GBAS Availability Analysis for Trabzon Airport Using True Terrain Masking Data Irfan Sayim, Taskin Kavzoglu, and Emrehan Sahin Gebze Technical University Kocaeli, Turkey
Abstract. Availability is one of the Ground Based Augmentation System (GBAS) requirement and indicates the fraction of time the navigation function meets the required performance of continuity, integrity, and accuracy for the initiation of the intended aircraft approach and landing. In this paper, an analysis is performed to predict availability of the GBAS whether it is safe prior to aircraft landing under the prescribed system parameters in Trabzon Airport. A precise terrestrial model of satellite masking was developed based on true 3D terrain data. Then true terrain masking data was used in evaluation of availability. It is observed that the required (%99.9) GBAS availability for Trabzon Airport is achievable when for full constellation (all 24 satellites) is in use for Category 1 (CAT 1) approach of aircraft and with B class airborne equipment. On the other hand, under worst case scenario of two satellites outages (at any time 22 out of 24 satellites), the availability requirement may be violated with the use of true terrain masking data with additional offset of 5 degree. Keywords. Satellite Outages, tarratial masking, VPL, VAL
1. INTRODUCTION The GBAS is a differential satellite-based navigation system designed to provide navigation services for civil aircraft users during precision approach and landing. In the design of system, navigation performance requirements are specified to support implementation of advanced navigation concepts as a function of operational categories [1]. These navigation performances are defined as accuracy, integrity, continuity, and availability. The availability is the fraction of time the navigation function that meets the required performance of continuity, integrity, and accuracy for the initiation of the intended approach and landing. It indicates how well the navigation system provides sufficient performances with use of nominal number (24) of satellites in GPS constellation. In general, however, it cannot be assumed that all 24 satellites will always be available for use in GBAS. For example, existing simulation results of GBAS operational availability in the standard (GBAS) [3] are based on the worst-case (lowest resulting availability) 22 satellite subset
geometries. In this context, the simulations executed here were repeated for all 22-satellite subset geometries as well. The results clearly show that in the presence of a modestly depleted constellation, there is a risk of meeting the availability requirement. This result is readily explained by the fact that when fewer satellites are visible the effects in the availability due to individual geometry-critical satellites are more pronounced. In analysis, availability was predicted via use of Ground Accuracy Designator (GAD) and Airborne Accuracy Designator (AAD) values. These models are defined in MASPS and LGF documents that indicate accuracy of different types of ground and airborne equipment (GPS receivers). For the residual error, two models were also presented namely ionosphere and troposphere due to spatial decorrelation. Then related availability was predicted by the consideration of true elevation mask of satellites. Elevation mask limits the visible satellites in use and directly reduces the availability of system. Unlike previously executed availability analyses [4], in this work a true terrestrial masking model was developed and used. Defined mask value, used by Reference Receivers, is 5 degree in general as indicated in [1]. In reality, however, true mask is well above 5 degree for some airports [3] due to natural masking of terrain or large structures in near vicinity of airports. Trabzon Airport is one of these sites assumed to suffer from visibility of satellites due to high elevation mountains located at its southern side. Therefore, Trabzon Airport is specifically selected for availability analysis in this paper. For analysis, a CAT-1 approach with B type airborne equipment is assumed. A CAT1 approach is defined [1,2, and 5] as a precision approach and landing with a decision height not lower than 60m and with either a visibility not less than 800m, or a runway visual range not less than 550m. Also for CAT-1 precision approach requirements, vertical accuracy (95%) is 5m, integrity is 4x10-8/approach, and availability is 0.999 within 10m of vertical alert limits (VAL) and 6sec of time to alarm. Required integrity of GBAS is ensured within the computation of the Vertical Protection Levels (VPLs) for every time increment and compared with the VAL. Exceeded VPL quantities to VAL are stored for the duration of 24 hours in analysis. These occurrences could be happened if the number of satellites in
view does not support an adequate positioning for initiation of intended aircraft approach and landing. Availability, therefore, can be simply explained by the number of satellites and their geometries in space. True masking is a natural limitation to reduce the number of satellites seen by ground reference receivers at LGF. In general, more satellites indicate better positioning or lesser VPL value and resulting high availability.
