Sensitivity Analysis of the JPALS Shipboard Relative GPS Measurement Quality Monitor

Transcription

1 Snsitivity Analysis of th JPALS Shipboard Rlativ GPS Masurmnt Quality Monitor Michal Konig, Dmoz Gbr-Egziabhr, Sam Pulln, Ung-Souk Kim, and Pr Eng Stanford Univrsity Boris S. Prvan and Fang Chng Chan Dpartmnt of Mchanical, Matrials, and Arospac Enginring, Illinois Institut of Tchnology Glnn Colby Naval Air Systms Command, Patuxnt Rivr, Maryland ABSTRACT Th Joint Prcision Approach and Landing Systm (JPALS) is bing dvlopd as a singl rplacmnt for th navigation, prcision approach and landing systms currntly usd by military aircraft. Shipboard Rlativ GPS (SRGPS) is a JPALS variant bing dvlopd to support flight opration in th shipboard nvironmnt. Bcaus of th stringnt SRGPS prformanc rquirmnts, diffrntial carrir phas solutions ar bing pursud. In th systm architctur currntly bing considrd, th JPALS Shipboard Intgrity Monitor (JSIM) is a rfrnc station basd intgrity monitoring concpt bing xplord. To som xtnt, JSIM is a shipboard analog of th LAAS Ground Facility (LGF) and its function is, in part, to dtct, isolat, and alarm signalin-spac and rfrnc rcivr failurs. Unlik th LGF howvr, JSIM is a mobil systm and has to dal with rfrnc rcivr antnna motion. Bcaus it oprats within a shipboard nvironmnt, it must also b robust to th ffcts of multipath. Th ffct of antnna motion and multipath is to introduc un-modld corrlatd carrirphas masurmnt rrors. This papr prsnts th rsults of a snsitivity analysis to assss th prformanc of a JSIM intgrity monitor known as th Masurmnt Quality Monitor rlativ to its quivalnt IMT monitor in th prsnc of un-modld corrlatd carrir-phas masurmnt rrors. A mthod for analyzing th ffct of un-modld carrir-phas nois, which involvs dvloping a frquncy rspons for th MQM, is prsntd. Th analysis mthod usd is to dvlop a rlationship btwn carrir-phas masurmnt nois and MQM alarm limits. Th rsults of this analysis mthod ar usd to show that larg, un-modld corrlatd nois triggrs th JSIM s fault dtction logic unncssarily, incrasing th fals alarm rat and advrsly affcting systm continuity. Th incras in fals alarm rat as a function of un-modld carrir-phas masurmnt rror is quantifid.. INTRODUCTION Th Joint Prcision Approach and Landing Systm (JPALS) is bing dvlopd as a singl rplacmnt for th multipl systms currntly usd to provid navigation, prcision approach, and landing srvics for US military aircraft. In som rspcts, JPALS is similar to th Local Ara Augmntation Systm (LAAS) bing dvlopd by th Fdral Aviation Administration (FAA), in that it will provid diffrntial corrctions and navigation systm intgrity mssags to usrs in th vicinity of th local rfrnc station. Shipboard Rlativ GPS (SRGPS) and Local Diffrntial GPS (LDGPS) ar two variants of JPALS. SRGPS is bing dvlopd to support prcision approach and landing oprations (including automatd landings) in th shipboard nvironmnt. LDGPS will support similar oprations at land basd facilitis In SRGPS architcturs undr currnt valuation, th task of intgrity monitoring is shard btwn th usr and th shipboard rfrnc station. Th objctiv of such intgrity monitoring is to, in a timly mannr, dtct, alarm, and isolat any failurs that can dgrad SRGPS prformanc. To this nd, th JPALS Shipboard Intgrity Monitor (JSIM) is on of th SRGPS rfrnc station basd intgrity monitoring concpts bing xplord. Th function of th JSIM is to provid intgrity monitoring with rspct to signal-in-spac and rfrnc rcivr failurs. In addition to its intgrity monitoring functions, JSIM is rsponsibl for gnrating and broadcasting high quality carrir- and cod-phas corrctions for multipl GPS frquncis.

