Techniques for Graceful Reversion from Dual to Single Frequency WAAS

Transcription

1 Technques for Graceful Reverson from Dual to Sngle Frequency WAAS Shau-Shun Jan, Todd Walter, Per Enge Department of Aeronautcs and Astronautcs Stanford Unversty, Calforna ABSTRACT Ths paper nvestgates technques to sustan dualfrequency onosphere performance when a dual-frequency arborne user loses all but one GPS frequency whle descendng nto the rado frequency nterference (RFI) feld. In ths paper, we are partcularly nterested n the case where the user transtons from L1-L5 to havng L5- only. That s because the uncertanty of the L5-only onospherc delay estmaton s larger than the L1-only onospherc delay estmaton. An L1-L5 dual-frequency user has LPV (HAL = 40m, VAL = 50m) [1] precson approach servces avalable 99.9% of tme over 100% CONUS, wth a nomnal σ of 0.32m [2]. An L5 sngle-frequency user has LPV precson approach servces avalable 99.9% of tme over 49.25% CONUS [3]. In ths stuaton, the nomnal σ s 6m at coast lnes, and 3.5m at the center. In other words, f an L1-L5 dual-frequency user loses L1 GPS frequency due to RFI and nstead uses the WAAS grd for onospherc delay estmaton, the loss of CONUS coverage of LPV servces wll be about 50%. Therefore, the obectve of ths paper s to fnd solutons that wll sustan a performance smlar to the mult-frequency onospherc delay estmaton. Based on the nformaton avalable to user, there are three technques to sustan the dual-frequency onospherc delay estmaton. Ths paper uses a typcal precson approach example based on San Francsco Internatonal Arport (SFO) to examne the possble solutons, and then uses the MATLAB Algorthm Avalablty Smulaton Tool (MAAST) [4] to measure all arports over CONUS. Frst, one can use the code-carrer dvergence to contnue onospherc delay estmaton; ths technque would requre a robust cycle slp detector. Ths technque provdes good onospherc delay estmaton (better than usng the WAAS [5] grd) for the full duraton of approach. Second, one can use the WAAS onospherc threat model to bound the error. Ths technque requres an onosphere storm detector. It provdes useful onospherc delay estmaton for at least 10 mnutes. Thrd, one can use the maxmum onospherc delay gradent model to estmate onospherc delay durng the onosphere storm perod. Ths technque should only be used when there s no avalable onosphere storm detector. The maxmum onospherc delay gradent technque also provdes useful onospherc delay estmaton for at least 10 mnutes. I. INTRODUCTION A dual-frequency GPS user can estmate the onospherc delay drectly and then subtract ths estmaton from the pseudorange measurements. Ths drect use of the dualfrequency wll be more accurate and offer hgher avalablty. [2] showed the smulaton results of the CONUS (CONtermnous US) coverage of the LPV [1] precson approach servces for a dual-frequency user. Whle experencng the RFI (Rado Frequency Interference), a dual-frequency user mght lose all but one GPS frequency, whch ntroduces the sngle-frequency GPS user cases. [3] showed the smulaton results of the CONUS coverage of the LPV precson approach servces for a sngle-frequency user. Whle comparng the results of [3] wth [2], the CONUS coverage of LPV precson approach servces for a sngle frequency user s less than the coverage for a dual-frequency user. Therefore, the obectve of ths paper s to nvestgate technques whch can sustan dual-frequency performance whle descendng nto the RFI feld. Ths paper dscusses the avaton applcaton, as the L1 and L5 GPS frequences are n ARNS (Aeronautcal Rado Navgaton Servces). We are partcularly nterested n the case where the user transtons from L1- L5 to havng L5-only. That s because the uncertanty of the L5-only onospherc delay estmaton s larger than the L1-only onospherc delay estmaton. Ths s because onospherc delay s nversely proportonal to frequency and L5 s a lower frequency than L1. Ths paper s organzed as follows. Secton II dscusses the problem, scenaros, and proposed technques. The code and carrer dvergence technque wll be dscussed n Secton III. Secton IV nvestgates the WAAS

2 onosphere threat model technque. The maxmum onospherc delay gradent model technque s dscussed n Secton V. Each secton wll nclude a typcal precson approach example based on San Francsco Internatonal Arport, and followed by the MAAST smulaton results for all arports wthn CONUS. Secton VI presents a summary and concludng remarks. II. PROBLEM STATEMENT AND SCENARIOS An L1-L5 dual-frequency user has LPV (HAL = 40m, VAL = 50m) precson approach servces avalable 99.9% of tme over 100% CONUS. The nomnal σ s 0.32m [2]. An L5 sngle-frequency user has LPV precson approach servces avalable 99.9% of tme over 49.25% CONUS [3]. In ths stuaton, the nomnal σ s 6m at the coast, and 3.5m n the center. In other words, f an L1-L5 dual-frequency user lose L1 due to RFI and nstead uses the WAAS grd for onospherc delay estmaton, the loss of CONUS coverage of LPV servces wll be about 50%. The loss of CONUS coverage of LPV servces s manly because of the