Airborne Accuracy Designator (AAD) Model. The AAD is similar to GAD, but is defined based on error due to wide band noise, interference and error due to airframe multipath. The achievable performance of the receiver technology for aviation for the best performance (B-Class equipment) is:
σpr _ air (θi ) ≤ 0.0741 + 0.18e −θi
(5)
27.7
More detail can be found in [1]. 2. MODELS USED IN AVAILABILITY ANALYSIS Availability analysis is performed based on the following models and assumptions [1, 2]. Vertical Protection Level (VPL). VPL uses two fault hypothesis: H0, ground measurements are fault free, VPL H0 =5.85
N
and H1, a fault exists on one or more measurements made by one reference receiver. N
∑S
2 vertical,n
n=1
Tropospheric Uncertainty (due to spatial decorrelation): The tropospheric error may be modeled as;
σ pr _ trop = 10−6 σR h 0
(1)
2 2 ⎤ +σ pr_res,n ∑ S2vertical,n ⎡⎣( σ2pr_gnd,n 3) +σpr_air,n ⎦ n=1
VPL H1 =5.85
Tropospheric Ionospheric Uncertainties. Accuracy models developed in this section are for the residual effects due to ionospheric and tropospheric spatial decorrelation: The two terms are defined separately and then combined into one residual uncertainty term.
(2)
2 2 ⎡( σ 2pr_gnd,n 2 ) +σ pr_air,n ⎤ +σ pr_res,n ⎣ ⎦
S is the projection matrix third row associates with the vertical component of positioning. It is obtained as a result of Least Square Position solution. Details can be found in [1] and LGF. Sigmas for ground, air and residual error are given in [1] as follows:
(
0.002 + sin 2 (θn ) 1 − e−Δ0
h0
)
(6)
where, σ R is refractivity uncertainty (10 unit-less), h 0 is tropospheric scale height (7600 meters), Δ 0 is aircraft distance above reference station (3000 meters). Ionospheric Uncertainty (due to spatial decorrelation): The ionosphere pseudorange error may be modeled as
σiono = FPP σvert _ iono _ grad (x air + 2τair νair ) where,
τair is
(100 sec),
(7)
the airborne carrier-smoothing time constant
ν air is the horizontal user velocity (~70 m/sec).
σvert _ iono _ grad is the ionospheric delay change (as a function
Ground Accuracy Designator (GAD) Model. The required accuracy allocation for ground error (C class ground equipment) is formed by the combining the contributions of receiver noise, multipath, and the SIS residual error as follows:
of ionospheric pierce-points separation between reference receiver and user, ~2 mm/km), x air is the user-reference
For θi > 35 and M = 3 ,
factor, R e is the approximate radius of Earth’s ellipsoid (6378.1363 km), h I is the height of the maximum electron
σ pr _ gnd (θi ) ≤
( 0.15 + 0.84e
)
−θİ 15.5 2
3 + 0.0016 + ( 0.01 sin θi )
2
(3)
For θi ≤ 35 and M = 3 , σ pr _ gnd (θi ) ≤
( 0.24 )
2
3 + 0.0016 + ( 0.01 sin θi )
(
separation, F = 1 − R cos(θ ) ( R + h ) 2 ( e PP n e I )
)
−1 2
is the obliquity
density of the ionosphere (~350 km). The residual uncertainty can now be formed as [3]:
σpr _ res = σpr2 _ tropo + σpr2 _ iono 2
(4)
Where, θi is the elevation angle and M is the number of reference receivers. This accuracy model stands for the performance reference receiver type of an advanced narrow correlator with a Multipath Limiting Antenna (MLA).
(8)
3. PRECISE MASKING MODEL FOR GBAS AVAILABILITY In order to evaluate the GBAS availability for the study site, Trabzon airport whose location is shown in Fig.1, a visibility analysis was performed using skyline feature also known as horizonline or ridgeline. The skyline map is produced by
drawing a line of sight from the observer point. A line of sight is estimated after each azimuth increment varied at each increment in degrees.
In addition, a graphical representation of the visibility map is presented with respect to elevation and azimuth in Fig. 4.