2 To som xtnt, th JSIM can b viwd as a shipboard analog of th LAAS Ground Facility (LGF) and its prototyp, th Stanford Univrsity Intgrity Monitor Tstbd (IMT) [, ], and as such, som of th intgrity monitoring algorithms of IMT will b usd as a starting point for th dsign of th JSIM intgrity monitors [3]. A simpl rus of all of th IMT intgrity monitors howvr, is not possibl bcaus thr ar sufficint diffrncs btwn SRGPS and LAAS (or LDGPS). For xampl, SRGPS is bing dsignd as a carrir-phas basd systm whil LAAS is a carrir-smoothd codphas systm. Mor importantly, thr ar two major assumptions built into algorithms of th IMT intgrity monitors that ar not ncssarily valid in SRGPS applications. Ths assumptions ar:. Th rfrnc antnnas providing th masurmnts usd by th intgrity monitors ar static.. Th GPS antnnas providing masurmnts usd by th intgrity monitors ar situatd such that th multipath thy s, if any, is uncorrlatd. Motion of a rfrnc antnna that is assumd or blivd to b static, has th ffct of introducing corrlatd carrir-phas masurmnt rrors,, quivalnt to th motion of th antnna. Figur dpicts a cas whr structural motion inducs a carrir phas masurmnt rror from a satllit dirctly ovrhad. In ordr to dal with carrir-phas masurmnt rrors rsulting from rfrnc antnna motion du to structural flxing, th us of a strapdown Inrtial Navigation Systm (INS) collocatd with th SRGPS rfrnc antnnas has bn proposd. Th output of th INS would provid an indpndnt masurmnt of, and compnsation for, th rfrnc antnna motion. It is postulatd that carrirphas multipath has an ffct similar to uncompnsatd antnna motion. To mitigat th ffcts of shipboard multipath, novl GPS antnnas, rcivrs, and signal procssing tchniqus hav bn proposd. Ths includ controlld rcption pattrn (phasd array) shipboard antnnas, as wll as bam-forming and null-string GPS rcivrs [4]. Figur. Carrir-Phas Masurmnt Error Du to Antnna Motion Rgardlss of th mthods and quality of snsors usd to dal with antnna motion, thr will always b som rsidual carrir phas masurmnt rror bcaus our knowldg of th antnna s location cannot b prfct. Mor importantly, howvr, ths rrors in our knowldg of th antnna s prcis location ar tim varying. Consquntly, thy ar diffrnt from th tim invariant survy rrors ncountrd in othr diffrntial systms such as LAAS. Similarly, multipath mitigation tchniqus cannot b prfct and will also introduc rsidual carrir-phas masurmnt rrors. Thus, during th dsign and dvlopmnt of JSIM, an important qustion that nds to b addrssd is to what dgr th prformanc of th intgrity monitors ar affctd by rfrnc antnna motion and othr corrlatd carrir phas masurmnt rrors? Th objctiv of th work rportd in this papr is to assss th prformanc of a particular JSIM intgrity monitor rlativ to its quivalnt IMT monitor in th prsnc of antnna motion and othr corrlatd carrirphas masurmnt rrors such as multipath. Th intgrity monitor w focus on in this papr is th Masurmnt Quality Monitor (MQM) and w will b intrstd in answring th following qustions:. What is th snsitivity of th MQM to rsidual carrir phas masurmnt rrors?. What is th prformanc (spcially, incrasd fals alarm rat) of th MQM in th prsnc of

3 rsidual carrir phas rror du to antnna motion and multipath? Accordingly, th rmaindr of this papr is organizd as follows: Sction provids an ovrviw of th JSIM and MQM. This will includ a qualitativ discussion of th ffct of uncompnsatd rfrnc antnna motion on th MQM s prformanc. In Sction 3, th frquncy rspons of th MQM is drivd and prsntd. In sction 4, th ffct of rsidual carrir phas rror on th MQM fals alarm rat is discussd. For conclusions, a summary and dirctions for futur work ar prsntd as Sction 5. OVERVIEW OF JSIM AND MQM Th JSIM architctur undr valuation currntly consists of multipl GPS rcivr-antnna pairs which ar installd shipboard. Multipl rcivr-antnna pairs provid robustnss to quipmnt failur, and as wll, a rdundant st of masurmnts for distinguishing rfrnc rcivr failurs from signal-in-spac failurs. Th rdundant masurmnts from th rcivr-antnna pair ar th input to various intgrity monitors. Th intgrity monitors ar algorithms that dtrmin th occurrnc of a postulatd failur mod. In addition to th intgrity monitors, an intgral part of th JSIM architctur is th Excutiv Monitor (EXM). Basd on th input from th various intgrity monitors, th Excutiv Monitor maks th dcision whthr to flag th SRGPS systms as unavailabl for opration. comput a carrir-phas stp rror, ( n ), in th following mannr: ( n ) = ( n ) ( n ) () p It is assumd that valus of ( n) largr than crtain prscribd limits ar indicativ of a carrir-phas anomaly. Such valus of ( n) will