uncertanty of the onospherc delay on L5. Ths stuaton s summarzed n Fgure 1. All VPL maps used n ths paper are for 99.9% avalablty, that s, a user at each specfc locaton had a VPL equal to or below the value ndcated by the color bar for 99.9% of tme. Consder a typcal precson approach example based on the San Francsco Internatonal Arport (SFO). In ths example, the fnal approach length s about 14.1 nm (26.1 km), and the fnal approach velocty for a general avaton (GA) arcraft s knots ( km/hour). Thus the fnal approach duraton s about 7-9 mnutes dependng on the fnal approach velocty. We assume that the arcraft enters the boundary of the L1 RFI feld when the arcraft reaches the fnal approach fx. Ths example s shown n Fgure 2. Therefore, for ths typcal precson approach example, a qualfed technque must provde at least 9-mnute of useful onospherc delay estmaton, smlar to performance of the dual-frequency onospherc delay estmaton. L1+L5 VPL Map for an L1-L5 user Lost L1 to RFI L5+WAAS VPL Map for an L5-only WAAS user 100% CONUS coverage of APV 1.5 Nomnal s _L1-L5 =0.32m 49.25% CONUS coverage of APV 1.5 Nomnal s _L5 =6.0m at coast lnes Nomnal s _L5 =3.5m at center <5 <10 <12 <15 <20 <30 <40 <50 >50 Good VPL ndexes n meter Fgure 1: The VPL maps llustrate the stuaton when an L1-L5 dual-frequency user s descendng nto an L1 RFI feld. The VPL map on the left s for an L1-L5 dual-frequency arborne user rght before enterng the L1 RFI feld. The VPL map on the rght s for an L5 sngle-frequency WAAS user. The loss of CONUS coverage of LPV servces wll be about 50% for ths example. Both plots are 99.9% VPL maps. Bad

3 L1+L5 Nomnal s _L1L5 = 0.32 m 90 ~ 120 knots 167 ~ 222 km/hr Ground L1 RFI Fnal approach fx Informaton avalable to arcraft: Before enterng the RFI zone: Good L1+L5 dual-frequency onospherc delay estmaton L5+WAAS Nomnal s _L5 = 6.0 m Flght path Fnal approach duraton 14.1 nm, 26.1 km, (7 ~ 9 mn.) SFO Touchdown Pont After enterng the RFI zone: L5 code and carrer phase measurements WAAS correctons The 9-mnute fnal approach duraton used n ths paper was derved from the fnal approach velocty of the general avaton (GA) arcraft, but these technques are not lmted to the GA arcraft. The fnal approach veloctes of the commercal arlner are faster than the GA arcraft, so the fnal approach duraton s shorter n tme. III. THE CODE AND CARRIER DIVERGENCE TECHNIQUE The basc observables of a sngle-frequency recever nclude [6]: ρ = R + b B + I + T + M + ν (1) Fgure 2: A typcal precson approach duraton example based on San Francsco Internatonal Arport (SFO). The arcraft enters the boundary of the L1 RFI feld when the arcraft reaches the fnal approach fx. The nomnal σ umps from 0.32m to 6.0m, whch results the loss of CONUS coverage of LPV servces. Fgure 2 also shows the avalable nformaton to an arcraft before and after enterng the RFI feld. Before enterng the L1 RFI feld, an arcraft has good L1-L5 dual-frequency onospherc delay estmaton. After enterng the L1 RFI feld, an arcraft has L5 snglefrequency code and carrer phase measurements, and WAAS correctons. We explore three technques to sustan the dual-frequency onospherc delay estmaton. L5 code and carrer dvergence. WAAS onospherc threat model. Maxmum onospherc delay gradent model. The requrements for these technques are shown n Fgure 3. The requrement for usng the L5 code and carrer dvergence technque s the absence of cycle slps. When cycle slps are present, and f there s no onosphere storm, one could utlze the WAAS onospherc threat model technque. If both cycle slps and onosphere storm may be present, one could use the maxmum onospherc delay gradent model technque. Presence of Cycle Slps Yes Ionosphere Storm Detector No Yes No L5 Code-Carrer Dvergence WAAS Iono. Threat Model Max. Iono. Gradent Model Fgure 3: Technques sustan the performance of the L1-L5 dualfrequency onospherc delay estmaton, and the requred condtons for usng these technques. Where, φ = R + b B I + T + N λ+ m + ε (2) ρ φ = + λ+ + ν ε (3) 2I N M m R = true range from SV to user b = recever offset from UTC B = satellte clock offset from UTC I = onospherc delay T = tropospherc delay M = multpath delay ν = recever thermal nose N λ = nteger ambguty One dstncton between the code and carrer observables s the magntude of the multpath and nose terms whch are fractons of a wavelength ( λl 1 19 cm, λ 24 cm, λ cm, and λ 300 m). For the carrer sgnal the L5 25 m and ρ ε terms are over two orders of magntude smaller than the correspondng M and v on the pseudorange observatons. At that level they are neglgble, and equaton (3) can be rewrtten as: ρ φ = + λ+ + ν (4) 2I N M In equaton (4) the v term, can be averaged out easly, and the M term can be mtgated by the arcraft antenna envronment. Although the multpath and nose errors could be lmted to a reasonably low level, equaton (4) stll suffers from an nteger ambguty ( N λ ). Fortunately, the nteger ambguty s a constant offset unless there s a cycle slp. As a result, there are two methods to solve the nteger ambguty n equaton (4).

