Signal Deformation Monitoring for Dual- Frequency WAAS

Transcription

1 Sgnal Deformaton Montorng for Dual- Frequency WAAS R. Erc Phelts, Gabrel Wong, Todd Walter, and Per Enge, Stanford Unversty BIOGRAPHY R. Erc Phelts, Ph.D., s a research engneer n the Department of Aeronautcs and Astronautcs at Stanford Unversty. He receved hs B.S. n Mechancal Engneerng from Georga Insttute of Technology n 995, and hs M.S. and Ph.D. n Mechancal Engneerng from Stanford Unversty n 997 and, respectvely. Hs research nvolves sgnal deformaton montorng technques and analyss for SBAS and GBAS. Gabrel Wong s an Electrcal Engneerng Ph.D. canddate at the Stanford Unversty GNSS Research Laboratory. He has prevously receved an M.S.(EE) from Stanford Unversty, and a B.S.(EECS) from UC Berkeley. Hs current research nvolves sgnal deformaton montorng and mtgaton for GNSS sgnals. Todd Walter, Ph.D., s a senor research engneer n the Department of Aeronautcs and Astronautcs at Stanford Unversty. Dr. Walter receved hs Ph.D. from Stanford and s currently workng on modernzaton of the Wde Area Augmentaton System (WAAS) and defnng future archtectures to provde arcraft gudance. Key contrbutons nclude early prototype development provng the feasblty of WAAS, sgnfcant contrbuton to the WAAS MOPS, desgn of onospherc algorthms for WAAS, and development of dual frequency algorthms for SBAS. He s a fellow of the Insttute of Navgaton and serves as ts presdent. Per Enge, Ph.D., s a professor of aeronautcs and astronautcs at Stanford Unversty, where he s the Klener-Perkns Professor n the School of Engneerng. He drects the GNSS Research Laboratory, whch develops satellte navgaton systems. He has been nvolved n the development of the Federal Avaton Admnstraton s GPS Wde Area Augmentaton System (WAAS) and Local Area Augmentaton System (LAAS). For ths work, Enge has receved the Kepler, Thurlow, and Burka awards from the Insttute of Navgaton (ION). He receved hs Ph.D. from the Unversty of Illnos. He s a member of the Natonal Academy of Engneerng and a Fellow of the IEEE and the ION ABSTRACT Prevous sgnal deformaton analyses and montor desgns have prmarly focused only on threats to the L C/A code. They have tradtonally reled on a combnaton of emprcal measurements and analytcal models of the threats and the user recevers. In the future however, to mtgate onospherc errors, WAAS wll leverage the L5 sgnal n addton to L. Ths means both sgnals wll need to be montored. Whle many famlar C/A code sgnal deformaton montor analyses can be etended and appled to the L5 codes, the montor needs to be far more senstve snce the dual-frequency combnaton desgned to remove onospherc errors wll amplfy any range bases on the sgnal. At the same tme, ths correcton wll drve the range error lmts to be smaller. In addton, the new sgnal deformaton montor needs to detect potental faults on the L5 sgnal a somethng the current desgn s not easly adapted to do. In ths paper, background s provded on the current WAAS sgnal deformaton montor along wth key measures of ts accompanyng performance analyss. In addton, the estng L fault threat analyses and user constrants are appled to L5 codes and future recevers. Measured data from a dual-frequency prototype sgnal deformaton montor recever are then used to nfer a reasonable nose model to compare current and proposed montor desgns. From ths data, a new sgnal deformaton fault detecton algorthm s analyzed and appled to the case of dual-frequency users to determne ts performance, relatve to the current system. Fnally, the results are used to make recommendatons on constrants on dual-frequency user recever confguratons. It s beleved that the montor desgn approach used here may be readly etended for sgnal deformaton montorng of other GNSS sgnals of varous code modulatons. INTRODUCTION Sgnal deformatons arse from hardware mperfectons or faults n the sgnal generaton hardware on GNSS satelltes. When the receved sgnals dffer from each other, bases and, subsequently, poston errors may

