Assessment of Combined Integrity Algorithms

Transcription

1 Assessment of Combine Integrity Algorithms C. Stöber an F. Kneißl Institute of Geoesy an Navigation, University FAF Munich ICG WG-B, Munich, /6

2 OUTLINE Overview User Equations Comparison of Integrity Measures Combine Algorithm Simulation Results Conclusions ICG WG-B, Munich, /6

3 Overview Definition of integrity Integrity enotes the measure of trust place in the correctness of the information provie by navigation systems. Users may etermine their integrity by - Receiver autonomous algorithms (RAIM) - External integrity ata sources (e.g. SBAS) - Integrity ata provie within the navigation ata message (e.g. Galileo) ICG WG-B, Munich, /6

4 Overview GPS Ranging VPL GPS + SBAS HPL SBAS Integrity Information Galileo Ranging Galileo Integrity Information VAL, HAL Integrity risk Systemlayout User information ICG WG-B, Munich, /6

5 Overview GPS GPS + SBAS + Galileo SBAS Galileo Ranging Integrity Information Ranging Integrity Information VAL, HAL VPL HPL? ICG WG-B, Munich, /6

6 Input quantities on user sie User Equations GPS + SBAS Geometry between GPS satellites an user erive from observations of the GPS satellites User ifferential range error σudre, transmitte by SBAS satellite Gri ionospheric vertical error σgive, transmitte by the SBAS satellite Tropospheric error σtropo erive from the moel efine within the Raio Technical Commission For Aeronautics (RTCA) publication, Minimum Operational Performance Stanars (MOPS) For Global Positioning System/Wie Area Augmentation System Airborne Equipment, RTCA DO-9D Error of airborne receiver errors σair, calculate epening on receiver properties an moels efine within RTCA DO-9D ICG WG-B, Munich, /6

7 User Equations GPS + SBAS Algorithm: Compute measurement variances Transform variances to the position omain Law of error propagation Topocentric geometry matrix Weight matrix Compute semi-major axis of horizontal error ellipse Give HPL an VPL as multiples of the compute variances σ = σ + σ + σ + σ G i i = i, flt i, UIRE i, air i, tropo [ cos El sin Az cos El cos Az sin El 1] east EN EU ET i EN north NU NT i EU NU U UT i ET NT UT T i = ( G T WG) 1 east + north east north major = + + VPL K HPL = K =, PA K V H, NPA H, PA major major U en route precision approach moe i EN inclusive non - precision approach ICG WG-B, Munich, /6

8 Input quantities on user sie User Equations Galileo Geometry between Galileo satellites an user position erive from observations of the Galileo satellites SISA as preiction of the expecte SIS error, transmitte by the Galileo satellites SISMA comprising the accuracy of the monitoring process of the SIS error at the Galileo groun segment, transmitte by the Galileo satellites Integrity flag transmitte by the Galileo satellites Horizontal alarm limit (HAL) an vertical alarm limit (VAL), chosen by the user accoring to the esignate application (e.g. laning approach) Remaining errors ICG WG-B, Munich, /6

9 User Equations Galileo Algorithm: Calculate overall Integrity risk PHMI as sum consisting of fault-free an faulty moe allocation tree, split into four inepenent calculate parts P P HMI HMI ( VAL, HAL) ( VAL, HAL) = P = P IR, V IR, H IR, V, FaultFreeMoe + P + P + P IR, H, FaultFreeMoe IR, V, FaultyMoe + P IR, H, FaultyMoe P 1 erf + + HMI 1 N j = 1 ( VAL, HAL) N u, V + u, V Pfail, sat 1 erf 1 erf j j = 1 σ u, V, FM σ u, V, FM P σ fail, sat VAL j = u, V, FF + e 1 χ, δ u, H HAL ξ VAL + µ FF HAL cf ξfm VAL µ Compute satellite to user geometry M topo = N T topo T 1 T ( H PH) H P Derive neee variances, e.g. = [ i] ( SISA σ ) N u, V, FF M topo 3, i u, L, i i= 1 σ + ICG WG-B, Munich, /6

10 User Equations Conclusions(I) SBAS + GPS integrity concept efines that all GPS satellites consiere healthy by the SBAS groun segment are working nominally an may be use by the user Both integrity concepts use vertical an horizontal components to assess the measure of integrity Analogy: ( SISA ) 144 i + σ u, L, i = ˆ σ i = σ i, flt + σ UIRE + i air + i i, σ, σ, Galileo GPS + SBAS tropo 4 3 Fault free allocation tree within the Galileo integrity concept implicitly equals the SBAS + GPS integrity concept except for the allocate confience intervals an the representation of the final result Final assessment of user integrity yiels one major ifference between the two concepts. SBAS + GPS concept uses HPL an VPL (in meters) erive from fixe error allocations, Galileo uses the probability PHMI with confience intervals chosen by the user in terms of HAL an VAL (in meters). ICG WG-B, Munich, /6

