to 3. This sets the t UDRE back to 119 s, the time of applicability of the last received fast correctio. If the user had missed the fast correctio at 119 s, the t UDRE would have bee set to 89 s. The above discussios eglected the cotributios of the log term error estimatio. The σ UDRE broadcast to the user must also iclude these error projectios. Sice they are a fuctio of user locatio, the value set correspods to the largest projectio withi the service regio. This term ca overwhelm the oise i the clock estimatio which has bee greatly exaggerated i these examples. Log Term Correctios The log term correctios are far less complicated tha the fast correctios. These correctios are cotaied i the back half of Type 4 or i Type 5 for GPS satellites. For Geostatioary satellites they are cotaied i Type 9. These packets cotai oly correctio iformatio as the error bouds for these message types are cotaied i the σ UDRE. There are terms that degrade the error boud whe missig oe of these correctio terms. These factors are relatively straight forward ad described i Sectio A.4.5.1.3 i [1]. Oe potetially cofusig item is the form of Equatio (A-5). If the curret time is betwee the time of applicability of the velocity code = 1 message, t, ad that time plus the v=1 update iterval, I ltc_v1, the the first term, C ltc_lsb, should also be set to zero. Thus for the time spa t t I ltc_v1 there is o applied degradatio factor. E Route Degradatio For precisio approach a user is oly allowed to miss oe of ay particular message. However, the user ca still operate i less striget phases of flight eve if they have missed two of ay particular fast or slow correctio messages. he users apply correctios beyod the precisio approach specified time-out, but before the E Route, Termial, NPA time-out period (i. e. 3 I + 1< t t I + 1 fc ), aother degradatio term is fc added to accout for the potetial error. hile performace is probably worse tha for a user ot missig ay messages, it will likely still provide sufficiet avigatio for these other phases of flight. This degradatio term is described i Sectio A.4.5.1.4 of [1]. IONOSPHERIC CORRECTIONS The ioospheric correctios ad itegrity boud iformatio are broadcast i Types 18 ad 6. Type 18 defies a mask of activated Ioospheric Grid Poits (IGP). This mask allows the user to determie the latitude ad logitude of the correctios ad cofideces i the Type 6 messages. The applicatio of ioospheric correctios requires the user to iterpolate correctios for their measuremets from a predefied grid of vertical delay values, τ vi. The user must determie which grid poits to use for iterpolatio ad the apply the proper weights to each oe to form their vertical delay estimate ad cofidece. This vertical
C H I B J G A K L IGPs with Valid Correctios IGPs without Valid Correctios IGPs Set to Do Not Use Virtual IGPs IPPs with Valid Correctios IPPs without Valid Correctios Regio with Valid Correctios Figure 5. A example grid of Ioospheric Grid Poits (IGPs) is show with the correspodig regio of valid correctio. IGPs defied i the mask are idicated by diamods if they have valid correctios by octagos if they have bee set to Do Not Use, or by circles if they are desigated Not Moitored. User Ioospheric Pierce Poits (IPPs) are also show alog with the idicatio of whether they ca be corrected or ot. [11] delay estimate at the user s Ioospheric Pierce Poit (IPP), τ vpp, is the scaled by the obliquity factor to covert it to a slat rage correctio. The mathematical formulatios for iterpolated vertical IPP delay, τ vpp, are fuctios of IPP latitude, φ pp, logitude, λ pp, ad umber of grid poits used for the iterpolatio (see Sectio A.4.4.1.3 of [1]). As depicted i Figure 5, the earth is divided ito four iterpolatio regios: 1) φ pp 55 ) 55 < φ pp 75 3) 75 < φ pp 85 4) φ pp > 85 The first two regios use rectagular grids with equal spacigs i latitude ad logitude. To save badwidth, the service provider has the optio of defiig both 5 ad 1 squares i Regio 1. I Regio 3 the user creates virtual 1 x1 cells for iterpolatio. Regio 4 is physically a circular regio ad the iterpolatio has slightly differet form. I all regios the user s IPP must be surrouded by active grid poits with valid data. The user first seeks to use the four active surroudig IGPs defied i the mask to create a square which ca be used to iterpolate to the locatio of the IPP. If there is o surroudig square the user the checks for a surroudig triagular regio. If this too is uavailable, the user caot form a differetial ioospheric correctio. The selectio criteria for choosig E D F IPP Regio # of IGPs i Mask # of Valid IGPs IPP ithi Triagle Valid Correctio A 1 4 4 - yes B 1 3 3 yes yes C 1 4 3 o o D 1 4 4 - yes E 1 4 3 yes yes F 1 3 3 o o G 4 3 