2 result. Hgh-ntegrty augmentaton systems such as space-base and ground-based augmentaton systems (SBAS and GBAS) employ sgnal deformaton montors (SDM) to measure the receved sgnals and attempt to ensure these errors reman acceptably small for a set of allowed avoncs recever confguratons. In all, an effectve SDM desgn wll accomplshes the followng tow thngs: ) Quckly detect anomalous deformatons should they arse n the presence of nose and multpath before they cause harm to the user, and ) Ensure any undetected nomnal or faulted sgnal deformatons do not result n unacceptably large range errors. For avaton users of GPS L, GBAS and SBAS have developed sgnal deformaton montorng technques for just ths purpose [], []. After accountng for envronmental nose, multpath, and nomnal sgnal deformaton bases, multple montor recevers compute lnear combnatons of the outputs from each correlator on the correlaton peak. The result s one or more detecton metrcs that are well-suted for L sgnals, but whch may requre sgnfcant modfcaton to be adaptable to other sgnals, such as L5. Ths s of partcular concern for WAAS, whch proposes to provde ntegrty for dualfrequency users n the future. The sgnal deformaton bas errors for these users are magnfed by the dual-frequency combnaton, whch s necessary to remove onospherc errors. In ths case, the detecton performance of the estng algorthm may not be satsfactory even for the L sgnal. And, for L5, none ests. It follows that to mprove SDM performance, one must ether sgnfcantly reduce the errors users eperence due to the faults or mprove the montor to detect more faults. And both of these approaches must take nto consderaton the L5 sgnal, whch wll have very dfferent characterstcs and constrants than does L. Reducng User Error Ideally, the user range errors can be reduced by smply lmtng the allowed recever desgns to those closest to the reference recever confguraton. In the best case, all recevers would match WAAS reference recever, makng all deformaton errors essentally cancel out wth the dfferental correcton. Whle desrable, ths s generally mpractcal snce the user recever desgns often cannot be changed at wll. Indeed, for L-only users, the user recever desgns were fed well before the sgnal deformaton threat was even defned. For dual-frequency users ths constrant may be more easly mposed snce the reverse s true the threat s defned and understood well n advance of the estence of any L5-capable avoncs recevers. However, t s stll not guaranteed. For ths reason, ths paper assumes the most of the current MOPS-defned recever confguratons wll also be permtted for dual-frequency users; t ecludes only double-delta trackng on L. It further assumes a relatvely broad regon wll be permtted for trackng the L5 sgnal as well. Improvng Fault Detecton Performance Assumng lmted control over the recever desgns dualfrequency WAAS users mplement, fault detecton must be mproved to acheve better SDM performance. Ths can be accomplshed by one or more of the followng: Wder montor recever bandwdth Reduced nose thresholds Improved detecton metrc desgn Montor recevers wth wde pre-correlaton bandwdths flter out less dstorton than one wth a narrower flter bandwdth. Ths makes anomalous oscllatons and asymmetres more detectable for a gven SDM archtecture. The drawback s that t potentally leads to larger errors f that bandwdth causes the dfferental range correcton to be less correlated wth those errors. Reduced nose thresholds mply better nose performance due to ether addtonal averagng or to better stng of the antenna. Ths too would make the montor more senstve. Stll, the antenna stes and numbers of recevers n WAAS (and many other systems) are fed and unlkely to change. Effectve metrc desgns attempt to mamze detecton senstvty by estmatng the dstorton n the presence of the nose n an optmzed way. Ths s the approach used n [3]; t s the method currently used n the WAAS. In general, ths s a preferred approach snce t s the most adaptable and amenable to changes n hardware and/or sgnals. BACKGROUND: Sngle-frequency SDM ICAO Threat Model Sgnal deformaton threats are defned by the Internatonal Cvl Avaton Organzaton (ICAO) Threat Model []. They model the types of correlaton peak dstorton of concern to avaton users. These nclude dstortons, false peaks, and deadzones. Tradtonally, augmentaton systems have developed ground-based montors equpped wth mult-correlator recevers to quckly detect when a receved correlaton peak s suffcently dstorted by one or more of these threats [].

3 The ICAO Threat model uses three parameters to descrbe a combnaton of analog and dgtal fault modes wth three parameters. A second-order step model descrbes the analog fault modes usng two parameters f d and, whch determne the oscllaton frequency and the dampng, respectvely. The dgtal fault mode s descrbed by a sngle parameter,, whch determnes the amount of advance (lead) or delay (lag) of the fallng edge of each chp transton. A full descrpton of these equatons s provded n [] and (more concsely) n [5]. Each of these parameters s llustrated n Fgure, and the parameter ranges are provded n Table. Volts /f d C/A PRN Codes Chps Normalzed Ampltude... Correlaton Peaks Code Offset (chps) Fgure. Combnaton of Analog (Fd and ) and Dgtal () Falure Modes (Ideal <dashed> and Evl <sold> Waveforms Shown.) Table. Sgnal deformaton threat model parameters Threat Case A (Dgtal Fault Only) Threat Case B (Analog Fault Only) Threat Case C (Analog + Dgtal Fault) f d (Mhz) N/A (MNepers/sec) N/A (ns), - - f d f d 3.. Dual-frequency Ionospherc Correcton, - - Currently sngle frequency users have only a sngle pseudorange sgnal, L, that requres montorng. Dual frequency users wll use a dfferent pseudorange, DF, that ncorporates nformaton from a second rangng sgnal on L5, L5. The dual-frequency pseudorange s modfed accordng to the equaton below. DF (). L. L5 The dual-frequency combnaton of Equaton elmnates the onospherc errors the largest error source for GPS. It permts the WAAS range error lmts, or UDREs, to be much smaller and ams to sgnfcantly ncrease avalablty for those users. However ths combnaton equaton also amplfes any bases present on the L sgnal by a factor of.; t scales any bases present on the L5 sgnal by a factor of.. Ths means any sgnal deformaton bases that occur on ether sgnal wll be sgnfcantly larger than they are for users of L only. Ths scalng, n combnaton wth the smaller error lmts, makes mtgatng sgnal deformatons for dual-frequency WAAS users sgnfcantly mode challengng than t s for sngle-frequency users. Sgnal Deformaton Montor for L-only Users The current WAAS sgnal deformaton montor (and reference recever) s a NovAtel G-II. It has an MHz bandwdth and uses an early-mnus-late (EML) dscrmnator wth.-chp spacng. Fgure shows the confguraton of ths recever relatve to the L-only avoncs recevers allowed by the MOPS DO-9D []. User Recever Double-Sded Bandwdth Ar BW (MHz) (MHz) User Recever Bandwdth (MHz).. Nomnal SD Range Error Contours for WAAS Users Current WAAS Reference MAX:.m; MIN:.55m Ar Correlator Spacng (chps) User Recever Correlator Spacng (chps) Fgure. Early-mnus-Late recever confguratons allowed by the Mnmum Operatonal Performance Standard (MOPS) DO-9D. The current WAAS reference recever (NovAtel G-II) has bandwdth of MHz and an early-mnus-late dscrmnator wth.- chp spacng. The G-II provdes 9 correlator outputs on each channel that are used to measure the symmetry of the correlaton peak. Each of the correlators are postoned at offsets relatve to an deal peak rangng from -.3 chps to +.3 chps, at.5-chp ntervals. Fgure 3 gves an llustraton of ths confguraton. r r r r 3 P d P r 5rr7 r r.7 Fgure 3. Illustraton of correlator outputs on an deal correlaton peak and the computaton of a sngle, normalzed detecton metrc, d.

