takeyasu sakai, k. matsunaga, and k. hoshinoo, electronic navigation research institute t. walter,...
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Takeyasu Sakai, K. Matsunaga, and K. Hoshinoo,Electronic Navigation Research Institute
T. Walter, Stanford University
Takeyasu Sakai, K. Matsunaga, and K. Hoshinoo,Electronic Navigation Research Institute
T. Walter, Stanford University
Computing SBAS Protection Levelswith Consideration ofAll Active Messages
Computing SBAS Protection Levelswith Consideration ofAll Active Messages
ION GNSS 2010ION GNSS 2010Portland, ORPortland, OR
Sept. 21-24, 2010Sept. 21-24, 2010
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 22
• GNSS: Essential Source of Performance-Based NavigationGNSS: Essential Source of Performance-Based Navigation::– RNP (Required Navigation Performance): The most important requirement is IntegrRNP (Required Navigation Performance): The most important requirement is Integr
ity; Protection of users from a large unexpected position error;ity; Protection of users from a large unexpected position error;
– SBAS: Integrity-assured international standard GNSS supporting a continental servSBAS: Integrity-assured international standard GNSS supporting a continental serv
ice coverage.ice coverage.
• Safety Mechanism of SBASSafety Mechanism of SBAS::– SBAS-capable receivers provide Protection Levels as well as position solution;SBAS-capable receivers provide Protection Levels as well as position solution;
– The complete safety analysis is required for certification of SBAS; SBAS shall not bThe complete safety analysis is required for certification of SBAS; SBAS shall not b
roadcast any misleading information;roadcast any misleading information;
– This means Protection Levels always overbound the actual user position error.This means Protection Levels always overbound the actual user position error.
• Additional SafetyAdditional Safety::– Usual receivers would compute Protection Levels using the latest messages;Usual receivers would compute Protection Levels using the latest messages;
– Possible variation of Protection Levels regarding active message combination;Possible variation of Protection Levels regarding active message combination;
– Ensuring safety and improving system availability.Ensuring safety and improving system availability.
IntroductionIntroduction
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 33MotivationMotivation
• The SBAS Protection Levels depend on received message setThe SBAS Protection Levels depend on received message set..– Must assure safety against any conditions of loss of messages;Must assure safety against any conditions of loss of messages;
– If a receiver loses four successive messages, it stops the current navigation;If a receiver loses four successive messages, it stops the current navigation;
– Message sequence is not specified and dependent upon the system. Message sequence is not specified and dependent upon the system.
• SBAS SARPs says ‘Any Combination of Active Data’SBAS SARPs says ‘Any Combination of Active Data’::– The SBAS part of ICAO GNSS SARPs (Standards and Recommended Practices) The SBAS part of ICAO GNSS SARPs (Standards and Recommended Practices)
addresses integrity shall be met for ‘Any Combination of Active Data’;addresses integrity shall be met for ‘Any Combination of Active Data’;
– ‘‘Active’ means ‘not timed out’; Receivers have a number of active data (messageActive’ means ‘not timed out’; Receivers have a number of active data (messages) and they are NOT updated by the latest data.s) and they are NOT updated by the latest data.
• Could we ignore ‘Old Active Data’ ?Could we ignore ‘Old Active Data’ ?– Usually considering the latest data is enough because degradation terms make thUsually considering the latest data is enough because degradation terms make th
e Protection Levels large for old active data;e Protection Levels large for old active data;
– Need to verify this to ensure integrity; We try to compute Protection Levels for all Need to verify this to ensure integrity; We try to compute Protection Levels for all possible combinations of active data using actual broadcast messages;possible combinations of active data using actual broadcast messages;
– Does the latest message set give the smallest Protection Levels?Does the latest message set give the smallest Protection Levels?
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 44SBAS CorrectionsSBAS Corrections
Orbit CorrectionOrbit Correction
TroposphereTroposphere
IonosphereIonosphere
Tropospheric CorrectionTropospheric Correction
Clock CorrectionClock Correction• Same contribution to any user Same contribution to any user
location;location;• Not a function of location;Not a function of location;• Fast Correction (FC). Fast Correction (FC).