11 User Equations Conclusions(II) With the transition of the SBAS + GPS integrity algorithm efinition containe within RTCA DO-9C to the newer version D, the rational for the efinition of the K values was change. Correction in Overbouning argumentation carrie out See paper Does the HPL Boun The HPE, Christian Tiberius an Dennis Oijk, Navitec 8 Corresponing argumentation use in baseline Galileo concept up to now As a consequence, only SBAS + GPS HPL an VPL are now conservative estimates, while the conservatism in the range omain is no longer guarantee. Protection levels an integrity risks at the alert limit are mathematically an inversion of the same context but cannot be compare irectly ue to the ifferent allocations -> solution strategies neee ICG WG-B, Munich, /6

12 Direct an inirect Integrity Formulation Direct problem (Galileo case): Specify alarm limit of operation Compute associate integrity risk Compare compute integrity against allowable integrity risk Compare Integrity Measures Inverse Problem (SBAS + GPS case) Specify on system level allowable integrity risk for the user equation part of allocation tree Compute upper boun for alarm limits not resulting in integrity risks violating the specifie allowable risk Compare upper boun alarm limit against allowable alarm limit of operation ICG WG-B, Munich, /6

13 Compare Integrity Measures Solving strategies (I) Integrity risk functions are separate into inepenent horizontal an vertical components ~ PHMI = PHMI, H ( HAL) + PHMI, V ( VAL) = P ( HAL, ) + P (, VAL) Resulting in solvable set of optimization problems HPL = max arg P ( HAL) IR HMI HAL R VPL = max arg P VAL R IR H IR HMI, H HMI, V V HMI ( VAL) IR IR V H ICG WG-B, Munich, /6

14 Resolve HPL first Check, if Allocate integrity risks to Compare Integrity Measures Solving strategies (I) P HMI, H IR ( HAL) IR = IR IR = IR P V H HMI, H ( HAL) Resolve VPL = max arg PHMI, VAL R V ( VAL) IR, HPL = HAL V Resolve VPL first Check, if Allocate integrity risks to P IR HMI, V ( VAL) IR = IR IR = IR P H V HMI, V ( VAL) Resolve HPL = max arg PHMI, HAL R H ( HAL) IR, VPL = VAL H ICG WG-B, Munich, /6

15 Fixe Allocation Split IR fixe to IR H an IR V Compare Integrity Measures Solving strategies (I) max HMI, H ( ) VPL = max P ( ) H HMI, V VAL IRV Resolve HPL = P HAL IR an HAL R VAL R Geometry epenent variable Allocation Split IR proportional to associate integrity risks IR H an R V at the alert limits PHMI, H ( HAL) Resolve IR an P ( HAL) P ( VAL) IR PHMI, V ( VAL) H = IR + P ( HAL) P ( VAL) IR V = + HMI, H HMI, V HMI, H HMI, V No analytical solution for solving strategies -> use of root fining algorithm ICG WG-B, Munich, /6

16 Compare Integrity Measures Solving strategies (I) Munich Plot fixe Munich Plot variabel VPL [m] VPL [m] Violation events: total 994 percentage HPL [m] Violation events: total 5147 percentage HPL [m] 6 7 Munich Plot HPL first Munich Plot VPL first VPL [m] Violation events: total 499 percentage HPL [m] VPL [m] Violation events: total 499 percentage HPL [m] Munich plots for ifferent solving strategies (I) ICG WG-B, Munich, /6

17 ICG WG-B, Munich, /6 Compare Integrity Measures Solving strategies (II) SBAS Integrity Risk Formulation en route computation No vertical guiance Horizontal protection level escribe as a quantile of the Raleigh istribution with respect to major HAL ( ) P = HMI, G, H HAL χcf u SBAS Integrity Risk Formulation precision approach Vertical protection level escribe as a quantile of the Normal istribution with respect to U ( ) 1 x P VAL 1 exp x HMI, G, V = Horizontal guiance escribe as a quantile of the Normal istribution with respect to major 1 x P ( HAL) 1 exp x HMI, G, H = VAL HAL u major π π u major

18 Combine Algorithm Possibilities on user sie to think of Using Galileo SISA within SBAS + GPS integrity concept, neglect SISMA Inepenent parallel calculation an a posteriori integration Using ata provie by SBAS within Galileo integrity concept No SBAS assumes on user level all satellites inicate healthy to be healthy, in Galileo integrity concept one satellite may be faulty Possible but suboptimal solution Integration of two inepenent results means averaging -> worse outcome compare to true combine algorithm Possible Accoring to RTCA DO9 SBAS assumes all satellites inicate healthy to be healthy -> per efinition SISMA is. Results in an aitional geometry inepenent integrity risk contribution. ICG WG-B, Munich, /6