4 The current WAAS detecton metrc s smply a lnear combnaton of those correlator outputs accordng to d r. () P In the above equaton, P s the prompt correlator (at an offset of chps) and s a constant. Fnally, the detecton metrc s referenced to the nomnal, undstorted sgnal accordng to d - medan d D. (3) Threshold In the above equaton, the nomnal metrc s represented as the medan of that metrc across all SVs n vew. In modelng analyses, however, the nomnal s smply the fltered, undstorted sgnal. Note that the current WAAS SDM algorthm s actually the mamum over four such metrcs each wth a dfferent set of constants tuned to detect dfferent parts of the threat model. For smplcty, t s equvalent to state that, when mamzed, these four metrcs acts a sngle effectve threshold-normalzed detecton metrc whch thereby determnes the ultmate detecton performance for the montor. DUAL-FREQUENCY SDM Threat Model The ICAO threat model used for L C/A code s also used to model deformaton of the L5 sgnal. The code on L5 has a chppng rate tmes as fast and ts nomnal chp duraton s tmes as short. It s straghtforward to apply the threat model transformatons to these codes as n [5]. The shortened chp duraton mples that the analog fault oscllatons on L5 chps appear at one-tenth the frequency they do on C/A chps. And dgtal faults on the L5 chps appear to be tmes as large as they do on the C/A code. There are three separate fault cases whch must be mtgated for L5 users. These are as follows: ) A fault occurs on L only ) A fault occurs on L5 only 3) A fault occurs on L and L5 smultaneously sgnal. The thrd, dual-frequency, case was conservatvely modeled as havng two ndependent, worst-case faults occur at the same tme one on each sgnal. Further, the magntudes of the mamum user errors on each sgnal were summed, not subtracted, as Equaton suggests. Whle ths s lkely an overlypessmstc threat assumpton, t helps us to compute an upper bound on the performance of any proposed dualfrequency SDM mtgaton strategy. User Recever Confguratons The Mnmum Operatonal Performance Standard (MOPS) verson DO-9D descrbes the allowed recever confguraton for L-only avaton users of WAAS []. These nclude constrants on dscrmnator type, correlator spacng, bandwdth, and pre-correlaton flter dfferental group-delay. Smlar constrants for dual-frequency users have not as yet been defned, but t s antcpated that the desgn space for these recevers wll be far more lmted, n order to reduce the magntude of the potental errors due to sgnal dstortons. However, for the analyses n ths paper, the constrants were assumed to be more akn to those of current WAAS recevers. Accordngly, the errors resultng from ths analyss should be consdered pessmstc. The constrants for the recevers modeled n ths paper are lsted n Table below. Table. User Recever Constrants Assumed for the SDM Modelng Analyss Sgnal Trackng Capablty Dscrmnator Type Correlator Spacng Bandwdth (MHz) Group Delay (ns) L-Only Early-mnus-Late (EML), Double-delta () EML:.5-. chps (ma) :.5-.3 chps (ma) (Vares wth bandwdth constrant as descrbed n []) EML: -MHz : -MHz (Vares wth correlator spacng constrant as descrbed n []) -ns (Vares wth bandwdth constrant as descrbed n []) Dual-Frequency L: Early-mnus- Late L5: Early-mnus- Late L: Same as L- only L5:.5-. chps L: Same as L- only L5: -MHz L: -ns (Vares wth bandwdth constrant []) L5: -5ns Agan, n each of the above cases, the mamum user errors assocated wth the fault are scaled accordng to the dual-frequency combnaton factors assocated wth each

5 SDM for Dual-Frequency Users WAAS wll soon upgrade to new, NovAtel G-III recevers that wll be capable of trackng the L5 sgnal. These recevers wll also have a wder (MHz) bandwdth, use an EML dscrmnator wth.-chp spacng, and output eght bn measurements based on the code chp shape, as opposed to the tradtonal correlator measurements output by the G-II [7]. Each of these new capabltes can be useful for mprovng WAAS SDM for dual-frequency users. The wder bandwdth of the G-III wll permt the sgnal dstorton be more observable to the montor. Stll, note from Fgure that ths bandwdth change moves the reference further away from the set of allowed user recevers. Ths shft generally leads to larger errors, makng prompt detecton (.e., wthn the -second tme to-alert requrement) more dffcult. User Recever Double-Sded Bandwdth Ar BW (MHz) (MHz) User Recever Bandwdth (MHz) New Reference.. Nomnal SD Range Error Contours for WAAS Users. Current Reference MAX:.m; MIN:.55m Ar Correlator Spacng (chps) User Recever Correlator Spacng (chps).7 Fgure. Early-mnus-Late recever confguratons allowed by the Mnmum Operatonal Performance Standard (MOPS) DO-9D. The current WAAS reference recever (NovAtel G-II) and the new reference recever (NovAtel G-III) confguratons are ndcated. Both use.-chp EML dscrmnators, but the G-III has a bandwdth MHz wder than the G-II. The chp-shape based outputs allow processng the dstortons pre-correlaton, thereby removng one addtonal flterng step n the process. That step, namely the correlaton process tself, typcally acts to reduce the amount of dstorton that can be observed by the montor. Combned wth the wder bandwdth, these precorrelaton, chp shape outputs can form a powerful tool for sgnal deformaton montorng. PRN codes and overlay one of the L5 codes measured on SVN []. (For clarty, 5 consecutve postve chps of the L5 sgnal are plotted.) It s readly observed that the codes shapes look qute smlar at the chp transtons. Note that ths presents promse not only for sgnal deformaton montorng of L and L5, but perhaps for other code modulatons as well. Normalzed Step Response.... Blk-IIF-SVN-L5 (5-chps) vs All SVN All SVN. Blk IIF-SVN-L5-I Blk IIF-SVN-L5-Q Tme [sec] Fgure 5. Measurements of C/A codes chps from 3 GPS SVs (red) and a fve consecutve L5 code chps (blue) from SVN. [] Fgure shows sample outputs from a NovAtel OEMV3 recever a recever qute smlar to the future WAAS G- III. (Ths s the recever used for the analyss n ths paper.) Observe that the actual L and L5 chp transtons concde eactly. It follows that any detecton method that acts on the code chp transtons for one code modulaton should be relatvely easly adapted to the other modulatons as well. Fgures 7 and llustrate how chp shape outputs are modeled for SDM analyses on both L and L5 codes, respectvely. Normalzed Ampltude Code Chp Outputs L L Chps Normalzed Ampltude Correlator Outputs L5 L Code Offset (chps) Fgure. Lve measurements of the chp shape outputs and the correspondng correlator outputs from PRN5. (Data taken wth a NovAtel OEM-V3.) The chp-based outputs have the added beneft of beng less dependent on the code modulaton of nterest. Fgure 5 shows actual hgh-resoluton measurements of 3 GPS