• Different contribution to different Different contribution to different user location;user location;
• Not a function of user location; but Not a function of user location; but a function of line-of-sight direction;a function of line-of-sight direction;
• Long-Term Correction (LTC).Long-Term Correction (LTC).
• Function of user location, especially height of user;Function of user location, especially height of user;• Up to 20 meters;Up to 20 meters;• Corrected by a fixed model (Tropospheric Correction; TC).Corrected by a fixed model (Tropospheric Correction; TC).
• Function of user location;Function of user location;• Up to 100 meters;Up to 100 meters;• Vertical structure is modellVertical structure is modell
ed as a thin shell;ed as a thin shell;• Ionospheric Correction (IIonospheric Correction (I
C).C).
Ionospheric CorrectionIonospheric Correction
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 55Structure of CorrectionStructure of Correction
Pseudorange CorrectionPseudorange Correction
SV Position and Clock CorrectionSV Position and Clock Correction
Ionospheric CorrectionIonospheric Correction
Fast CorrectionFast Correction
Long-Term CorrectionLong-Term Correction
• FC, LTC, and IC are calculated FC, LTC, and IC are calculated from the appropriate messages;from the appropriate messages;
• TC is obtained by the pre-defined TC is obtained by the pre-defined model;model;
• The correction is sum of them; The correction is sum of them; Possibility of various Possibility of various combinations.combinations.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 66Structure of PL EquationStructure of PL Equation
PL EquationPL Equation
Time-Dependent Components (Degradation)Time-Dependent Components (Degradation)
• PL is also the sum of components PL is also the sum of components regarding associate corrections.regarding associate corrections.
• mean the degradation terms mean the degradation terms representing increase of uncertainty representing increase of uncertainty with progress of time.with progress of time.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 77SBAS MessagesSBAS Messages
MTMT
00
11
22~~ 55
66
77
99
1010
1212
1717
1818
ContentsContents
Test modeTest mode
PRN maskPRN mask
Fast correction & UDREFast correction & UDRE
UDREUDRE
Degradation factor for FCDegradation factor for FC
GEO navigation dataGEO navigation data
Degradation parameterDegradation parameter
SBAS time informationSBAS time information
GEO almanacGEO almanac
IGP maskIGP mask
MaxMaxIntervalInterval
6 s6 s
120120
60/660/6
66
120120
120120
120120
300300
300 s300 s
300300
2424
2525
2626
2727
2828
6363
FC & LTCFC & LTC
Long-term correctionLong-term correction
Ionospheric delay & GIVEIonospheric delay & GIVE
SBAS service messageSBAS service message
Clock-ephemeris covarianceClock-ephemeris covariance
Null messageNull message
66
120120
300300
300300
120120
——
MTMT ContentsContents MaxMaxIntervalInterval
PreamblePreamble8 bits8 bits
Message TypeMessage Type6 bits6 bits
Data FieldData Field212 bits212 bits
CRC parityCRC parity24 bits24 bits
1 message = 250 bits per secondTransmitted FirstTransmitted First
• Colored message: need to consider combinations of active data;Colored message: need to consider combinations of active data;• Mask data and degradation factors basically do not change frequently.Mask data and degradation factors basically do not change frequently.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 88Message TimingMessage Timing
Message
TypeComponent
Timeout Interval for NPA mode
Timeout Interval for PA mode
Max Interval
2 to 5
24
Fast
Correction18 to 180 s 12 to 120 s 6 to 60 s
UDRE 18 12 6
6 UDRE 18 12 6
9 GEO Nav Data 360 240 120
24 / 25Long-Term
Correction360 240 120
26Ionospheric
Correction600 600 300
28Clock-Ephemeris
Covariance360 240 120
• At least receivers have 3 active messages for NPA and 2 for PA at the max interval rate;At least receivers have 3 active messages for NPA and 2 for PA at the max interval rate;• Usually more active messages are available.Usually more active messages are available.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 99Differences: Fast CorrectionDifferences: Fast Correction
• The differences between ‘Active’ Fast Corrections;The differences between ‘Active’ Fast Corrections;• The largest difference: 2.0 m for NPA (PRN 24, interval 12 s) and 1.875 m The largest difference: 2.0 m for NPA (PRN 24, interval 12 s) and 1.875 m
for PA (PRN 24, interval 6 s)for PA (PRN 24, interval 6 s)• MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).