19 Combine Algorithm Proceure Computation of measurement variances an biases following the escription of each system Single Point Positioning for combine Measurements 4 Parameter estimation (inter system bias known) 5 Parameter estimation (inter system bias estimate) Application of the law of error propagation eriving variances an noncentralities on the position omain Integrate the tails of the probability ensity functions starting from respective alarm limits Sum up all integrity risk components incluing the unallocate error of SBAS user equations Algorithm equals Galileo user equation with Pfail= for GPS satellites with an aitional fixe risk component ICG WG-B, Munich, /6

20 Combine Algorithm Currently weak point Since transition of RTCA Do 9 from issue C to issue D the choice of the K-factors is somewhat arbitrary Conservatism only guarantie in position omain Possible solutions Free insie view into SBAS Groun segment algorithms Generation of conservative estimations in range omain, e.g. slightly egraation factor Aitional Data provie by SBAS satellites (L frequency incorporating new integrity ata?) ICG WG-B, Munich, /6

21 Key Functionality Combine Algorithm Integrity Simulation Tool SBAS ata processing conforming DO-9 SBAS performance estimation on a global scope Galileo integrity performance estimation Combine algorithm performance estimation Aitional Functionality Raw measurement generation Ranom measurement egraation Flexible ata interfaces Groun Segment to Space Segment Groun Segment to User Segment Integrity Tool works on real time ata generate by the Integrity Simulation Tool ICG WG-B, Munich, /6

22 Simulation Results Single epoch PHMI Galileo vertical (SISA.85m) 5 PHMI Galileo vertical (SISA 1.5m) PHMI Galileo vertical (SISA.m) 5 PHMI Galileo vertical (SISA 3.m) Receiver noise Galileo. m Tropospheric noise.5 m Orbit an Clock noise variable Galileo (SISA) Galileo ionosphere factor. SISMA.8 m HAL 1 m VAL m Comparison of Galileo only vertical integrity risks for ifferent SISA values ICG WG-B, Munich, /6

23 Simulation Results Single epoch 4 HPL Galileo GPS 5 combine [m] HPL GPS only [m] Co Latitue [ ] HPL GPS minus HPL Galileo GPS 5 combine [m] Longitue [ ] Comparison between combine algorithm an SBAS + GPS, assuming equal magnitue of measurement errors Receiver noise (GPS an 1. m Galileo) Tropospheric noise.5 m Orbit an Clock noise GPS. m (σ UDRE ) Orbit an Clock noise. m Galileo (SISA) GPS ionosphere factor. Galileo ionosphere factor. SISMA.8 m HAL 1 m VAL m ICG WG-B, Munich, /6

24 Simulation Results Timeline analysis HPL Galileo GPS combine Mean value [m] HPL Galileo only Mean value [m] Co Latitue [ ] Co Latitue [ ] Longitue [ ] Longitue [ ] HPL Galileo GPS combine Epoch percentage above threshol 1m 1 HPL Galileo only Epoch percentage above threshol 1m 1 Co Latitue [ ] Co Latitue [ ] Longitue [ ] HPL Galileo GPS combine Epoch percentage above threshol 9m Longitue [ ] Co Latitue [ ] Co Latitue [ ] Longitue [ ] HPL Galileo only Epoch percentage above threshol 9m Longitue [ ] Receiver noise (GPS an 1. m Galileo) Tropospheric noise.5 m Orbit an Clock noise GPS. m (σ UDRE ) Orbit an Clock noise. m Galileo (SISA) GPS ionosphere factor. Galileo ionosphere factor. SISMA.8 m HAL 1 m VAL m Comparison of combine algorithm an Galileo-only algorithm for ifferent threshols ICG WG-B, Munich, /6

25 Conclusions Planne performance of the Galileo system is challenging an highly epenent on the clock an orbit accuracy Inverting strategies for shifting protection level formulations to integrity risk formulations provie a better comparability of Galileo integrity with SBAS + GPS integrity The conservative joint of the ifferent integrity risk allocation trees results in an aitional aitive an geometry-inepenent integrity risk component for all GPS satellites. The simulation results emonstrate that this aitive term in the combine algorithm oes not eplete the geometry an reunancy inuce avantages. Consequently, combine use of integrity information outperforms either single system use alone It is the solely ecision of all involve service proviers to jointly efine an certify combine integrity processing schemes, combine equipment regulatory an combine proceures. ICG WG-B, Munich, /6

26 Thanks for your attention C. Stöber an F. Kneißl Institute of Geoesy an Navigation, University FAF Munich ICG WG-B, Munich, /6 The presente work was one within the framework of the UniTaS IV project foune by the Bunesministerium für Wirtschaft un Technologie (BMWi) aministere by the Agency of Aeronautics of the DLR in Bonn (FKZ 5 NA 734).