Takeyasu Sakai, K. Matsunaga, and K. Hoshinoo, Electronic Navigation Research Institute T. Walter, Stanford University

1. ION GNSS 2010 Portland, OR Sept. 21-24, 2010 Computing SBAS Protection Levels with Consideration of All Active Messages Takeyasu Sakai, K. Matsunaga, and K. Hoshinoo, Electronic Navigation Research Institute T. Walter, Stanford University

2. Introduction • 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: • 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: • 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.

3. Motivation • 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’: • 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’ ? • 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. SBAS Corrections Clock Correction Ionospheric Correction • Same contribution to any user location; • Not a function of location; • Fast Correction (FC). • Function of user location; • Up to 100 meters; • Vertical structure is modelled as a thin shell; • Ionospheric Correction (IC). Orbit Correction • Different contribution to different user location; • Not a function of user location; but a function of line-of-sight direction; • Long-Term Correction (LTC). Ionosphere Tropospheric Correction • Function of user location, especially height of user; • Up to 20 meters; • Corrected by a fixed model (Tropospheric Correction; TC). Troposphere

5. Structure of Correction Pseudorange Correction Ionospheric Correction Fast Correction SV Position and Clock Correction Long-Term Correction • FC, LTC, and IC are calculated from the appropriate messages; • TC is obtained by the pre-defined model; • The correction is sum of them; Possibility of various combinations.

6. Structure of PL Equation PL Equation • PL is also the sum of components regarding associate corrections. Time-Dependent Components (Degradation) • e mean the degradation terms representing increase of uncertainty with progress of time.

7. Preamble 8 bits Message Type 6 bits Data Field 212 bits CRC parity 24 bits 1 message = 250 bits per second Transmitted First MT Contents Max Interval MT Contents Max Interval 0 Test mode 6 s 17 GEO almanac 300 s 1 PRN mask 120 18 IGP mask 300 2～5 Fast correction & UDRE 60/6 24 FC & LTC 6 6 UDRE 6 25 Long-term correction 120 7 Degradation factor for FC 120 26 Ionospheric delay & GIVE 300 9 GEO navigation data 120 27 SBAS service message 300 10 Degradation parameter 120 28 Clock-ephemeris covariance 120 12 SBAS time information 300 63 Null message — SBAS Messages • Colored message: need to consider combinations of active data; • Mask data and degradation factors basically do not change frequently.

8. Message Timing • At least receivers have 3 active messages for NPA and 2 for PA at the max interval rate; • Usually more active messages are available.

9. Differences: Fast Correction PA Mode NPA Mode • 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) • MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).

10. Differences: Long-Term Corr. PA Mode NPA Mode • The differences between ‘Active’ Long-Term Corrections; • 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; • MSAS (PRN 137) broadcast during 09/1/16 to 21 (6 days).

11. Differences: Long-Term Corr. PA Mode NPA Mode • The differences between ‘Active’ Long-Term Corrections; • Only pairs with different IOD; • 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.

12. Differences: Ionospheric Corr. • The differences between ‘Active’ Ionospheric Corrections; • 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).

13. Correction Degradation Message Message Message Simple Case: GEO, LTC, COV Choice of applied message • Which messages should be applied? There is a choice from active messages; • Could minimize / maximize Protection Levels.

14. 3 RRC Choice 1 RRC Choice Correction 2 RRC Choice Degradation Message Message Message Message Choice of PRC and RRC: FC Choice of applied message • PRC is directly derived from FC; Receivers have a choice of FC; • RRC (Range Rate Correction) is computed from a FC pair; • Receivers also have a choice of RRC; Should minimize Protection Levels.

15. Interpolation for IPP 2 or more messages for IGP 2 IGP2 IGP1 2 or more messages for IGP 1 IPP ypp IGP3 IGP4 xpp Correction Correction Correction Correction 2 or more messages for IGP 3 2 or more messages for IGP 4 Degradation Degradation Degradation Degradation Message Message Message Message Message Message Message Message Message Message Message Message Lots of Combinations: IC • 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.

16. 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. Reduce Computational Load (1) • 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 si depending on corrections; The inverse matrix (GTWG)-1 must be computed for each combination of corrections. • 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): • Reduces messages yielding larger/smaller Protection Levels among same kind of messages; • Valid for FC and IC.

18. Strategy Latest Data Minimize PL Maximize PL PL Variation Reduce PL MSAS PRN 137 09/1/16 07:00 - 08:00 • Vertical Protection Levels obtained by different PL computation strategies; • All-in-View including SBAS satellites; • Minimizing PL strategy reduces Protection Levels in comparison with Latest strategy.

19. Strategy Latest Data Minimize PL Maximize PL PL Variation MSAS PRN 137 09/1/16 00:00 - 24:00 • 24H computation; • Average improvement by Minimize PL Strategy: 0.30m of HPL and 0.39m of VPL.

20. Verify All Active 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: • 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. Reduce Computational Load (2) • 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: • 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. Hypercube Method N satellites in view • Position solution is projected at each vertex of polyhedron with 2^N vertexes; • The largest position error likely appears as one of them. Range of Sum of Corrections FC+LTC+IC (LTC: projection to LOS) Try each corner of hypercube to find the largest position error

23. Stanford Chart MSAS PRN 137 09/1/16 07:00 - 08:00 All-in-View and Latest Message • PL Computation Strategy: Latest; • Satellite Combination: All-in-View only; • Position error is small and resulted PLs are very conservative.

24. Stanford-ESA Chart All satellite combinations and Latest Message N-2 Coverage and Latest Message • PL Computation Strategy: Latest; • 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.

25. Preliminary Result Needs detailed investigation Complete Integrity Chart All satellite combinations and All active message combinations • PL Computation Strategy: All Corners of Hypercube; • Satellite Combination: All possible combinations; • 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.

26. Contributing Component Contribution of FC Contribution of LTC • Hypercube made for the range of min/max of FC instead of FC+LTC+IC; • Satellite Combination: All possible combinations; • The largest contribution. • Hypercube made for the range of min/max of LTC instead of FC+LTC+IC; • Satellite Combination: All possible combinations.

27. 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; • Satellite Combination: All possible combinations. • Hypercube made for the range of min/max of FC+LTC+IC; • Satellite Combination: All combinations with loss of up to 2 satellites; • Not enough by comparison with slide 24.

28. Conclusion • 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: • 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: • Verify safety for alarm conditions (IODF=3) and ionospheric storm conditions; • Further reduction of computational load.