NPA ModeNPA Mode PA ModePA Mode
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1010Differences: Long-Term Corr.Differences: Long-Term Corr.
• The differences between ‘Active’ Long-Term Corrections;The differences between ‘Active’ Long-Term Corrections;• Satellite orbit correction converted into line-of-sight component from Tokyo;Satellite orbit correction converted into line-of-sight component from Tokyo;• The largest difference: 1.186 m for NPA (PRN 31, interval 340 s) and <0.4 m for PA;The largest difference: 1.186 m for NPA (PRN 31, interval 340 s) and <0.4 m for PA;• MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).
NPA ModeNPA Mode PA ModePA Mode
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1111Differences: Long-Term Corr.Differences: Long-Term Corr.
• The differences between ‘Active’ Long-Term Corrections;The differences between ‘Active’ Long-Term Corrections;• Only pairs with different IOD;Only pairs with different IOD;• The largest difference: <0.625 m for NPA and 0.250 m for PA;The largest difference: <0.625 m for NPA and 0.250 m for PA;• Change of IOD (change of ephemeris) is not the cause of the differences.Change of IOD (change of ephemeris) is not the cause of the differences.
NPA ModeNPA Mode PA ModePA Mode
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1212Differences: Ionospheric Corr.Differences: Ionospheric Corr.
• The differences between ‘Active’ Ionospheric Corrections;The differences between ‘Active’ Ionospheric Corrections;• The largest difference: 8.250 m (IGP at 15N 135E, interval 288 s);The largest difference: 8.250 m (IGP at 15N 135E, interval 288 s);• MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1313Simple Case: GEO, LTC, COVSimple Case: GEO, LTC, COV
• Which messages should be applied? There is a choice from active messages;Which messages should be applied? There is a choice from active messages;• Could minimize / maximize Protection Levels.Could minimize / maximize Protection Levels.
ChoiceChoiceofof
appliedappliedmessagemessage
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessage
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1414Choice of PRC and RRC: FCChoice of PRC and RRC: FC
ChoiceChoiceofof
appliedappliedmessagemessage
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessageMessageMessage
3 RRC Choice3 RRC Choice
2 RRC Choice2 RRC Choice
1 RRC Choice1 RRC Choice
• PRC is directly derived from FC; Receivers have a choice of FC;PRC is directly derived from FC; Receivers have a choice of FC;• RRC (Range Rate Correction) is computed from a FC pair;RRC (Range Rate Correction) is computed from a FC pair;• Receivers also have a choice of RRC; Should minimize Protection Levels.Receivers also have a choice of RRC; Should minimize Protection Levels.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1515Lots of Combinations: ICLots of Combinations: IC
• Receivers compute ionospheric delay and its uncertainty at the IPP by inReceivers compute ionospheric delay and its uncertainty at the IPP by interpolating delays and uncertainties at the surrounding four IGPs;terpolating delays and uncertainties at the surrounding four IGPs;
• Any combination of active IGPs are possible; Lots of choice.Any combination of active IGPs are possible; Lots of choice.
IGP1IGP1IGP2IGP2
IGP4IGP4IGP3IGP3xxpppp
yypppp
IPPIPP
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessage
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessage
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessage
Cor
rect
ion
Cor
rect
ion
Deg
rada
tion
Deg
rada
tion
MessageMessage MessageMessage MessageMessage
2 or more messages for IGP 22 or more messages for IGP 2 2 or more messages for IGP 12 or more messages for IGP 1
2 or more messages for IGP 32 or more messages for IGP 3 2 or more messages for IGP 42 or more messages for IGP 4
Interpolation for IPPInterpolation for IPP
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1616PL Computation StrategyPL Computation Strategy
(1) Latest Data(1) Latest Data::– Apply the most recent active message for each correction;Apply the most recent active message for each correction;
– Considered usually provide smaller Protection Levels because degradation terConsidered usually provide smaller Protection Levels because degradation terms are minimum; Needs to be verified;ms are minimum; Needs to be verified;
– Natural way to apply SBAS augmentation messages. Natural way to apply SBAS augmentation messages.