4 Frst, one can take advantage of the nteger ambguty soluton before losng all but one GPS frequency whle descendng nto the RFI feld, and then subtract ths soluton from equaton (4). Thus, the onospherc delay can be calculated as n equaton (5-6). ρ φ = 2 ˆ I (5) ˆ ρ φ I = (6) 2 Second, one can take advantage of the WAAS onosphere correctons to solve the nteger ambguty from the nformaton fuson vewpont [7]. Specfcally, user nteger ambguty can be estmated by combnng the user local observables and WAAS messages, as shown n equaton (7). f I λ φ N λ φ N φ 2 L1 = L1 L1 L1 ( fl 1 f) ( ) ( ) (10) The carrer measurement of the onospherc delay s sgnfcantly less nosy than the code measurement, but ths measurement I L1φ of the delay was offset from the correct absolute value because of the nteger ambguty. In Fgure 4 the I L1φ was re-centered usng the tmeaveraged code measurement I. The green lne s L1ρ I L1ρφ gven n equaton (8). N λ ρ φ + ξ = + IWAAS (7) Where, ξ s the resdual error of the estmaton, and I WAAS s the WAAS onosphere correctons. Therefore, the onospherc delay can be estmated by the code and carrer dvergence technque, as n equaton (8). ˆ ˆ ρ φ Nλ I ρφ = (8) Ths paper uses the observables of satellte number 20 collected at Stanford Unversty on July 13, 2001 as an example. Fgure 4 shows the slant onospherc delay n meters measured n three methods. The blue lne shows the onospherc delay I L1 ρ at the L1 frequency as measured by the L1 and code dfference. The equaton wth whch pseudorange measurements ρ L1 and ρ at the L1 and frequency, respectvely, can be used to measure the onospherc delay I L1ρ at L1 s I 2 f = ρ ρ ρ ( ) ( ) fl 1 f L1 L1 Ths measurement of the slant onospherc delay s nosy but unambguous. The red lne plots the delay I L1 φ at L1 as obtaned from the L1 and carrer phase measurements, φ L1 and φ. The equaton wth whch carrer phase measurements φ L1 and φ at the L1 and frequency, respectvely, can be used to measure the onospherc delay I L1 φ at L1 s (9) Fgure 4: Slant onospherc delay to satellte number 40 at Stanford Unversty on July 13, As shown n Fgure 4, the code and carrer dvergence technque provdes good onospherc delay estmaton (the standard devaton σ Code _ Carrer s m n ths example), but cycle slps can not be tolerated. If cycle slps are present, the Phase Lock Loop (PLL) of GPS recever wll lose carrer trackng. Momentary loss of phase lock can result n a dscontnuty n the nteger cycle count. As a result, the nteger ambguty also has to be resolved. For our precson approach example, when one arcraft loses L1 whle descendng nto the RFI feld, ths arcraft can use the L5 code and carrer dvergence technque to contnue the onospherc delay estmaton. The nomnal σ wll change as follow: σ = σ + σ = (m) _ L1L5 Code _ Carrer (11) The σ n equaton (11) s much less than the nomnal σ usng the WAAS grd whch s of 6.0m. Based _ L5

5 on ths model, users at SFO wll be able to mantan good onospherc delay estmaton wthout usng the WAAS grd for full duraton of approach, provded cycle slps can be avoded. The SFO example s summarzed n Fgure 5. SFO Flght path Ground Touchdown 9 mn. Not n scale Pont s _L5 = 6.0 m s _L1L5 = 0.32 m s = 0.56 m Fgure 5: The nomnal σ varaton along wth the fnal approach n SFO. When the user lost L1 whle descendng nto the RFI feld, the user apples the L5 code and carrer dvergence technque to contnue to estmate the onospherc delay nstead of usng the WAAS grd. Ths technque provdes good onospherc delay estmaton for the full duraton of the approach. Fgure 5 shows the smulaton result for the typcal precson approach example based on SFO. Next, we wll use MAAST [4] to measure arcrafts applyng ths code carrer dvergence technque at all arports wthn CONUS. The MAAST smulaton confguraton s specfed n Table 1. Satellte Constellaton 24 standard GPS satelltes (WAAS MOPS) Table 1: The MAAST smulaton Confguraton. GEO 2 GEO s (AOR-W, POR) User 1-degree user grd wthn CONUS Tme Step 30-second over a 24- hour perod VAL 50 m HAL 40 m The MAAST s modfed to adopt the changes n the calculaton for an L1-L5 dual-frequency user losng L1 frequency whle descendng nto the RFI feld and then applyng the L5 code and carrer dvergence technque to contnue the onospherc delay estmaton. The new UDRE calculaton used n the MAAST smulaton s gven n equaton (12). Ths σ value may be arcraft specfc. σ = σ _ L1L5 + σcode _ Carrer = σ _ L1L (m) (12) Fgure 6 shows the smulaton result, whch s the 99.9% VPL contour for an L1-L5 dual-frequency user applyng the code and carrer dvergence