6 b b 7 b Normalzed Ampltude Normalzed Ampltude... b 5 d b P Chps Code Offset (chps) Fgure 7. Dstorted (red) and nomnal (blue) models of chp shape outputs and correlaton peak outputs for L. Analog threat shown (fd=mhz, =.MNepers/sec). Normalzed Ampltude Chps Normalzed Ampltude Code Offset (chps) Fgure. Dstorted (red) and nomnal (blue) models of chp shape outputs and correlaton peak outputs for L5. Analog threat shown (fd=mhz, =.MNepers/sec). The chp-based metrcs evaluated n ths paper are very straghtforward. They are smply dfferences between the normalzed ampltudes of the ndvdual measurements relatve to the nomnal sgnal. (See Fgure 9 below.) Each ndvdual measurement s smply d b. () P P P In the above equaton,, where P s the prompt measurement from the tradtonal correlaton peak (n Eq. ) and s a scalng constant used to normalze the nomnal chp measurements to values between ±. Gven a detecton threshold at each bn offset,, each of the ndvdual detecton metrcs s then found accordng to D d T - medan d. (5) The fnal metrc s then the mamum over all ndvdual threshold-normalzed metrcs. b b b 3 b Fgure 9. Illustraton of chp shape bn outputs on an deal chp transton and the computaton of a sngle, normalzed chp (ampltude) based detecton metrc, d, where ranges from to. In ths paper, to compare the detecton approaches usng a common reference, the NovAtel OEM-V3 was used to appromate the outputs from a WAAS G-III recever and compute common thresholds. The G-III s not yet felded and s stll unavalable, but the OEM-V3 behaves smlarly to the G-III. It s L5-capable, has a MHz bandwdth, and t produces chp-shape bn outputs. It can also produce tradtonal correlaton peaks. There are some small dfferences however. For one, the OEM-V3 uses NovAtel s propretary PAC trackng technque nstead of narrow correlator (.-chp EML on L); they both use wde correlator trackng for L5 (. chp EML on L5). However, ths should have lttle effect for the analyss of ths paper, whch does not rely on ths data to model the dfferental correcton. Also, ths analyss uses very conservatve nose estmates, so any potental advantage offered by the PAC technology under nomnal envronmental/multpath condtons s negated. Another dfference s that the OEM-V3 has slghtly dfferent correlator locatons than wll the G-III, and t has one less bn output and correlator output on the late sde (.e., rght sde) of the correlaton peak. The G-III wll have bns, and can produce 9 correlator outputs whle the OEM-V3 has only 7 bns, leadng to correlator outputs. (Refer to Fgure.) Agan, the effect on the results here should be mnor, snce all the bn and correlator locatons requred are stll qute close to those of the G-III. The models appromate the true G-III trackng and correlator characterstcs more precsely (e.g., Fgures 7 and ), and the nose estmates were, agan, worse (hgher) than those used n WAAS. ANALYSIS All of the nputs needed to analyze the relatve performance have been dentfed n the precedng sectons. Gven the threat model, Equatons 3 and 5 can be used to generate the mamum, steady-state montor

7 responses to each threat. The threat model combned wth the user recever desgn constrants of Table can be used to model the mamum, steady-state user range errors correspondng to each montor response. Usng the OEM-V3, thresholds for each bn can be determned. The correlaton peaks can then be computed along wth the current WAAS metrcs to generate detecton thresholds for those as well. Fnally, each of the detecton methods can then be drectly compared to each other to determne ther relatve performance. Ths relatve measure s nsuffcent, however, to fully assess the performance of a proposed montor desgn. The montor must mtgate the hazardous sgnal deformaton faults wthn the -second tme-to-alert requrement for all desred error lmts. To ths end, t s helpful to compute the error lmts as a functon of the montor response. Tme-to-Alert Analyss: Tme-varyng MERR Once the montor metrcs m are desgned and the approprate threshold estmates are appled to them the net step s to analyze the ablty of these metrcs to detect hazardous faults wthn the tme-to-alert. In other words the montor must mtgate the threats before they reach the user error lmt and lead to hazardously msleadng nformaton (HMI). For WAAS SDM, ths error lmt s also referred to as the Mamum ERror n Range, or MERR. Table 3. Statc MERR Error Lmts for L-Only and Dual-frequency Users UDRE Inde (UDREI) UDRE MERR for L-only Users MERR for Dualfrequency Users The statc (.e., tme-nvarant) MERR s a functon of the UDRE. Ths error lmt can be met smply by ensurng the mamum user range error from any undetected sgnal deformatons reman below t. Ths quantty s defned for L-only and dual-frequency users accordng to the table below. Note that when the UDRE nde (UDREI) s small, the statc error lmts are sgnfcantly larger for L-only users than t s for dualfrequency users. Ths s because the error lmts for L- only users nclude terms to account for onospherc errors. (See Table 3.) An effectve sgnal deformaton montor, however, must detect the deformatons promptly, before they cause harm for the users. Accordngly they must take nto account the followng two addtonal consderatons: ) No HMI should occur durng the transent response between fault onset and steady-state for both user range error, E, and montor metrc, m. ) There should be adequate margn between the mamum steady-state user range error and the statc MERR of Table 3. A tme-varyng MERR analyss was developed to address both of these concerns [9]. A detaled dervaton of the tme-varyng MERR formulaton eplanng how t ntegrates the tme and margn nformaton nto a sngle pass-fal test for meetng the current fault tree allocaton for these faults s provded n Append A. The sectons below descrbe the nputs and assumptons used to get the results presented n ths paper. MERR Analyss Inputs The transent responses for SDM are domnated by the responses of the user carrer smoothng flter and smoothng flter used to average the montor measurements. The tme constants for the user smoothng flter and the montor metrc flters are seconds and 5 seconds, respectvely. (The user smoothng flter tme constant s recommended by MOPS-9D [5].) The constants, K ffd and K md derve from the false-alarm (P fa ) and mssed detecton probabltes (Pmd), respectvely. P fa comes from the current contnuty requrement and targets one false alarm per satellte per year; ths results n a P fa of 3. -/SV. It should be noted that ths s a conservatve value, snce the SQM test statstcs are hghly correlated (over 5 to seconds) and ths value assumes ndependent eposures to false alarm for each second. When epressed n terms of a sgma multpler for a normal, zero mean probablty dstrbuton, the threshold for PFA = 3 - yelds a K ffd of 5.5. For a P md of -, K md equals, at most,.. For ths analyss the undetected fault allocaton, Pa =.5 -/hr was assumed. The fault pror (P f ) used was *.7-5 faults per SV, per hour.

