1. 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 Levels with Consideration of All Active Messages Computing SBAS Protection Levels with Consideration of All Active Messages ION GNSS 2010 Portland, OR Sept. 21-24, 2010

2. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 1 GNSS: Essential Source of Performance-Based Navigation:GNSS: Essential Source of Performance-Based Navigation: –RNP (Required Navigation Performance): The most important requirement is Integrity; Protection of users from a large unexpected position error; –SBAS: Integrity-assured international standard GNSS supporting a continental service coverage. Safety Mechanism of SBAS:Safety Mechanism of SBAS: –SBAS-capable receivers provide Protection Levels as well as position solution; –The complete safety analysis is required for certification of SBAS; SBAS shall not broadcast any misleading information; –This means Protection Levels always overbound the actual user position error. Additional Safety:Additional Safety: –Usual receivers would compute Protection Levels using the latest messages; –Possible variation of Protection Levels regarding active message combination; –Ensuring safety and improving system availability. Introduction

3. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 2Motivation The SBAS Protection Levels depend on received message set.The SBAS Protection Levels depend on received message set. –Must assure safety against any conditions of loss of messages; –If a receiver loses four successive messages, it stops the current navigation; –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) addresses integrity shall be met for ‘Any Combination of Active Data’; –‘Active’ means ‘not timed out’; Receivers have a number of active data (messages) 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 the Protection Levels large for old active data; –Need to verify this to ensure integrity; We try to compute Protection Levels for all possible combinations of active data using actual broadcast messages; –Does the latest message set give the smallest Protection Levels?

4. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 3 SBAS Corrections Orbit Correction Troposphere Ionosphere Tropospheric Correction Clock Correction Same contribution to any user location;Same contribution to any user location; Not a function of location;Not a function of location; Fast Correction (FC).Fast Correction (FC). Different contribution to different user location;Different contribution to different user location; Not a function of user location; but a function of line-of-sight direction;Not a function of user location; but 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 modelled as a thin shell;Vertical structure is modelled as a thin shell; Ionospheric Correction (IC).Ionospheric Correction (IC). Ionospheric Correction

5. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 4 Structure of Correction Pseudorange Correction SV Position and Clock Correction Ionospheric Correction Fast Correction Long-Term Correction FC, LTC, and IC are calculated from the appropriate messages;FC, LTC, and IC are calculated from the appropriate messages; TC is obtained by the pre-defined model;TC is obtained by the pre-defined model; The correction is sum of them; Possibility of various combinations.The correction is sum of them; Possibility of various combinations.

6. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 5 Structure of PL Equation PL Equation Time-Dependent Components (Degradation) PL is also the sum of components regarding associate corrections.PL is also the sum of components regarding associate corrections.  mean the degradation terms representing increase of uncertainty with progress of time.  mean the degradation terms representing increase of uncertainty with progress of time.

7. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 6 SBAS Messages MT 0 1 2～52～52～52～5 6 7 9 10 12 17 18 Contents Test mode PRN mask Fast correction & UDRE UDRE Degradation factor for FC GEO navigation data Degradation parameter SBAS time information GEO almanac IGP mask MaxInterval 6 s 120 60/6 6 120 120 120 300 300 s 300 24 25 26 27 28 63 FC & LTC Long-term correction Ionospheric delay & GIVE SBAS service message Clock-ephemeris covariance Null message 6 120 300 300 120 — MTContentsMaxInterval Preamble 8 bits Message Type 6 bits Data Field 212 bits CRC parity 24 bits 1 message = 250 bits per second Transmitted 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.

8. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 7 Message Timing Message Type Component Timeout Interval for NPA mode Timeout Interval for PA mode Max Interval 2 to 5 24 Fast Correction 18 to 180 s12 to 120 s6 to 60 s UDRE18126 6UDRE18126 9GEO Nav Data360240120 24 / 25 Long-Term Correction 360240120 26 Ionospheric Correction 600 300 28 Clock-Ephemeris Covariance 360240120 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.

9. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 8 Differences: 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 for PA (PRN 24, interval 6 s)The largest difference: 2.0 m for NPA (PRN 24, interval 12 s) and 1.875 m 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 Mode PA Mode

10. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 9 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 Mode PA Mode

11. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 10 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 Mode PA Mode

12. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 11 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).

13. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 12 Simple 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. Choiceofappliedmessage Correction Degradation MessageMessageMessage

14. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 13 Choice of PRC and RRC: FC Choiceofappliedmessage Correction Degradation MessageMessageMessageMessage 3 RRC Choice 2 RRC Choice 1 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.

15. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 14 Lots of Combinations: IC Receivers compute ionospheric delay and its uncertainty at the IPP by interpolating delays and uncertainties at the surrounding four IGPs;Receivers compute ionospheric delay and its uncertainty at the IPP by interpolating 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. IGP1IGP2 IGP4IGP3 x pp y pp IPP Correction Degradation MessageMessage Message Correction Degradation MessageMessage Message Correction Degradation MessageMessage Message Correction Degradation MessageMessage Message 2 or more messages for IGP 2 2 or more messages for IGP 1 2 or more messages for IGP 3 2 or more messages for IGP 4 Interpolation for IPP

16. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 15 PL Computation Strategy (1) Latest Data: –Apply the most recent active message for each correction; –Considered usually provide smaller Protection Levels because degradation terms are minimum; Needs to be verified; –Natural way to apply SBAS augmentation messages. (2) Minimize PL: –Apply the message with the smallest uncertainty for each correction; –Gives the smallest Protection Levels; Possibly smaller than case of Latest Data Strategy if degradation terms are not so large; –Smaller Protection Levels increase availability of the system; –This strategy is allowed to receivers with respect to the SBAS SARPs specifies that integrity must be met for any combination of active data. (3) Maximize PL: –Use the message with the largest uncertainty for each correction; –Gives the largest Protection Levels; Lowers availability of the system.

17. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 16 Reduce Computational Load (1) Consideration of computational load:Consideration of computational load: –There are lots of possible combinations of active corrections; –To ensure integrity, should also consider combinations of visible satellites with various number (4 to N) of satellites; –The weighting matrix W consists of  i depending on corrections; The inverse matrix (G T WG) - 1 must be computed for each combination of corrections. Binding Process:Binding Process: –Detects two or more identical messages and reduces them into one. –Valid for LTC, GEO (MT9 GEO Navigation Message), and COV (MT28 Covariance 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 of messages; –Valid for FC and IC.

18. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 17 PL Variation Latest Data Minimize PL Maximize PL Strategy MSAS PRN 137 09/1/16 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 strategy.Minimizing PL strategy reduces Protection Levels in comparison with Latest strategy. Reduce PL

19. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 18 PL Variation Latest Data Minimize PL Maximize PL Strategy MSAS PRN 137 09/1/16 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.

20. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 19 Verify All Active Messages User Position Error depends on the combination of applied messages:User Position Error depends on the combination of applied messages: –The message combination giving the largest position error is unknown; –Position error depends on applied corrections, not on protection levels; –Need to focus which combination of corrections should be tried to detect the largest position error and to verify it is overbounded properly. Ensuring Safety via Integrity Chart:Ensuring Safety via Integrity Chart: –Triangle chart (Stanford Chart) is useful for safety analysis; Colored histogram plotting Position Error versus Protection Level; –First extension was introducing consideration of all combinations of satellites instead of all-in-view: ‘Stanford-ESA Chart’; –The second extension would be consideration of all combinations of all active messages instead of combination of the latest messages: ’Complete Integrity Chart’.

21. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 20 Reduce Computational Load (2) Needs another reduction of computational load:Needs another reduction of computational load: –After applying Binding Process, there still are lots of active messages, 2-3 FCs, 2-3 LTCs, and 8-12 IONOs… –To verify position errors regarding all combinations of all active messages, Pruning Process can not be applied; –The complete combinations of them relates to the vast number of position solution; Very time consuming. Hypercube Method:Hypercube Method: –For safety reason, we are interested in the largest position error; –Position solution is obtained via linearized equation; The relationship between correction and the associate position error is linear; Likely enough to consider both ends of the range of pseudorange correction (needs proof); –Find 2 message combinations giving the minimum and maximum value of the sum of corrections (FC+LTC+IC) for each satellite; –Computes position solutions at 2^N corners of Hypercube; Here N is the number of satellites.

22. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 21 Hypercube Method Range of Sum of Corrections FC+LTC+IC (LTC: projection to LOS) Try each corner of hypercube to find the largest position error N satellites in view Position solution is projected at each vertex of polyhedron with 2^N vertexes;Position solution is projected at each vertex of polyhedron with 2^N vertexes; The largest position error likely appears as one of them.The largest position error likely appears as one of them.

23. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 22 Stanford 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 Message MSAS PRN 137 09/1/16 07:00 - 08:00

24. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 23 Stanford-ESA Chart PL Computation Strategy: Latest;PL Computation Strategy: Latest; Satellite Combination: All possible combinations and All combinations with loss of up to 2 satellites (N-2 coverage);Satellite Combination: All possible combinations and All combinations with loss of up to 2 satellites (N-2 coverage); ESA proposed this chart; Computing for all possible combinations of visible satellites improves integrity.ESA proposed this chart; Computing for all possible combinations of visible satellites improves integrity. All satellite combinations and Latest Message N-2 Coverage and Latest Message

25. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 24 Complete 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; Possibility of ground multipath not overbounded by the airborne model.Just a preliminary result: needs detailed investigation of large errors; Possibility of ground multipath not overbounded by the airborne model. All satellite combinations and All active message combinations Preliminary Result Needs detailed investigation

26. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 25 Contributing Component Contribution of FC Contribution of LTC Hypercube made for the range of min/max of FC instead of FC+LTC+IC;Hypercube made for the range of min/max of FC instead of FC+LTC+IC; Satellite Combination: All possible combinations;Satellite Combination: All possible combinations; The largest contribution.The largest contribution. Hypercube made for the range of min/max of LTC instead of FC+LTC+IC;Hypercube made for the range of min/max of LTC instead of FC+LTC+IC; Satellite Combination: All possible combinations.Satellite Combination: All possible combinations.

27. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 26 Contributing Component Contribution of IC N-2 Coverage and All Messages Hypercube made for the range of min/max of IC instead of FC+LTC+IC;Hypercube made for the range of min/max of IC instead of FC+LTC+IC; Satellite Combination: All possible combinations.Satellite Combination: All possible combinations. Hypercube made for the range of min/max of FC+LTC+IC;Hypercube made for the range of min/max of FC+LTC+IC; Satellite Combination: All combinations with loss of up to 2 satellites;Satellite Combination: All combinations with loss of up to 2 satellites; Not enough by comparison with slide 24.Not enough by comparison with slide 24.

28. ION GNSS 21-24 Sept. 2010 - ENRI S LIDE 27Conclusion PL Computation Strategy:PL Computation Strategy: –Receivers have a number of active data not timed out; –It is possible to choose the applied messages so to minimize Protection Levels, instead of applying the latest messages. Safety Case of SBAS:Safety Case of SBAS: –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; –To achieve this, computational load is an issue; Binding and Pruning Processes and Hypercube Method reduce the load down to realistic level; –This approach derives the Complete Integrity Chart; Achieves further improvement of integrity. Further Investigations:Further Investigations: –Verify safety for alarm conditions (IODF=3) and ionospheric storm conditions; –Further reduction of computational load.