technque to contnue the onospherc delay estmaton whle losng L1-frequency to RFI. Fgure 6 shows the VPL values are less than 40m for 99.9% of tme over 100% CONUS (Note: LPV VAL = 50m). Based on ths smulaton result, the L1-L5 dualfrequency arcraft whle losng L1-frequency to RFI wthn CONUS wll be able to use ths technque to mantan good onospherc delay estmaton wthout usng the WAAS grd for full duraton of approach. Fgure 6: The 99.9% VPL contour for an L5 sngle-frequency user applyng the code and carrer dvergence technque to estmate the onospherc delay after losng L1 frequency whle descendng nto the RFI feld. In order to show the beneft for usng the code and carrer dvergence technque, the comparson of two VPL contours s shown n Fgure 7. Frst, the VPL contour on the left s for an L1-L5 dual-frequency user usng the code and carrer dvergence technque to estmate the onospherc delay after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 12m but less than 40m. Second, the VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 30m, and some places are hgher than 50m (LPV VAL). Therefore, the VPL contour for usng the code and carrer dvergence technque s better than the VPL contour for usng the WAAS grd. However, the cycle slp rsk s accumulated. An L1-L5 dual-frequency user usng the code and carrer dvergence technque to estmate the onospherc delay after losng L1 frequency to the RFI can have a performance smlar to the L1-L5 dual-frequency user. GPS recever manufactures have ther own algorthms to detect cycle slps. If there are cycle slps, the arborne user wll no longer be able to use ths technque and wll have to use one of the other two technques: the WAAS onosphere threat model technque, and the maxmum onospherc delay gradent model technque.

6 L5 user wth the code and carrer dvergence technque L5-only WAAS user <5 <10 <12 <15 <20 <30 <40 <50 >50 Good VPL ndexes n meter Bad Fgure 7: The comparson of the VPL contours. The VPL contour on the left s for an L1-L5 dual-frequency user usng the code and carrer dvergence technque to estmate the onospherc delay after losng L1 frequency to the RFI. The VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The color bar shows the VPL ndexes n meters. The use of the code and carrer dvergence technque provded better onospherc delay estmaton than usng the WAAS grd for an L1-L5 dual-frequency arborne user descendng nto an L1 RFI feld. IV. THE WAAS IONOSPHERE THREAT MODEL TECHNIQUE A future WAAS message could possbly nclude the new message bts to ndcate the presence of an onosphere storm n addton to the GIVE message. If there are cycle slps and the arcraft has such an onosphere storm detector avalable, that arcraft can use the WAAS onosphere threat model technque to bound the onosphere error whle descendng nto the RFI feld. Ths WAAS onosphere threat model s detaled n [8]. That s a temporal threat model whch models the devatons n tme snce the last planar ft. A plot of the temporal threat model s shown n Fgure 8, whch plots the hstogram of equaton (13). I = Iˆ Iˆ (13) t= tono t= tono t= t0 Where, Î s the estmated onospherc delay at a specfc tme. In [8], only the ponts that pass the ch-square test are used n determnng the threat model. The ch-square test s a relable ndcator of the goodness of ft, and s used to detect the onosphere rregularty. Readers can refer to [9] for more nformaton about the ch-square test and the onosphere rregularty detecton. Fgure 8: The temporal threat model. The maxmum gradent occurs around 300 seconds whch s 1.62m. (Courtesy: Lawrence Sparks) Fgure 9 shows the dfferences between ft resduals at the tme of a ft and ft resduals at subsequent tmes. The gradent shows the ROT (Rate of TEC (.e. Ionospherc delay)). In Fgure 8 the maxmum gradent occurs around 300 seconds whch s 1.62m. The equaton to overbound the ROT n Fgure 8 s as follow: ROTbound 1.62 m, f t<120sec = + t f t>120sec 1.62 (5.33* *( 120)) m, (14) The blue lne n Fgure 9 plots the ROT bound and the red lne n Fgure 9 plots the confdence σ ROT, whch s calculated n equaton (15). σ ROT 1.62 (m), f t<120sec (5.33* *( t 120)) = 5.33 f t>120sec (m), (15) Where, 5.33 s K HMI value defned n Appendx J of the WAAS MOPS [10], and 5.33 s used to convert a 10 7 error bound to one sgma level. The overbound model s orgnally desgned to protect the WAAS users usng GIVE messages. As a result, ths model s vald before the tme recevng the next GIVE message, whch s 600 seconds [8]. However, the blue lne n Fgure 9 stll bounds the data shown n Fgure 8 at 800 seconds.