8 Steady-state User and Montor Responses Usng the equatons outlned n Append A and the nputs outlned n the prevous secton, a MERR bound can be found at each desred WAAS error lmt (or UDRE) by determnng the ma E ss, the steady-state user range error (gven the dscretzed ICAO threat model) that corresponds to a gven m ss, the mamum steady-state montor metrc value. The horzontal as s the mamum Threshold-normalzed detecton metrc, m ss =m/t (where, for the current WAAS system, m ss s the fnal, medan-adjusted detecton metrc as dscussed []). The threshold s the sum of K ffd multpled by the (mamum) montor nose constant mon. (Refer to Table ) A plot of E ss vs. m ss for L-only WAAS users at a UDRE of 5m (UDREI=3) s gven n Fgure. It corresponds to the case where there the current WAAS reference recever (G-II) dfferental correcton s appled. The user recever flters nclude all the generalzed flters allowed by the MOPS DO-9D (as llustrated n Fgure ) []. Each pont n the plot corresponds to a dfferent threat n the threat model. The blue lne provdes an upper bound on the error as a functon of the mnmum montor response. Ma Range User Range Error, (m) E ss (m) WAAS Sgnal Deformaton Montor Senstvty for Sngle Frequency Users RISING SV - New (nflated) Nose Model L: Current (MHz) BW, Ma SF User Errors L: Worst Case SF User Error.5 T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure. E ss vs. m ss for the current WAAS system for L-only users. (Reference MHz,. chp). The procedure for determnng the tme-varyng MERR bound that takes these nputs nto account, accounts for margn, and plots the smallest error bound as a functon of montor response, m ss as s as follows: Procedure: ) For a gven tme-varyng metrc, m, Fnd P md (m(t)) usng assumed nose statstcs (.e., mon ) about m(t) at each tme n the step response (gven by Eq. A-3) evaluated at the threshold. In other words, solve md R ffd P mt K mt over a range of steady-state montor responses, m ss. Note that the upper-lmt for ths range need not eceed the mamum m ss for all deformatons. ) Solve for the protecton level probablty (P pl ) constant, K pl, usng K pl () R R P a Ppl, ma Pmd ( mt ( )) P f (7) 3) Solve for the bound on E(t) usng Equaton A-7. (Note that ths bound depends on the UDRE.) ) Dvde ths bound by the step response n Eq. A- and take the mnmum over all tme to yeld the mnmum E ss vs. m ss curve, or the "tme-varyng MERR" curve. 5) Compute the scale factors, S, requred to reduce the montor nose and thereby ensure the MERR curve bounds all threats accordng to Equaton. Note that for L-only users, these are pre-determned; a dfferent curve apples to each UDREI. Usng these establshed factors we can set the mnmum performance level (.e., MERR bounds) of the estng montor. Any proposed montor desgn should meet these requrements to be vald. S mn E( t) S MERR P md Pa ( m( t) S ) P f () Fgure plots the MERR lmts for each UDRE n addton to the same E ss vs. m ss upper bound from Fgure. These are the mnmum montor responses requred to meet the tme-to-alert requrement at each UDREI. The MERR curves (.e., the dashed black lnes) are never crossed by the mamum user error curve; they successfully bound the E ss vs. m ss curves whenever all the ponts le to the rght and/or below them. Ths mples the current system meets the requrement. Note, however, that even for the smallest error lmt, the MERR s always greater than (appromately) meters. Ths s because for L-only users, the onosphere error terms are ncluded n the MERR computaton.