caus th MQM to alarm. In addition to carrir-phas stp rrors, th MQM also monitors carrir phas ramp and acclration. This is accomplishd by monitoring th valus of th ramp and acclration trms givn by β in Equation () abov. Excssiv ramp and acclration byond prscribd limits will also caus th MQM to issu an alarm. Th distributions of ( n ), β ar not ncssarily Gaussian. Thy can, howvr, b ovrboundd by a Gaussian distribution [, ]. Th MQM limits for ( n ), β ar thrfor stablishd using th Gaussian ovr-bound. Ths limits ar st in ordr to maintain th fals alarm rat at or blow som prscribd limit. On of th many intgrity monitors in JSIM is th Masurmnt Quality Monitor (MQM). Th MQM nsurs that only high quality carrir-phas masurmnts ar usd in formulating SRGPS position solutions. To accomplish this, th MQM dtcts, alarms, and isolats rfrnc rcivr failurs, as wll as signal-in-spac anomalis du to GPS satllit clock failurs. Th MQM dtcts such failurs by monitoring th carrirphas masurmnts obtaind from th multipl rcivrs that ar part of th JSIM. Mor prcisly, it monitors th statistics of th computd variabl ( n ) which is rlatd to th carrir-phas diffrntial corrction [, ]. This drivd quantity is usd to form a scond ordr polynomial fit of th following form: ( n ) = β 0 + β t + β t () At ach masurmnt poch, this polynomial fit is usd to comput a prdictd valu of ( n ) which is dnotd by th variabl p ( n). This variabl p ( n) is in turn usd to Figur. Effct of Carrir-Phas Error on MQM Tst Statistics. (In this cas, stp tst statistic) Figur qualitativly dpicts th ffct of carrir-phas masurmnt rrors du to antnna motion or multipath on th prformanc of th MQM. Th Gaussian ovrbound distribution markd original rprsnts th distribution of ( n ), β in th absnc of antnna motion or multipath. Th distribution markd actual rprsnts th distribution of ths variabls in th prsnc rsidual carrir-phas rrors aftr compnsation for antnna motion and multipath (i..

4 prcivd carrir-phas). Th protction limits for ( n ), β ar stablishd basd on th original distribution bcaus w ar unawar of th actual distribution. If th MQM limits ar basd on th original distribution and th standard dviation of actual distribution is largr than that of th original distribution, thn thr will b an incrasd fals alarm rat. On of th objctivs of this work is to prcisly quantify this incras in fals alarm rats. As will b shown latr, th incras in fals alarm rats is a function of th incras in th standard dviations of ( n ), β which ar dnotd by, β and β, rspctivly. But first w will hav to stablish a rlationship btwn th additional carrir-phas masurmnt rror,, causd by antnna motion and multipath, to standard dviations of th carrir-phas stp rror, rror, β, and acclration, β., ramp W start this analysis b noting that th MQM can b viwd as a Singl-Input Multipl-Output (SIMO) dynamic systm as shown in Figur 3. As such, w can driv a transfr function for th MQM using standard mthods dvlopd for handling such systms. Th MQM is a discrt-tim or sampld-data systm and, thrfor, gnrating a transfr function for it involvs taking th z-transform of Equation. Driving transfr functions for such discrt-tim systms is a standard tchniqu discussd in most systm nginring txt books such as [5] and will not b discussd in any mor dtail in this papr. Whn th MQM is viwd as a s SIMO, th input to th systm is th drivd quantity, ( n ) dscribd arlir. Th outputs of th systm ar th carrir-phas stp rror, vlocity, and acclration. Th discrt transfr functions H() z, Hv() z, and Ha( z) rlat th computd valu of ( n ), to ( n ), β, rspctivly. Givn ths transfr functions, it is asy to rlat th standard dviation of th carrir-phas masurmnt rror du to antnna motion and multipath, to th MQM tst statistics. Figur 4. MQM Stp Tst Frquncy Rspons Figur 3. MQM Block Diagram 3. MQM FREQUENCY RESPONSE Th MQM targts rapidly varying carrir phas rrors. Statd diffrntly, th MQM is dsignd to dtct rrors with high frquncy contnt. Thrfor, it is rasonabl to xpct that both th magnitud and frquncy contnt of influnc th MQM s prformanc. W will show that this is indd th cas by analyzing th MQM s frquncy rspons. Figur 4 is a plot of th frquncy rspons for ( n ). Figur 5 and Figur 6 ar similar plots for β, rspctivly. Th abscissa of this plot is prsntd in th normalizd (or digital) frquncy form. That is,.0 on th abscissa corrsponds to th JSIM sampling frquncy, which is th rat at which th carrir phas is sampld for procssing by th MQM. Thrfor, givn th standard dviation and corrlation (i.., th powr spctrum) of, dtrmining th standard dviation for ( n ), β is just a mattr of intgratd convolution.