7 Fgure 10 shows the smulaton result for the typcal precson approach example based on SFO. Next, we wll use MAAST to measure arcrafts applyng ths WAAS onosphere threat model technque at all other arports wthn CONUS. The MAAST smulaton confguraton s specfed n Table 1. The MAAST s modfed to adopt the changes n the calculaton for an L1-L5 dual-frequency user losng L1 frequency whle descendng nto the RFI feld and then applyng the WAAS onosphere threat model technque to contnue bound the onosphere error. Fgure 9: The WAAS onosphere threat model (ROT overbound model). The blue lne s ROT overbound model, and the red lne represents the confdence of t. For our precson approach example, when an arcraft lost L1 whle descendng nto the RFI feld, ths arcraft can use the WAAS onosphere threat model technque to bound the onospherc error. The nomnal σ at the touchdown pont can be calculated by substtutng t = 540 sec nto equaton (15). σ ROT bound SFO (5.33* *( )) = 5.33 = (m) σ = σ + σ = (m) _ L1L5 ROTbound SFO (16) (17) Ths new calculaton s a tme dependent functon; therefore, MAAST smulated the arcraft usng the WAAS onosphere threat model technque to bound the onosphere error whle 9-mnute (at the touchdown pont) after descendng nto the RFI feld. The correspondng new UDRE calculatons used n the MAAST smulaton are gven n equaton (18), respectvely. σ = σ + σ = σ _ L1L (m) _ L1L5 ROT bound _9mn (18) Fgure 11 shows the smulaton result, whch s the 99.9% VPL contour for an L1-L5 dual-frequency user applyng the WAAS onosphere threat model technque to bound the onosphere error 9-mnute after losng the L1- frequency to RFI. Fgure 13 shows the VPL values are less than 40m for 99.9% of tme over 100% CONUS (Note: LPV VAL = 50m). Based on ths smulaton result, the arcraft wll be able to use ths technque to bound the onosphere error wthout usng the WAAS grd 9-mnute after enterng the RFI feld. The σ n equaton (17) s much less than the nomnal σ _ L5 = 6.0m for L5-only user. Based on ths model, users at SFO wll be able to mantan useful onospherc delay estmaton wthout usng the WAAS grd for at least 10 mnutes. The SFO example s summarzed n Fgure 10. SFO Flght path Ground Touchdown s _L1L5 = 0.32 m 9 mn. Not n scale Pont s _L5 = 6.0 m s _L1L5 = 0.76 m Fgure 10: The nomnal σ varaton along wth the fnal approach n SFO. When user lost L1 whle descendng nto the RFI feld, user apples the WAAS onosphere threat model technque to bound the onospherc delay error and nstead uses the WAAS grd. Ths technque provdes good onospherc delay estmaton for at least 10 mnutes. Fgure 11: The 99.9% VPL contour for an L5 sngle-frequency user applyng the WAAS onosphere threat model technque to bound the onosphere error after 9-mnute descendng nto the RFI feld (or at the touchdown pont).