yes yes H 4 4 - yes I 3 3 o o J 3 4 4 - yes K 3 4 3 o o L 4 - o Table 4. For the idicated IPPs i Figure 5, the followig are listed: regio, umber of surroudig IGPs defied i the mask, subset of IGPs havig valid correctios, determiatio of IPP cotaimet withi a valid triagle, ad possibility of differetial correctio. surroudig grid poits is give i Sectio A.4.4.1. of [1]. The user always begis by checkig the mask. If the user s IPP is i Regio 1 ad the four grid poits correspodig to the 5 x5 surroudig grid cell are activated i the mask, the user the iterpolates usig at least 3 of those 4 IGPs. If the correctio iformatio for those IGPs does ot support a valid correctio the user may ot attempt to use the IGPs correspodig to a surroudig 1 x1 cell. If o 5 x5 square or surroudig triagle is defied i the mask, the user may the check for a surroudig 1 x1 cell. If the four possible larger cells are ot defied or do ot have valid correctios creatig a triagular regio cotaiig the IPP, the o ioospheric correctio ca be formed for that IPP. The rules for selectig IGPs i Regio are idetical to Regio 1 except oly 1 x1 cells are possible. If the four surroudig IGPs are defied ad have valid correctios the all are used to iterpolate the ioospheric correctios. If oly three are defied ad/or valid ad they form a triagle cotaiig the IPP the the user may also form a correctio uless the fourth poit has bee set to Do Not Use. I this case, o iterpolatio is allowed i ay of the four squares surroudig that IGP. If the user is outside of the triagle or there are fewer tha three defied ad valid IGPs the o correctio ca be formed. Regio 3 has 1 logitudial spacig at the 75 latitude lie but 9 spacig at the 85 lie. The user must liearly iterpolate virtual grid poits alog this lie to form 1 x1 cells. Oce the virtual 1 x1 cell
is formed the same rules apply to this regio as described for Regio. If both true IGPs are ot defied at 85 latitude, o virtual IGPs may be created. I Regio 4 there are oly four possible IGPs so selectio is straight forward. Istead of beig i square or triagular regios the user must either be i the full circle or the semi-circle described by three poits. To provide examples of how these rules work, Figure 5 shows a particular mask ad valid IGP cofiguratio. There is a shaded regio correspodig to all the areas where a differetial correctio is possible accordig to the rules of selectio. Also show are some sample IPPs ad whether they ca be differetially corrected (see Table 4). Most of the examples are relatively obvious, for example, IPPs A ad H are iside well defied square cells, while IPPs B ad G are iside well defied triagular cells. IPPs D, E, ad F are i regio 1 but have either square or triagular 5 x5 cells defied i the mask aroud them. Therefore, oe looks to see if the IPPs are surrouded by 1 x1 cells. IPPs D ad E are surrouded by a square ad a triagular cell respectively, but IPP F is i either. The IPP marked C is iterestig because it is outside of the 5 triagle of valid grid poits, but if the o valid IGP below ad right of it had ot bee defied i the mask, this IPP would have bee cotaied i a 1 x1 right triagle ad could have bee corrected. However, sice that IGP is i the mask ad has either ot bee received, timed-out, set to Do Not Use or set to Not Moitored, the IPP caot be differetially corrected as stads. IPP I is i Regio ad clearly falls out of the triagle of valid correctio. IPPs J ad K fall i Regio 3 first requirig iterpolatio alog 85 latitude to form virtual IGPs. These poits ca be used to form a 1 x1 box aroud J so that it ca be corrected. However, IPP K falls outside of the triagular regio created by the two virtual IGPs ad the lower true IGP so it caot be corrected. Fially IPP L lies i Regio 4, but oly two IGPs are defied i this example so o differetial correctio is possible. This figure is for illustrative purposes oly ad is ot meat to represet a likely sceario. Fially, we tur to the calculatio of the weights used to form the correctio at the IPP from the IGPs. These weights are described i Sectio A.4.4.1.3 of [1]. Example 6. Suppose a user has a pierce poit at (36 N, 1 i Regio 1. The 5 boudig rectagle for this IPP is 35-4 N ad 1-15. If these IGPs are specified ad valid, the user iterpolates usig all four poits. The weights the user applies would be give by (A-4) - (A-3) = 8., = 1., ( 4 N, 15 ( 4 N, 1 = 3., = 48. ( 35 N, 15 ( 35 N, 1 (11) If the IGP at (4 N, 15 is ot moitored, a user could still perform triagular iterpolatio, because the IPP is i the regio bouded by the other three grid poits. For this case the weights become (A-34) - (A-36) =., =., ( 4 N, 15 ( 4 N, 1 = 4., = 4. ( 35 N, 15 ( 35 N, 1 (1) Example 7. Suppose a user has a pierce poit at (81 N, 14 i Regio 