takeyasu sakai, k. matsunaga, and k. hoshinoo, electronic navigation research institute t. walter,...

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


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?


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


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.


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.


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.


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.


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


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).



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.



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).


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


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



• 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.


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


Cor

rect

ion

Cor

rect

ion

Deg

rada

tion

Deg

rada

tion


Cor

rect

ion

Cor

rect

ion

Deg

rada

tion

Deg

rada

tion


Cor

rect

ion

Cor

rect

ion

Deg

rada

tion

Deg

rada

tion


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


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.


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.


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


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.


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’.


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.


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.


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


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


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


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.


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.


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.

takeyasu sakai, k. matsunaga, and k. hoshinoo, electronic navigation research institute t. walter,...

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