Fig. 4 True Mask with added 5 degree elevation offset Fig. 1 Satellite View
The azimuth and vertical angle from the observer point to each vertex is calculated in the analysis of skyline graph. In the implementation of skyline Skyline tool of ArcGIS software (version 10.2) was employed. The terrestial model of the study area was produced from 1:25,000 scale topographic map using a triangulated irregular networks (TIN) model using digitized contours. Afterwards, a precise terrestrial model of satellite masking was produced with additional offset of 5 degree based on true 3D terrain data. 2D and 3D sky visibility maps are shown in Fig.2 and Fig. 3, respectively.
Fig. 2 2D View
4. AVAILABILITY ANALYSIS The GBAS availability is the fraction (duration of time GBAS meets requirements/duration of total simulation time) of time and indicates how well the navigation system provides sufficient performance for continuity, integrity, and accuracy of the navigation function to initiate the intended aircraft approach and landing. Availability is quantified trough computation of VPL. VPL defines position error upper bounds of the aircraft to indicate whether or not the GBAS supports the availability of precision approach and landing under the following two fault hypothesis: H0, ground measurements are fault free, and H1, a fault exists on one or more measurements made by one reference receiver. Two main factors affecting the VPL quantity are considered here: 1- error accuracy models (sigmas) and 2- the visible satellite geometries in space (projection matrix third row, Svertical). The error models are described in GBAS standard in terms of accuracy expectations for ground and airborne equipment and also residual errors. For analysis, we can use these values directly from the specifications. However, the satellite geometries are site dependent. Location of GBAS reference receivers sitting may be affected by masking (i.e., lesser number of visible satellites) and also by their geometries/positions in space at any time. A simulation was executed with the use of GPS constellation to perform availability analysis for Trabzon Airport. The details of the geometries used in simulation are: Constellation: Nominal 24-satellite constellation as defined in RTCA DO-229A. LGF Location: Trabzon Airport Elevation Mask Data: Terrestrial model (Fig. 4 and 5) Simulated Duration: 24 hours Time interval: 0.5 sec (2Hz)
Fig. 3 3D View
Satellite Outage Conditions: 1. complete 24-satellite constellation and 2. The worst-case (most sensitive) 22satellite constellation subsets were simulated. Reference Receivers Failure Conditions: 1. all reference receivers are fault free (H0), 2. one reference receiver is faulty (H1).
taken into account for duration of 24 hours. The value of VAL (10m) is also plotted for comparison. For example, in both cases (H0 and H1), maximum value of VPLs are obtained about 5 meter that is far enough from nominal value of 10 meter of VAL. Therefore, these availability results are fully consistent with specifications (>99.9%) for both cases.
Geometries not meeting the GBAS availability criteria, (i.e., VPL is greater than VAL) were excluded and determined as unavailability since aircraft approaches and landing would not be conducted in these cases. When the availability condition is satisfied as defined in specifications, the prediction for GBAS will be rated safe for aircraft approach and landing. In previous section, details of accuracy models were given for GAD and AAD. Using these models/values, the computed VPLs may not exceed to VAL (i.e., no threat of GBAS availability) when full constellation is used. However, undoubtedly, the worst cases satellite outages (depleted constellation, 22 satellite subsets out of 24) may not necessarily guarantee such results especially when required availability is 99.9% for any LGF site. In addition to that, availability can be worse if elevation mask increases and the number of satellite in use decreases significantly at the same instant time. In Fig. 5, 24 nominal satellite passes of a full constellation on the sky are plotted. True terrain mask data (Fig. 4) is applied to satellite passes in the view. In addition to true mask data, five-degree of elevation mask is also added (offset) as defined in [1] and [2].
Fig. 6 VPL Variation in 24 hours duration (with full constellation)
In Fig. 7, multiple VPL curves are plotted for duration of 24 hours. Each curve represents one pair of satellite outage. A horizontal dashed line shows required VAL for CAT-1. It is also seen that VPL exceeded VAL for some subsets of 22 satellites out of 24. The availability is basically quantified as summation of all the system time spending below the VAL. In other words, values of VPLs above the VAL indicate the unavailability of GBAS.