8 To show the beneft for usng the WAAS onosphere threat model technque, the comparson of two VPL contours s shown n Fgure 12. Frst, the VPL contour on the left s for an L1-L5 dual-frequency user usng the WAAS onosphere threat model technque to bound the onosphere error after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 12m but less than 40m. Second, the VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 30m, and some places are even greater than 50m (LPV VAL). Therefore, the VPL contour for usng the WAAS onosphere threat model technque s better than the VPL contour for usng the WAAS grd. However, ths technque requres an onosphere storm detector. An L1-L5 dual-frequency user usng the WAAS onosphere threat model technque to estmate the onospherc delay after losng L1 frequency to the RFI can have a performance smlar to the L1-L5 dualfrequency user. V. THE MAXIMUM IONOSPHERIC DELAY GRADIENT MODEL TECHNIQUE If there may be cycle slps and there s no avalable onosphere storm detector, that arcraft can use the maxmum onospherc delay model technque to bound the onosphere error whle descendng nto the RFI feld. Ths maxmum onospherc delay gradent model s detaled n [11]. In her work, she analyzed the supertruth data, whch s the onosphere data obtaned for the past few years for the CONUS regon from the twenty-fve WRS s. She found that the maxmum onospherc delay gradent s 6m/19km n vertcal. In other words, the dfference of the measured onospherc vertcal delay at locaton A and the measured onospherc vertcal delay at locaton B whch s 19km apart from locaton A, could be 6m n the worst case, as shown n Fgure 13. Thus, the confdence bound can be calculated as σ MAX _ IONOgradent 6 d = (19) L5 user wth the WAAS threat model technque (after 9 mnutes enterng the RFI feld) L5-only WAAS user Where, 5.33 s K HMI value defned n Appendx J of the WAAS MOPS d s dstance from the current poston to the place wth the last dual-frequency onospherc delay estmaton <5 <10 <12 <15 <20 <30 <40 <50 >50 Good VPL ndexes n meter Bad Fgure 12: The comparson of the VPL contours. The VPL contour on the left s for an L1-L5 dual-frequency user usng the WAAS onosphere threat model technque to bound the onosphere error after 9-mnute losng L1 frequency to the RFI. The VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The color bar shows the VPL ndexes n meter. The use of the WAAS onosphere threat model technque provded better onospherc delay estmaton than usng the WAAS grd for an L1- L5 dual-frequency arborne user descendng nto an L1 RFI feld. The use of the WAAS onosphere threat model technque requres an onosphere storm detector. Ths onosphere storm detector would need to lsten to a new WAAS message whch s desgned to ndcate the presence of an onosphere storm. If there s an onosphere storm or there s no avalable onosphere storm detector, an arcraft wll have to use the maxmum onospherc delay gradent model technque to sustan a performance smlar to the dual-frequency onospherc delay estmaton whle descendng nto the RFI feld. The Max. onospherc delay gradent from Datta-Barua s work n Stanford WAAS Lab: 6 m / 19 km (n vertcal) Dfference n onospherc vertcal delay A 19 km 6 m Separaton dstance ( Usng WAAS Ionospherc Data to Estmate LAAS Short Baselne Gradents, ION NTM 2002) Fgure 13: The maxmum vertcal onospherc delay gradent model. The maxmum dfference n the onospherc vertcal delay for places 19 km apart ( A and B ) s 6m [11]. If an arcraft loses L1 whle descendng nto the RFI feld, ths arcraft can use the maxmum onospherc delay gradent model technque to bound the onospherc error. The nomnal σ at the touchdown pont can be calculated by substtutng d = 26.1 km nto equaton (19). B

9 σ MAX _ IONOgradentSFO σ = σ + σ = (m) = = (m) (20) _ L1L5 MAX _ IONOgradentSFO (21) The σ n equaton (21) s much less than the nomnal σ _ L5 = 6.0m for L5-only user. Based on ths model, users at SFO wll be able to mantan useful onospherc delay estmaton wthout usng the WAAS grd for at least 10 mnutes. Ths SFO example s summarzed n Fgure 14. Fgure 15 shows the smulaton result, whch s the 99.9% VPL contour for an L1-L5 dual-frequency user applyng the maxmum onospherc delay gradent model technque to bound the onosphere error 9-mnute after losng the L1-frequency to RFI. Fgure 15 shows the VPL values are less than 50m for 99.9% of tme over 100% CONUS (Note: LPV VAL = 50m). Based on ths smulaton result, the L1-L5 dual-frequency arcraft whle losng L1- frequency to RFI wthn CONUS wll be able to use ths technque to bound the onosphere error wthout usng the WAAS grd 9-mnute after enterng the RFI feld. SFO Flght path Ground Touchdown s _L1L5 = 0.32 m 9 mn. Not n scale Pont s _L5 = 6.0 m s _L1L5 = 1.9 m Fgure 14: The nomnal σ varaton along wth the fnal approach n SFO. When the user lost L1 whle descendng nto the RFI feld, that user apples the maxmum onospherc delay gradent model technque to bound the onospherc delay error and nstead uses the WAAS grd. Ths technque provdes good onospherc delay estmaton for at least 10 mnutes of margn. The σ at the touchdown pont s 1.9m whch s hgher than the user wth the WAAS onosphere threat model n Fgure 11. Fgure 15: The 99.9% VPL contour for an L5 sngle-frequency user applyng the maxmum onospherc delay gradent technque to estmate the onospherc delay