(2) Minimize PL(2) Minimize PL::– Apply the message with the smallest uncertainty for each correction;Apply the message with the smallest uncertainty for each correction;
– Gives the smallest Protection Levels; Possibly smaller than case of Latest DatGives the smallest Protection Levels; Possibly smaller than case of Latest Data Strategy if degradation terms are not so large;a Strategy if degradation terms are not so large;
– Smaller Protection Levels increase availability of the system;Smaller Protection Levels increase availability of the system;
– This strategy is allowed to receivers with respect to the SBAS SARPs specifies This strategy is allowed to receivers with respect to the SBAS SARPs specifies that integrity must be met for any combination of active data.that integrity must be met for any combination of active data.
(3) Maximize PL(3) Maximize PL::– Use the message with the largest uncertainty for each correction;Use the message with the largest uncertainty for each correction;
– Gives the largest Protection Levels; Lowers availability of the system.Gives the largest Protection Levels; Lowers availability of the system.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1717Reduce Computational Load (1)Reduce Computational Load (1)
• Consideration of computational loadConsideration of computational load::– There are lots of possible combinations of active corrections;There are lots of possible combinations of active corrections;
– To ensure integrity, should also consider combinations of visible satellites with To ensure integrity, should also consider combinations of visible satellites with various number (4 to N) of satellites;various number (4 to N) of satellites;
– The weighting matrix W consists of The weighting matrix W consists of ii depending on corrections; The inverse m depending on corrections; The inverse m
atrix atrix ((GGTTWGWG))--11 must be computed for each combination of corrections. must be computed for each combination of corrections.
• Binding ProcessBinding Process::– Detects two or more identical messages and reduces them into one.Detects two or more identical messages and reduces them into one.
– Valid for LTC, GEO (MT9 GEO Navigation Message), and COV (MT28 CovariValid for LTC, GEO (MT9 GEO Navigation Message), and COV (MT28 Covariance Matrix); Should not apply to FC because RRC computation.ance Matrix); Should not apply to FC because RRC computation.
• Pruning Process (for Minimize/Maximize PL Strategy)Pruning Process (for Minimize/Maximize PL Strategy)::– Reduces messages yielding larger/smaller Protection Levels among same kind Reduces messages yielding larger/smaller Protection Levels among same kind
of messages;of messages;
– Valid for FC and IC.Valid for FC and IC.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1818PL VariationPL Variation
Latest DataLatest Data
Minimize PLMinimize PL
Maximize PLMaximize PL
StrategyStrategy
MSAS PRN 137MSAS PRN 13709/1/16 07:00 - 08:0009/1/16 07:00 - 08:00
• Vertical Protection Levels obtained by different PL computation strategies;Vertical Protection Levels obtained by different PL computation strategies;• All-in-View including SBAS satellites;All-in-View including SBAS satellites;• Minimizing PL strategy reduces Protection Levels in comparison with Latest Minimizing PL strategy reduces Protection Levels in comparison with Latest
strategy.strategy.
Reduce PL
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 1919PL VariationPL Variation
Latest DataLatest Data
Minimize PLMinimize PL
Maximize PLMaximize PL
StrategyStrategy
MSAS PRN 137MSAS PRN 13709/1/16 00:00 - 24:0009/1/16 00:00 - 24:00
• 24H computation;24H computation;• Average improvement by Minimize PL Strategy: 0.30m of HPL and 0.39m of VPL.Average improvement by Minimize PL Strategy: 0.30m of HPL and 0.39m of VPL.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2020Verify All Active MessagesVerify All Active Messages
• User Position Error depends on the combination of applied messagesUser Position Error depends on the combination of applied messages::– The message combination giving the largest position error is unknown;The message combination giving the largest position error is unknown;
– Position error depends on applied corrections, not on protection levels;Position error depends on applied corrections, not on protection levels;
– Need to focus which combination of corrections should be tried to detect the laNeed to focus which combination of corrections should be tried to detect the largest position error and to verify it is overbounded properly.rgest position error and to verify it is overbounded properly.