5 of uncompnsatd antnna motion of a givn magnitud and frquncy, what do th MQM limits hav to b to maintain a fals alarm rat that is similar to that of th IMT? Figur 5. MQM Ramp Tst Frquncy Rspons Figur 4 highlights svral important aspcts of th MQM s prformanc in th prsnc of antnna motion or multipath. Prhaps th most important aspct, is that th output of th MQM is affctd by both th magnitud and frquncy contnt of th input. Thrfor, to dtrmin th ffct of antnna motion on th MQM on nds to know th powr spctrum of th antnna motion. A dscription of antnna motion by simply stating th magnitud of displacmnt is not sufficint. Anothr significant point to not is that th magnitud of th frquncy rspons at zro frquncy ( DC ) is zro. This mans that antnna installation or survy rrors do not affct th MQM s ability to dtct carrir-phas stps or xcssiv acclrations. Figur 6. MQM Acclration Tst Frquncy Rspons 4. MQM PERFORMANCE Throughout this papr w hav notd that antnna motion and multipath can b tratd as an additiv carrir phas masurmnt nois. This is a consqunc of modling th MQM as a linar systm. Th MQM frquncy rspons analysis discussd in th prvious sction showd how to account for this addd carrir phas masurmnt nois. In this sction w prsnt th ffct of this additiv nois on th prformanc of th MQM. In particular, w ar intrstd in th following: Firstly, givn an additiv nois of som magnitud, what is th incras in fals alarm rats of th MQM? Qualitativly, on can fors that incrasd masurmnt nois will rsult in th MQM alarming at a highr rat. Ths will b fals alarms, of cours, bcaus thr ar no inhrnt failurs in th GPS signal as th uncompnsatd antnna motion is apparing as nois. Scondly, in th prsnc Bfor w prsnt th analysis rsults answring th aformntiond qustions, it is worth noting a fw points. Firstly, whn w us th trm fals alarm rat, w man fals alarm rat of th MQM only. At this point in th dsign of th SRGPS architctur, w cannot quantify th fals alarm rat of th ntir JSIM. This is bcaus, as notd arlir, th ultimat dcision to dclar th systm unavailabl for us is mad by th Excutiv Monitor. Th Excutiv Monitor maks this dcision basd on, in part, input from othr intgrity monitors. In th absnc of th complt dsign of th othr intgrity monitors, it is difficult to quantify th ntir JSIM s fals alarm rat. With this cavat, w can now discuss th MQM s prformanc quantitativly. Figur 7 shows th MQM stp tst fals alarm rat as function of th rror ratio, r, which is dfind as follows: r = (3) This is th ratio of th standard dviation of th distribution of (n) du to rsidual carrir-phas rror in th prsnc of antnna motion or multipath to th standard dviation of this tst statistic in th absnc of antnna motion or multipath. In Figur 7, w hav lctd to plot th fals alarm rat as a function of r and not th ratio a plot basd on. This is bcaus would not b gnral. That is, such a plot would imply that w know th spctrum of th additional carrir phas masurmnt rror. This is mad clar by th curvs in Figur 8 which show th ffct of carrir phas rror,, (modld as a first ordr Gauss- Markov procss with a standard dviation,, of unity and a corrlation tim τ) on th MQM tst statistics and β th ffct of on. What is apparnt from Figur 8 is that and β corrlation tim (or frquncy contnt) of. dpnds on th Anothr point to not about Figur 7 is that, th fals alarm rats hav bn paramtrizd by th MQM alarm st-points. Th alarm st points ar stablishd at six-,

6 svn- and ight-. W us to stablish tst limits and not th actual distribution obtaind whn antnna motion and multipath ar prsnt bcaus that distribution is unknown. Figur 7. MQM Stp Tst Fals Alarm Rat As Function of Error Ratio. From Figur 7 w not that th fals alarm rats ar almost constant for rror ratios lss than approximatly 0%. This implis that if th additional carrir phas masurmnt rror du to antnna motion and multipath is kpt at a valu that yilds an rror ratio valu lss than of approximatly 0%, thn additional carrir-phas masurmnt nois can b almost ignord whn stablishing th MQM alarm st points. Th sam argumnt also applis to th ramp and acclration tsts bcaus thir plots of fals alarm rat