9 Ma Range User Range Error, (m) E ss (m) MERR Bounds for decreasng UDRE L: Current (MHz) BW, Ma SF User Errors L: Worst Case (L-only) User Error MERR Bound at UDREI=5 for L-only Users.5 T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure. E ss vs. m ss for the current WAAS system for L-only users. (Reference MHz,. chp) MERR bounds for each UDRE are shown (black, dashed). As prevously stated, for the montor analyss of ths paper, t was necessary to compute new thresholds (usng the NovAtel OEM-V3 recever) for each montor desgn change. Ths provdes a common bass wth whch to compare ther relatve performance. Fgure plots two L-only E ss vs. m ss curves one where the montor m ss has been normalzed usng the current WAAS thresholds (from Fgures and ) and one where m ss has been normalzed usng the OEM-V3 evaluaton thresholds. It can be seen that the latter thresholds are sgnfcantly more conservatve than those used n the current WAAS sgnal deformaton montor. Ma Range User Range Error, (m) E ss (m) WAAS Sgnal Deformaton Montor Senstvty for Dual Frequency Users RISING SV - New (nflated) Nose Model Evaluaton Thresholds WAAS Thresholds L: Current (MHz) BW, Ma DF User Errors L: Worst Case DF User Error L: Current (MHz) BW, Ma SF User Errors L: Worst Case SF User Error.5 T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure. E ss vs. m ss for the current WAAS system for L-only users (Reference G-II: MHz,. chp) compared to the E ss vs. m ss computed usng new, evaluaton (OEM-V3 recever) thresholds. Fgure once agan plots the (threshold-adjusted) E ss vs. m ss curve correspondng to L-only users. Ths fgure also overlays the tme-varyng MERR bounds for dualfrequency users. Note that here the MERR curve (at the smallest UDREI) descends nearly to zero. And the MERR bound at UDREI=5 s now less than.5m snce t does not nclude any onospherc error terms. Ma Range Error, E ss (m) User Range Error (m) WAAS Sgnal Deformaton Montor Senstvty for Dual Frequency Users RISING SV - New (nflated) Nose Model MERR Bounds for decreasng UDRE MERR Bound at UDREI=5 for Dualfrequency users L: Current (MHz) BW, Ma User Errors L: Worst Case User Error.5 T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure. E ss vs. m ss for the current WAAS system for L-only users (Reference G-II: MHz,. chp) usng new, evaluaton (OEM-V3 recever). MERR bounds at each UDRE shown (black, dashed) for dual-frequency users. RESULTS Usng all the aforementoned nputs, tools, and analyss technques the followng montor and fault cases were compared: L-only users and a montor recever usng current G-II (MHz) recever and Current WAAS correlator-based metrc. Ths s the baselne case prevously dscussed. User errors are not scaled. (Refer to Fgures and.) Dual-frequency Users and a SDM usng the new G- III (MHz) recever wth the Current WAAS correlator-based detecton metrc. The fault occurs only on L. User errors on each sgnal are scaled by.. Dual-frequency Users and a SDM usng the new G- III (MHz) recever wth the new chp shape-based detecton metrc. The fault occurs only on L. User errors are scaled by.. Dual-frequency Users and a SDM usng the new G- III (MHz) recever wth the new chp shape-based detecton metrc. The fault occurs only on L5. User errors are scaled by.. Dual-frequency Users and a SDM usng the new G- III (MHz) recever wth the new chp shape-based detecton metrc. The worst-case fault occurs smultaneously on both L and L5. User errors from

10 threats on each sgnal are scaled by. and. (respectvely) then summed. The results of each of cases are plotted n Fgure 3. It can be seen that, for dual-frequency users, just the addton of the wder bandwdth recever (dark green lne) adds a lttle detecton capablty over the baselne case (blue lne) n some nstances. However, the larger user errors from the bandwdth dfference and the dualfrequency scalng easly negate ths advantage for almost all threat cases. The ntroducton of the chp-based detecton metrc (the red lne), however, produces a sgnfcant advantage over the prevous technques. The ncreased detecton senstvty over the current correlator-based technques s evdent. Even the scalng of the errors by. s manageable for the majorty f threat cases. Ths advantage holds up for both the L5-faulted case and the smultaneous L, L5 fault case as well. Fgure shows a zoomed n vew of Fgure 3. In addton, t plots the MERR bounds for dual-frequency users. It can be seen that, gven the conservatve assumptons of ths analyss and no addtonal consderatons, the chp-based metrc could, enable a mnmum UDREI for dual-frequency users. To enable a smaller UDRE, addtonal measures would lkely need to be taken to reduce the mamum errors. Ma Range User Range Error, (m) E ss (m) WAAS Sgnal Deformaton Montor Senstvty for Dual Frequency Users RISING SV - New (Inflated) Nose Model L: Current (MHz) BW, Current Metrcs L: MHz BW, Current Metrcs L: MHz BW, Chp-based Metrc L5: MHz BW, Chp-Based Metrc L,L5: MHz BW, Chp-Based Metrc.5 T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure 3. Relatve effectveness of desgns for dualfrequency users (as compared to the current WAAS montor for L-only users). Ma Range User Range Error, (m) E ss (m) WAAS Sgnal Deformaton Montor Senstvty for Dual Frequency Users RISING SV - New (Inflated) Nose Model L: Current (MHz) BW, Current Metrcs L: MHz BW, Current Metrcs L: MHz BW, Chp-based Metrc L5: MHz BW, Chp-Based Metrc L,L5: MHz BW, Chp-Based Metrc MERR Bounds for decreasng UDRE MERR Bound at UDREI=5 for Dualfrequency Users T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure. Relatve effectveness of desgns for dualfrequency users (as compared to the current WAAS montor for L-only users). MERR bounds overlad for comparson. All of the prevous analyses consdered the case when the fault s dfferentally corrected by the reference recever. However, a more nsdous fault condton ests where the dfferental correcton cannot be appled. In ths case, the magntudes of the user errors are even larger. To meet ths challenge, WAAS uses another montor n conjuncton wth the SDM to mtgate the threat wthn the tme-to-alert. The WAAS code-carrer coherence (CCC) montor s capable of assstng the SDM when ths type of sgnal deformaton fault occurs []. The detals of ths montor and ts MERR analyses are beyond the scope of ths paper. However, presumng ths montor s n place, we can assess the ablty of the SDM to effectvely mtgate the remanng, un-corrected faults n the same way we have before. The results of the uncorrected fault case are shown n Fgure 5. Here, meetng the smultaneous L-L5 fault case (heavy, sold black lne) for dual frequency users s sgnfcantly more challengng than most of the other montorng cases. However, the plot stll shows that the chp-based montorng detecton metrc stll nearly enables the system to a mnmum UDREI of. It also outperforms the current metrc whch would be ncapable of mtgatng the threats wth such large errors and s not desgned to mtgate threats on L5.