3. The boudig rectagle for this IPP is 75-85 N ad 1-11 i Regio 3. If the IGPs at (85 N, 18 ad (85 N, 9 are specified ad valid, the user forms virtual grid poits at (85 N, 11 ad (85 N, 1. The values of the virtual grid poits would the be 7 τ = τ + τ v v v 9 9,( 85 N, 11,( 85 N, 18,( 85 N, 9 1 8 τ = τ + τ v v v 9 9,( 85 N, 1,( 85 N, 18,( 85 N, 9 The weights the user forms would be give by = 4., = 36., ( 85 N, 11 ( 85 N, 1 = 16., = 4. ( 75 N, 11 ( 75 N, 1 (13) (14) If the IGP at (75 N, 11 is ot moitored, a user could still perform triagular iterpolatio, because the IPP is i the regio bouded by the other three grid poits. For this case the weights become = 4., =., ( 85 N, 11 ( 85 N, 1 =., = 4. ( 75 N, 11 ( 75 N, 1 (15) Example 8. For a user with a IPP i Regio 4 at (87 N, 14 the weights would be give by =. 59, =. 141, ( 85 N, 9 E) ( 85 N, =. 35, =. 565 ( 85 N, 18 ( 85 N, 9 (16) ad for a IPP at (86 N, 7 the weights would be give by
=. 3, =. 7, ( 85 S, 13 E) ( 85 S, 4 E) =. 66, =. 634 ( 85 S, 14 ( 85 S, 5 CONCLUSIONS (17) The AAS MOPS achieves remarkable performace despite the severe costraits placed upo it. Although the badwidth is extremely limited, the quatizatio error ad restricted update rates do ot curretly limit system performace. The MOPS achieves its goals of creatig ad documetig a iterface betwee the service provider ad the user that is capable of satisfyig the aviatio requiremets for accuracy, itegrity, cotiuity ad availability. This paper represets the views of the author ad does ot ecessarily covey the opiio of RTCA, the FAA or Staford Uiversity. Although the author believes all of this iformatio to be accurate, mistakes ad misuderstadigs may have occurred i this iterpretatio of the MOPS. Please check our web site at http://waas.staford.edu/mops.html for updated versios of this mauscript. The author will correct ay errors foud with ewer versios at that site. Note that the MOPS is still beig revised. Ay chages or additios will also be updated at this locatio. Commets questios ad cocers ca be registered at the same address. This paper provides examples of how the differet message types are coected together ad how the itegrity bouds are calculated. These examples are meat to aid i uderstadig the itet of the MOPS. It is importat that these cocepts be well uderstood to be implemeted correctly. It is hoped that havig examples to complimet the rules listed i the MOPS will be helpful to ew readers. Correct implemetatio leads directly to flight safety. ACKNOLEDGMENTS The author wishes to thak all the people who participated i the developmet of the MOPS. I particular JP Ferow ad Bruce Decleee provided may helpful isights. Sicere thaks also go to Adrew Hase for his may cotributios to this documet ad for creatig the web site. Thaks also go to Per Ege for may helpful discussios. This work was sposored by the FAA GPS Product Team (AND-73). REFERENCES [1] RTCA Special Committee 159 orkig Group, Miimum Operatioal Performace Stadards for Global Positioig System / ide Area Augmetatio System Airbore Equipmet, RTCA Documet Number DO- 9A Jue, 1998. [] Ege, P., AAS Messagig System: Data Rate, Capacity, ad Forward Error Correctio, NAVIGATION, Sprig, 1997. [3] Comp, C., alter, T., Fuller, R., Barrows, A. K., Alter, K., Gebre, D., Hayward, R., Jeigs, C., Hase, A., Phelts, E., Archdeaco, A., Ege, E., Powell, J. D., ad Parkiso, B., Demostratio of AAS Aircraft Approach ad Ladig i Alaska, i proceedigs of ION GPS-98, Nashville, TN, September 1998. [4] Tsai, Y. J., Ege, P., Chao, Y. C., alter, T., Kee, C., Evas, J., Barrows, A., Powell, D. ad Parkiso, P., Validatio of the RTCA Format for AAS, i Proceedigs of ION GPS-95, Palm Sprigs, CA., September, 1995. [5] Loh, R., ullschleger, V., Elrod, B., Lage, M., ad Haas, F., The U.S. ide-area Augmetatio System (AAS), NAVIGATION, Fall, 1995. [6] alter, T., Ege, P., ad Hase, A., A Proposed Itegrity Equatio for AAS MOPS, i proceedigs of ION GPS-97, pp. 475-484, Kasas City, MO, September 1997. [7] Comp, C., Gazit, R., alter, T., ad Ege, P., Improvig AAS Itegrity ad Availability: UDRE ad GIVE Time Updates, i proceedigs of ION GPS-97, pp. 1315-134, Kasas City, MO, September 1997. [8] Slattery, R., Peck, S., Aagost, J., ad Moo, M., Guarateeig Itegrity for all Users of Active Data, to be published i Global Positioig System: Papers Published i Navigatio Volume VI. [9] Global Positioig System Stadard Positioig Service Sigal Specificatio, Jue, 1995. [1] Chao, Y. C. ad Parkiso, B.., The Statistics of Selective Availability ad its Effect o Differetial GPS, Proceedigs of ION GPS-93, Salt Lake City, Utah, September, 1993. [11] essel, P. ad Smith,. H. F., New Versio of the Geeric Mappig Tools Released, EOS Tras. Amer. Geophys. U., vol. 76, pp 39, 1995.