after 9-mnute descendng nto the RFI feld (or at the touchdown pont). Fgure 14 shows the smulaton result for the typcal precson approach example based on SFO. Next, we wll use MAAST to measure arcrafts applyng ths maxmum onospherc delay gradent model technque at all other arports wthn CONUS. The MAAST smulaton confguraton s specfed n Table 1. The MAAST s modfed to adopt the changes n the calculaton for an L1-L5 dual-frequency user losng L1 frequency whle descendng nto the RFI feld and then applyng the maxmum onospherc delay gradent model technque to contnue bound the onosphere error. Ths new calculaton s also a tme dependent functon; therefore, MAAST smulated the arcraft usng the maxmum onospherc delay gradent model technque to bound the onosphere error whle 9-mnute (at the touchdown pont) after descendng nto the RFI feld. The correspondng new UDRE calculatons used n the MAAST smulaton are gven n equaton (22). σ = σ + σ = σ _ (m) _ L1L5 MAX _ IONOgradent 9mn L L (22) To show the beneft for usng the maxmum onospherc delay gradent model technque, the comparson of two VPL contours s shown n Fgure 16. Frst, the VPL contour on the left s for an L1-L5 dual-frequency user usng the maxmum onospherc delay gradent model technque to bound the onosphere error after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 20m but less than 50m. Second, the VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The VPL values n CONUS of ths plot are greater than 30m, and some places are even greater than 50m (LPV VAL). Therefore, the VPL contour for usng the maxmum onospherc delay gradent model technque s better than the VPL contour for usng the WAAS grd. An L1-L5 dual-frequency user usng the maxmum onospherc delay gradent model technque to estmate the onospherc delay after losng L1 frequency to the RFI can have a performance smlar to the L1-L5 dual-frequency user.

10 L5 user wth the Max. Iono. gradent technque (after 9 mnutes enterng the RFI feld) L5-only WAAS user Comparson of the Technques for Graceful Reverson from Dual to Sngle Frequency WAAS The Code and Carrer Dvergence Technque <5 <10 <12 <15 <20 <30 <40 <50 >50 Good VPL ndexes n meter Bad Fgure 16: The comparson of the VPL contours. The VPL contour on the left s for an L1-L5 dual-frequency user usng the maxmum onospherc delay gradent model technque to bound the onosphere error 9-mnute after losng the L1 frequency to the RFI. The VPL contour on the rght s for an L1-L5 user usng the WAAS grd to estmate the onospherc delay after losng L1 frequency to the RFI. The color bar shows the VPL ndexes n meter. The use of the maxmum onospherc delay gradent model technque provded better onospherc delay estmaton than usng the WAAS grd for an L1-L5 dual-frequency arborne user descendng nto an L1 RFI feld. The WAAS Iono. Threat Model Technque In summary, based on the nformaton avalable to user, there are three technques to sustan the dual-frequency onospherc delay estmaton. Ths analyss uses the typcal precson approach example based on SFO to examne the possble solutons, and then use the MAAST to measure all arports over CONUS. Frst, one can use the code-carrer dvergence technque to contnue onospherc delay estmaton; ths technque would requre that there are no cycle slps. Ths technque provdes good onospherc delay estmaton (better than usng the WAAS grd) for the full duraton of approach. Second, one can use the WAAS onosphere threat model technque to bound the error. Ths technque requres an onosphere storm detector. It provdes useful onospherc delay estmaton for at least 10 mnutes. Thrd, one can use the maxmum onospherc delay gradent model technque to estmate onospherc delay durng the onosphere storm perod. The maxmum onospherc delay gradent model technque also provdes useful onospherc delay estmaton for at least 10 mnutes. Fgure 20 shows a summary comparson of the uses of these three technques at the touchdown pont. The VPL contour plots are shown n the order of the VPL performance from the left to the rght. The use of the code and carrer dvergence technque s the best, the use of the WAAS onosphere threat model technque s the second, and the use of the maxmum onospherc delay gradent technque s the thrd. All of these technques outperform the WAAS grd. The Max. Iono. Delay Gradent Model Technque Fgure 20: A summary comparson of the uses of these three technques at the touchdown pont. The VPL contour plots are shown n the order of the VPL performance from the left to the rght. All of these technques outperform the use of WAAS grd. VII. CONCLUSIONS Ths paper dscussed the stuaton when an L1-L5 dualfrequency arborne user descended nto the RFI feld. Ths paper provded technques for users to sustan a performance smlar to the dual-frequency users. These technques are the code and carrer dvergence technque, the WAAS onosphere threat model technque, and the maxmum onospherc delay gradent model technque. Ths paper frst used a typcal precson approach example based on San Francsco Internatonal Arport (SFO) to examne these technques, and then used the MAAST to measure all arports over CONUS. The results are summarzed n Table 2. Ths paper demonstrated that a dual-frequency user can mantan the desred level of avalablty for LPV even when they lose all but one GPS frequency at the fnal approach fx pont.