11 Ma Range User Error, (m) E ss (m) WAAS Sgnal Deformaton Montor Senstvty for Dual Frequency Users RISEN SV - New (Inflated) Nose Model MERR Bounds for decreasng UDRE MERR Bound at UDREI=5 for Dualfrequency Users L: Current (MHz) BW, Current Metrcs L: MHz BW, Current Metrcs L: MHz BW, Chp-based Metrc L5: MHz BW, Chp-Based Metrc L,L5: MHz BW, Chp-Based Metrc T Threshold-Normalzed Detecton Metrc Threshold-normalzed Detecton Metrc, m ss Fgure 5. Relatve effectveness of montor desgns for dual-frequency users (as compared to the current WAAS montor for L-only users) wth no dfferental correcton appled. MERR bounds shown for comparson. Conservatve Measures The results presented here are somewhat pessmstc for several reasons. For one, the dual-frequency threat model s more conservatve here than wll be assumed n practce. The analyss used here presumed an ndependent fault on each sgnal that was addtve. In realty, WAAS wll assert that only a sngle fault can affect both sgnals smultaneously; ths wll result n some cancellaton of the bases n the dual-frequency combnaton equaton. The worst case bas magntude wll then become the case of a sgnal fault on L only. A second pessmstc assumpton was that the dualfrequency WAAS avoncs recevers wll have nearly the same desgn lattude as do current L-only users. In realty, proposals are already n the works to lmt the constrant space to the vcnty of the ground reference recever. Whle t s not certan that such a proposal wll be fnalzed, t s clear that the confguratons wll be far more lmted than those analyzed here. Ths wll further reduce the mamum errors eperenced by dualfrequency users Fnally, none of these results nclude the benefts for sngle-frequency users. The new recevers and metrcs wll lkely be n place servng L-only WAAS users long before there are suffcent L5 sgnals on orbt to serve the needs of dual-frequency users. However, benefts for sngle frequency users should not be dsmssed. The chpbased detecton metrc effectveness curves for snglefrequency users reduce to the L-only case (the red curves of n Fgures 3,, and 5), wthout the dual-frequency amplfcaton factor of.. Ths effectvely means the smallest error lmts (UDREI=) could be enabled for sngle-frequency users. Alternatvely, the current performance could be met usng much larger montor thresholds, thereby further reducng the probablty of false alarms. CONCLUSION In ths paper the challenge of mtgatng sgnal deformaton faults for dual-frequency WAAS users s dscussed. To ths end, a new detecton metrc was proposed based on the capabltes of the new WAAS recever whch has a wde (MHz) bandwdth and provdes outputs of the code chp shape. Whle the bandwdth slghtly ncreases detecton performance, the chp-based measurements are more senstve than tradtonal correlaton peak-based ones manly because they avod the correlaton process, whch tends to average out some of the dstorton effects. It s shown that the new metrc s easly appled to the L5 sgnal n addton to L and s senstve enough to detect the threats far better than the estng WAAS SDM algorthm. Whle the estng error lmt s currently.m for L-only users, the addton of the new MHz montor recevers, combned wth the new metrc, should permt an error lmt as small as 3. meters for dualfrequency users. The detecton performance results presented are lkely more pessmstc here than they would be n the WAAS system for the followng reasons: The two-frequency fault case a smultaneous fault occurrng on both sgnals of the same satellte was sgnfcantly more conservatve n ths analyss than wll ultmately be asserted. Whle addtve errors were modeled here, a notable degree of error cancellaton s epected for that scenaro. The allowed recever confguratons wll lkely be constraned to those desgns more akn to the ground recever, sgnfcantly reducng the worst case user errors Benefts to L-only users are perhaps as mportant as those for dual-frequency users. Sgnfcant reductons n the mnmum achevable UDRE and/or ncreases to the SDM detecton thresholds may be possble wth ths new hardware and detecton method. Ths, n combnaton wth other system mprovements may lead to mproved avalablty for sngle frequency users [].

12 APPENDIX A: Dervaton of the Tme-Varyng MERR Ths secton develops a mathematcal formulaton for the tme-varyng Mamum allowable ERror n Range (MERR) for sgnal deformaton bases. For a morecomplete descrpton ncludng addtonal background concernng relatonshp to the statc MERR concept as used n the Phase I WAAS SV9/CCC montor analyss [], refer to [9]. If the fault-nduced rangng error eceeds the MERR bound at any tme, SBAS ntegrty cannot be ensured. For a system anomaly to result n a hazardous error, two smultaneous falures must occur. Frst, ground montorng must fal to detect the anomaly, and second, the protecton level (PL) must fal to bound the resultng navgaton error. The MERR wll be defned to reflect the condtonal rsks assocated wth ths Pa Ppl () t Pmd () t P f (A-) Ths MERR formulaton recognzes than both the probablty of eceedng the VPL P pl (t) and the probablty of detectng the fault Pmd(t) are both functons of tme. P a /P f s a constant. It s the rato of the fault tree allocaton (P a ) for the montor to the pror probablty (P f ) of the fault. The equaton for P md (t) s gven by T m t T m t R R Pmd ( trdt) mon mon (A-) Threshold Threshold (t) system must reach the user n a tmely fashon. The requred tme between the onset of a hazardous condton and the arrval of the warnng message at the user s called Tme-to-Alert (TTA). The actual worst case Tmeto-Transmt (TTT) the warnng message may be longer or shorter than the requred TTA. If transmsson tme s longer than the specfed TTA, the montor must make up the dfference by trggerng early. If the transmsson tme s shorter than the allowed alert tme, then the montor may trgger late, after the fault becomes hazardous. In ether case, the tme dfference s referred to as the Relatve Detecton Tme (RDT). RDT = TTA TTT. For WAAS, RDT =. The probablty that the fault eceeds the protecton level s gven by P pl VPL Sv, E() t R Sv, UDREI _ nom, (A-3) In the above equaton, VPL s the desred vertcal protecton level. E(t) s the tme-varyng user range error. S v, are the senstvty weghts that transform the range error nto the vertcal drecton. σ UDREI_nom, s the varance on the th rangng sgnal. In the vertcal drecton (for the th satellte), VPL K S ffd v, tot, (A-) where σtot, s the MERR values tabulated n Table 3 (dvded by 5.33) as a functon of UDREI. The error seen by the user s gven by the sum of the bas component and the random component accordng to v, pl v, UDRE_ nom, Vertcal Poston Error S E t K S (A-5) PDF.. p(m fault ) m fault / mon The protecton level s not eceeded provded the followng holds S E K S K S v, ffd v, tot, pl v, UDREI_ nom, (A-) Fgure A-. Montor P md evaluaton. To address the tme-to-alert requrement, n the above equaton we have defned a term, RDT to ndcate the Relatve Tme-to-Detect. The warnng from the ground