Fig. 5 Satellite Passes and true masking (Full Constellation)
True terrain elevation mask blinds or limits a significant portion of satellite passes. As seen in Fig. 5, true masking starts from east side (~90 degree azimuth) increases gradually up to south side (~200 degree azimuth) and follows as gradual decrease up to the west side (~290 degree azimuth). About a maximum of 5-degree true elevation angle occurs at south side. This elevation masking profile (Fig. 5) was applied to entire calculations in analysis. In Fig. 6, computed VPLs from equation 1 (H0 case) and 2 (H1 case) are plotted together. All satellites (nominal 24) are
Fig. 7 VPL Variation for duration of 24 hours (with 2 satellite outage)
Previous availability analysis was repeated (for all subset geometries of 22 satellites) in terms of incremented elevation offset angle from 0 to 5 degree. Time for VPLs exceeded to VAL was counted for each increment of 0.25 elevation mask degree. Then associated availability was obtained for all subset geometries. These results were plotted in the upper curve in Fig. 8. Horizontal axis represents the increments of offset angles for masking. Vertical axis represents the
corresponding availability. It is noted that, zero point on the horizontal axis of Fig. 8 represents the initial value of elevation mask angle (i.e., true terrain mask profile). Similarly, first value of availability (vertical axis) corresponds to the true terrain elevation mask value.
• However, two satellite outages with both true terrain and 5 degree offset mask (Fig. 4, and 8) results a considerable degradation on the GBAS availability. Degradation is quantified in terms of elevation mask angle. • The GBAS availability is worsen for the H1 case (fault measurements made by one reference receiver) as given in lower curve in Fig. 8.
Acknowledgment The views expressed in this paper belong to the authors alone and do not necessarily represent the position of any other organization or person.
References Fig. 8 Availability vs. Elevation Mask (H0 and H1 Cases) Analysis of depleted constellation was repeated for H1 case and plotted in the lower curve in Fig. 8. It is assumed that, in this case, a fault exists on the one reference receiver measurement and also assumed that one receiver is excluded not to be used at LGF. Exclusion of one reference receiver indicates a significant increase on the ground error sigmas (standard deviations) and related VPL value. Having greater VPL values with crossing VAL indicate degradation on the system availability. 5. CONCLUSIONS Availability prediction analysis is performed for one of the critical locations where the GBAS is assumed to be installed in future. A true precise terrestrial model was developed for masking the visibility of satellites. A CAT-1 aircraft approach with B-Class airborne and C-Class ground equipment is considered in simulation. Satellite outages were also taken into account. Depleted constellation, 22 satellites out of 24 satellites, is used as the worst case scenario. Considering the produced results, some conclusions can be drawn from this work. • True terrestrial model shows that mask angles exceeded 5 degree nominal values about 120 degree of azimuth along south-side of airport. • For both H1 and H0 cases, use of full constellation with 24 satellites allows the availability of GBAS about 100% which is consistent with the specification. • Two satellite outages (22 out of 24 satellites) with only true terrain masking (without 5 degree offset) results the availability of GBAS about (99.912%) which can be regarded as acceptable.
[1] FAA Specification (2005) Category I Local Area Augmentation System Ground Facility. FAA, Washington, D.C., FAA-E-AJW44-2937A, October 21 [2] RTCA (SC-159/WG-4), (1998) Minimum Aviation System Performance Standards for the Local Area Augmentation System (LAAS),” RTCA/DO-245, RTCA Inc., Washington DC, 28 September 1998. [3] Wang Z., Macabiau C., Zhang J., and Escher A. C. (2014) “Prediction and analysis of GBAS integrity monitoring availability at LinZhi airport”, GPS Solution, Volume 18, pp 17-40 [4] Reddy A. S., Jhansi B., and Sarma A. D., (2012) “Analysis of Future LAAS ‘Availability’ at Hyderabad Station for Precision Approach of Aircraft”, India Conference (INDICON), 2012 Annual IEEE, Kochi, Kerala, India, Date 7-9, Dec. 2012 [5] Murphy T., and Imrich T., (2008) "Implementation and Operational Use of Ground-Based Augmentation Systems (GBASs) - A Component of the Future Air Traffic Management System," Proceedings of the IEEE, Volume 96, Number 12, pp 1936 - 1957