11 User Type L1-L5 dual-frequency L1-only snglefrequency L5-only snglefrequency L5-only wth the code and carrer dvergence technque L5-only wth the WAAS onosphere threat model technque (after 9- mnute losng L1) L5-only wth the maxmum onospherc delay gradent model technque (after 9- mnute losng L1) Table 2: The MAAST smulaton results. CONUS Coverage of APV 1.5 precson approach servces (Avalablty 99.9%) 100% 97.58% 49.25% 100% 100% 100% VPL (n meter) 12 VPL < VPL 30 VPL 12 VPL < VPL < VPL < 50 HPL (n meter) 5 HPL < HPL 25 HPL 5 HPL < 20 5 HPL < HPL < 30 The 9-mnute fnal approach duraton used n ths paper was derved from the fnal approach velocty of a general avaton (GA) arcraft, but these technques are not lmted to GA arcraft. The fnal approach veloctes of the commercal arlner are faster than the GA arcraft, so the fnal approach duraton s shorter n tme. Therefore, these technques wll perform better on the commercal arlners than on the GA arcrafts. ACKNOWLEDGEMENTS The work n ths paper s supported by the FAA Satellte Program Offce under research grant 95-G-005. The authors gracefully acknowledge ths support. The authors would also lke to thank Dr. Demoz Gebre-Egzagher from Unversty of Mnnesota-Twn Ctes for hs thoughtful comments. Proceedngs of ION GPS 2001, Salt Lake Cty, UT, September 11-14, [5] Enge, P., Walter, T., Pullen, S., Kee, C., Chao, Y.-C., Tsa, Y.-J., Wde Area Augmentaton of the Global Postonng System, Proceedngs of the IEEE, Volume: 84 Issue: 8, August, [6] Msra, P., Enge, P., Global Postonng System Sgnal, Measurements, and Performance, Ganga-Jamuna Press, Lncoln, MA, [7] Da, D. H., Walter, T., Enge, P., Powell, J. D., Optmal Use of Ionospherc Correctons for Wde Area Augmentaton System (WAAS) Users, IEEE Poston Locaton and Navgaton Symposum, Rancho Mrage, CA, Aprl 20-23, [8] Sparks, L., Mannucc, A. J., Altshuler, E., Fres, R., Walter, T., Hansen, A., Blanch, J., Enge, P., The WAAS Ionospherc Threat Model, Beacon Satellte Symposum, Boston, MA, [9] Walter, T., Hansen, A., Blanch, J., Enge, P., Mannucc, T., P, X., Sparks, L., Ima, B., El-Arn, B., Leeune, R., Hagen, M., Altshuler, E., Fres, R., Chu, A., Robust Detecton of Ionospherc Irregulartes, Proceedngs of ION GPS 2000, Salt Lake Cty, UT, September 19-22, [10] RTCA SC-159, Mnmum Operatonal Performance Standard for Global Postonng System/Wde Area Augmentaton System Arborne Equpment, RTCA/DO-229B, October 6, [11] Datta-Barua, S., Walter, T., Pullen, S., Luo, M., Blanch, J., Enge, P., Usng WAAS Ionospherc Data to Estmate LAAS Short Baselne Gradents, Proceedngs of ION NTM 2001, San Dego, CA, January 28-30, [12] RTCA SC-159, Mnmum Avaton System Performance Standard for Local Area Augmentaton Systems, RTCA/DO-245, September 28, REFERENCES [1] Navgaton and Landng Transton Strategy, Federal Avaton Admnstraton (FAA), Washngton, D.C., August [2] Jan, S.-S., Walter, T., Enge, P., Analyss of a Three- Frequency GPS/WAAS Recever to Land an Arplane, Proceedngs of ION GPS 2002, Portland, OR, September 24-27, [3] Jan, S.-S., Gebre-Egzabher, D., Walter, T. Enge, P., Worst-Case Analyss of a 3-Frequency Recever to Land a General Avaton Arplane, Proceedngs of ION NTM 2002, San Dego, CA, January 28-30, [4] Jan, S.-S., Chan, W., Walter, T., Enge, P., MATLAB Smulaton Toolset for SBAS Avalablty Analyss,