• Ensuring Safety via Integrity ChartEnsuring Safety via Integrity Chart::– Triangle chart (Stanford Chart) is useful for safety analysis; Colored histogram Triangle chart (Stanford Chart) is useful for safety analysis; Colored histogram
plotting Position Error versus Protection Level;plotting Position Error versus Protection Level;
– First extension was introducing consideration ofFirst extension was introducing consideration of
all combinations of satellites instead of all-in-view:all combinations of satellites instead of all-in-view:
‘‘Stanford-ESA Chart’;Stanford-ESA Chart’;
– The second extension would be consideration ofThe second extension would be consideration of
all combinations of all active messages insteadall combinations of all active messages instead
of combination of the latest messages:of combination of the latest messages:
’’Complete Integrity Chart’.Complete Integrity Chart’.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2121Reduce Computational Load (2)Reduce Computational Load (2)
• Needs another reduction of computational loadNeeds another reduction of computational load::– After applying Binding Process, there still are lots of active messages, 2-3 FCAfter applying Binding Process, there still are lots of active messages, 2-3 FC
s, 2-3 LTCs, and 8-12 IONOs…s, 2-3 LTCs, and 8-12 IONOs…
– To verify position errors regarding all combinations of all active messages, PruTo verify position errors regarding all combinations of all active messages, Pruning Process can not be applied;ning Process can not be applied;
– The complete combinations of them relates to the vast number of position solutThe complete combinations of them relates to the vast number of position solution; Very time consuming. ion; Very time consuming.
• Hypercube MethodHypercube Method::– For safety reason, we are interested in the largest position error;For safety reason, we are interested in the largest position error;
– Position solution is obtained via linearized equation; The relationship between Position solution is obtained via linearized equation; The relationship between correction and the associate position error is linear; Likely enough to consider correction and the associate position error is linear; Likely enough to consider both ends of the range of pseudorange correction (needs proof);both ends of the range of pseudorange correction (needs proof);
– Find 2 message combinations giving the minimum and maximum value of the Find 2 message combinations giving the minimum and maximum value of the sum of corrections (FC+LTC+IC) for each satellite;sum of corrections (FC+LTC+IC) for each satellite;
– Computes position solutions at 2^N corners of Hypercube; Here N is the numbComputes position solutions at 2^N corners of Hypercube; Here N is the number of satellites.er of satellites.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2222Hypercube MethodHypercube Method
Range of Sum of Corrections FC+LTC+ICRange of Sum of Corrections FC+LTC+IC(LTC: projection to LOS)(LTC: projection to LOS)
Try each corner of hypercubeTry each corner of hypercubeto find the largest position errorto find the largest position error
N satellites in viewN satellites in view
• Position solution is projected at each Position solution is projected at each vertex of polyhedron with 2^N vertexes;vertex of polyhedron with 2^N vertexes;
• The largest position error likely appears The largest position error likely appears as one of them.as one of them.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2323Stanford ChartStanford Chart
• PL Computation Strategy: Latest;PL Computation Strategy: Latest;• Satellite Combination: All-in-View only;Satellite Combination: All-in-View only;• Position error is small and resulted PLs are very conservative.Position error is small and resulted PLs are very conservative.