as a function of rror ratio ar idntical to Figur 7. alarm rat. In th prsnc of such larg antnna motion or multipath th fals alarm rat can b maintaind at a constant valu if th fals alarm st point is incrasd rlativ to its initial valu. To illustrat this point w considr th cas whr, in th absnc of uncompnsatd antnna motion and multipath, w want to maintain a MQM fals alarm rat consistnt with a 7- alarm st point. To continu maintaining this sam fals alarm rat in th prsnc of uncompnsatd antnna motion or multipath (i.., in th prsnc of incrasing valus or r ) will rquir changing th MQM alarm st point to a valu of k- whr k is som numbr largr than 7. Figur 9 shows th rlationship btwn th multiplir k of usd in stablishing MQM alarm st points (or th k-factor ) and th rror ratio r for a givn fals alarm rat. Whil Figur 9 shows that incrasing th k-factor in th prsnc of an incrasing valus of r can allow maintaining a constant fals alarm rat, th rquird valu of k can b vry larg for high valus of th rror ratio. Th valu of k cannot b incrasd indfinitly bcaus thr is an uppr limit on th accptabl valus of carrir phas stp, ramp or acclration. Simply incrasing th k-factor to maintain a dsird fals alarm rat can advrsly affct th ovrall systm s intgrity by incrasing th numbr of MQM missd dtctions. Figur 9. MQM Alarm St Point Limit As a Function of Error Ratio. 5. CONCLUSIONS AND FUTURE WORK Figur 8. Mapping of Carrir Phas Masurmnt Error with a Standard Dviation of Unity into MQM Stp and Acclratio Tst Statistics For a fixd fals alarm st point, Figur 7 shows that a larg rror ratio lads to a highr fals alarm rat. Statd in practical trms, for a fixd fals alarm st point, larg antnna motion or multipath lads to an incrasd fals This papr prsntd a mthodology for rlating th carrir phas masurmnt rrors to th MQM alarm st points. Th rlationship highlights th important fact that th MQM alarm st points ar a function of both th magnitud as wll as th frquncy contnt (or corrlation) of th carrir-phas masurmnt rrors. It was shown that larg, un-modld carrir-phas masurmnt rrors du to antnna motion or multipath advrsly affct continuity by triggring th MQM alarm st points unncssarily. Th JSIM s protction limits

7 can b rlaxd to accommodat such uncompnsatd antnna motion. Whil this may dcras th fals alarm rats (and nhanc continuity), it has th potntial of advrsly affcting th systm s intgrity by incrasing th numbr of MQM missd dtctions. Assssing th ffct of ths rlaxd limits on ovrall systm continuity and intgrity is difficult. This is bcaus whn w whn discuss missd dtctions, w ar quantifying th numbr of tims th MQM fails to flag a carrir phas jump or acclration that is largr than th alarm. This dos not man howvr, that th JSIM as a whol has ignord an unsaf condition, bcaus thr ar othr monitors that could potntially flag th unsaf condition. Quantifying th ffct of rlaxd limits of spcific individual intgrity monitors on th ovrall systm prformanc, thrfor, can b accomplishd aftr all th intgrity monitors that will b part of JSIM hav bn dsignd. This is th subjct of ongoing work. 6. ACKNOWLEDGEMENTS Th authors gratfully acknowldg th U.S. Navy s Naval Air Warfar Cntr for supporting this rsarch. Howvr, th viws xprssd in this papr blong to th authors alon and do not ncssarily rprsnt th position of any othr organization or prson. REFERENCES [] M. Luo, S. Pulln, t.al., Dvlopmnt and Tsting of th Stanford LAAS Ground Facility Prototyp, Procdings of th ION National Tchnical Mting. Anahim, CA,, Sptmbr 000. [] G. Xi, S. Pulln, t al. Intgrity and Updatd Tst Rsults for th Stanford LAAS Intgrity Monitor Tstbd, Procdings of th ION-National Mting, Albuqurqu, NM. Jun 00. [3] B. Prvan, F.C. Chan, t al, Systm Concpts for Cycl Ambiguity Rsolution and Vrification for Aircraft Carrir Landings, Procdings of th ION-GPS. Salt Lak City, UT, Sptmbr 00. [4] A. Brown and N. Grin, Tst Rsults from a Digital P(Y) Cod Bamstring Rcivr for Multipath Minimization, Procdings of th ION 57 th Annual Mting, Albuqurqu, NM, Jun -3, 00. [5] G. Franklin, J. D. Powll and M. L. Workman, Digital Control of Dynamic Systms, Addison Wsly, 990