13 .5 S v,k *E(t) Mamum User Error E ss as a functon of the Mamum Montor Statstc m ss. PDF VPL p(e v,p ) VPL E v,p / v,p Fgure A-. Montor P pl evaluaton In the above equaton, K ffd s the constant multpler requred to meet the contnuty (.e., false alarm) requrement. After smplfyng the above equatons, the bound on the error E(t) becomes Where Et K K () ffdtot, pludre _ nom, F tot, UDRE PP UIRE (A-7). (A-) The probablty of eceedng the protecton level (.e., the error bound n range doman) s then Ppl E t K UDRE _ nom, R tot, () ffd and the ntegrty test n rsk form s gven by P () () P E t P m t, (A-9) a pl md P f (A-) In the above equaton, E(t) s the tme-varyng user range error and m(t) s the tme-varyng montor response. The ntegrty test n MERR form becomes E() t MERR P () t pl, ma (A-) where Pa Ppl,ma P md m t P f, (A-) and P pl,ma s the mamum probablty of eceedng the protecton level. Ths MERR s a lne that bounds the The frst-order fltered, montor response m(t), normalzed by ts steady-state value for each sgnal deformaton n the threat model mss s gven by a unt step response of the correlator metrcs wth Gaussan statstcs. mt t / mon e mss (A-3) In the above equaton, τ mon s the nomnal tme constant for the montor metrc smoothng flter. The frst-order fltered, user error E(t) normalzed by ts steady-state value for each sgnal deformaton n the threat model E ss s gven by a unt step response of the code range error metrcs wth Gaussan statstcs. E t t / csc e Ess (A-) In the above equaton, τ csc s the nomnal tme constant for the user carrer smoothng flter. The probablty of hazardous msleadng nformaton (P HMI ) due to undetectable sgnal deformaton range bases s found drectly from satsfyng the above equatons. It takes nto account nomnal correcton errors (satellte clock and ephemers, onosphere) present n the system, and s accordngly equal to the fault tree allocaton. A smple procedure for computng the tmevaryng MERR curve for SQM s outlned n the Analyss secton. ACKNOWLEDGEMENTS Ths work was sponsored by the FAA GPS Satellte Product Team (AND-73). REFERENCES [] Lu, F., Brenner, M., Tang, C.Y., Sgnal Deformaton Montorng Scheme Implemented n a Prototype Local Area Augmentaton System Ground Installaton, Proceedngs of the 9 th Internatonal Techncal Meetng of the Satellte Dvson of the Insttute of Navgaton, ION GNSS-, September. [] Phelts, R.E., () Multcorrelator Technques for Robust Mtgaton of Threats to GPS Sgnal Qualty, Ph.D. Thess, Stanford Unversty, Stanford, CA. [3] Phelts, R. E., Walter, T., Enge, P., Toward Real- Tme SQM for WAAS: Improved Detecton

14 Technques, Proceedngs of the th Internatonal Techncal Meetng of the Satellte Dvson of the Insttute of Navgaton, ION GPS/GNSS-3, September 3. [] Internatonal Standards and Recommended Practces, Aeronautcal Telecommuncatons, ICAO, Vol., Anne, July. [5] Phelts, R. E., Akos, D. M., Effects of Sgnal Deformatons on Modernzed GNSS Sgnals, Journal of Global Postonng Systems, Vol. 5 No. -, Hong Kong, Chna,. [] Mnmum Operatonal Performance Standards (MOPS) for WAAS, DO-9D. RTCA. [7] Fenton, P., Jones J.,., The Theory and Performance of NovAtel Inc. s Vson Correlator, Proceedngs of the 9 th Internatonal Techncal Meetng of the Satellte Dvson of the Insttute of Navgaton, ION GNSS-, September [] Wong, G., Phelts, R.E., Walter, T., Enge, P., Alternatve Characterzaton of Analog Sgnal Deformaton for GPS Satelltes, Internatonal Techncal Meetng of the Insttute of Navgaton, January,. [9] Rfe, J., Phelts, R. E., Formulaton of a Tme- Varyng Mamum Allowable Error for Ground- Based Augmentaton Systems, Natonal Techncal Meetng of the Insttute of Navgaton, January -,. [] Hsu, P., Chu, T., Golubev, Y., Phelts, R. E., Test Results for the WAAS Sgnal Qualty Montor, Proceedngs of Poston Locaton and Navgaton Symposum, IEEE/ION PLANS,. [] Shloss, P., Phelts, R. E., Walter, T., Enge, P., A Smple Method of Sgnal Qualty Montorng for WAAS LNAV/VNAV, Proceedngs of the 5 th Internatonal Techncal Meetng of the Satellte Dvson of the Insttute of Navgaton, ION GPS/GNSS-, September. [] Blanch, J., Phelts, R.E., Walter, T., Enge, Per, Near Term Improvements to WAAS Avalablty, Internatonal Techncal Meetng of the Insttute of Navgaton, January -3, 3.