All-in-View and Latest MessageAll-in-View and Latest Message
MSAS PRN 137MSAS PRN 13709/1/16 07:00 - 08:0009/1/16 07:00 - 08:00
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2424Stanford-ESA ChartStanford-ESA Chart
• PL Computation Strategy: Latest;PL Computation Strategy: Latest;• Satellite Combination: All possible combinations and All combinations with Satellite Combination: All possible combinations and All combinations with
loss of up to 2 satellites (N-2 coverage);loss of up to 2 satellites (N-2 coverage);• ESA proposed this chart; Computing for all possible combinations of visible ESA proposed this chart; Computing for all possible combinations of visible
satellites improves integrity.satellites improves integrity.
All satellite combinations and Latest MessageAll satellite combinations and Latest Message N-2 Coverage and Latest MessageN-2 Coverage and Latest Message
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2525Complete Integrity ChartComplete Integrity Chart
• PL Computation Strategy: All Corners of Hypercube;PL Computation Strategy: All Corners of Hypercube;• Satellite Combination: All possible combinations;Satellite Combination: All possible combinations;• Achieves further improvement of integrity;Achieves further improvement of integrity;• Just a preliminary result: needs detailed investigation of large errors; PossiJust a preliminary result: needs detailed investigation of large errors; Possi
bility of ground multipath not overbounded by the airborne model.bility of ground multipath not overbounded by the airborne model.
All satellite combinations and All active message combinationsAll satellite combinations and All active message combinations
Preliminary ResultPreliminary ResultNeeds detailed investigationNeeds detailed investigation
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2626Contributing ComponentContributing Component
Contribution of FCContribution of FC Contribution of LTCContribution of LTC
• Hypercube made for the range of Hypercube made for the range of min/max of FC instead of FC+LTC+IC;min/max of FC instead of FC+LTC+IC;
• Satellite Combination: All possible Satellite Combination: All possible combinations;combinations;
• The largest contribution.The largest contribution.
• Hypercube made for the range of Hypercube made for the range of min/max of LTC instead of FC+LTC+IC;min/max of LTC instead of FC+LTC+IC;
• Satellite Combination: All possible Satellite Combination: All possible combinations.combinations.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2727Contributing ComponentContributing Component
Contribution of ICContribution of IC N-2 Coverage and All MessagesN-2 Coverage and All Messages
• Hypercube made for the range of Hypercube made for the range of min/max of IC instead of FC+LTC+IC;min/max of IC instead of FC+LTC+IC;
• Satellite Combination: All possible Satellite Combination: All possible combinations.combinations.
• Hypercube made for the range of Hypercube made for the range of min/max of FC+LTC+IC;min/max of FC+LTC+IC;
• Satellite Combination: All combinations Satellite Combination: All combinations with loss of up to 2 satellites;with loss of up to 2 satellites;
• Not enough by comparison with slide 24.Not enough by comparison with slide 24.
ION GNSS 21-24 Sept. 2010 - ENRIION GNSS 21-24 Sept. 2010 - ENRI
SSLIDELIDE 2828ConclusionConclusion
• PL Computation StrategyPL Computation Strategy::– Receivers have a number of active data not timed out;Receivers have a number of active data not timed out;
– It is possible to choose the applied messages so to minimize Protection Levels, insIt is possible to choose the applied messages so to minimize Protection Levels, ins
tead of applying the latest messages.tead of applying the latest messages.
• Safety Case of SBASSafety Case of SBAS::– In order to ensure complete safety, position solutions for all possible combinations In order to ensure complete safety, position solutions for all possible combinations
of visible satellites and active data should be protected by the associate PLs;of visible satellites and active data should be protected by the associate PLs;
– To achieve this, computational load is an issue; Binding and Pruning Processes anTo achieve this, computational load is an issue; Binding and Pruning Processes an
d Hypercube Method reduce the load down to realistic level;d Hypercube Method reduce the load down to realistic level;
– This approach derives the Complete Integrity Chart; Achieves further improvement This approach derives the Complete Integrity Chart; Achieves further improvement
of integrity.of integrity.
• Further InvestigationsFurther Investigations::– Verify safety for alarm conditions (IODF=3) and ionospheric storm conditions;Verify safety for alarm conditions (IODF=3) and ionospheric storm conditions;
– Further reduction of computational load.Further reduction of computational load.