ABCDEFGHIJKLMNOPQRSTUVWXYZAAABACADAEAFAGAHAIAJAKALAMANAOAPAQARASATAUAVAWAXAYAZBABBBCBDBEBFBGBHBIBJBKBLBMBNBOBPBQBRBSBTBUBVBWBXBYBZCACBCCCDCECFCGCHCICJCKCLCMCNCOCPCQCR
1
CBTO & CBFO Model - Dr Bobby UlichInputs to CBTO and CBFO ModelsCBTO OutputsCBFO OutputsTrue Altitude CalculationCBTO MODELAircraft VelocitySatellite ECEF VelocityUnit vector from Satellite to Ground StationSatellite Velocity Toward Ground StationDownlink Doppler ShiftUnit Vector from Satellite to AircraftSatellite Velocity Toward AircraftUplink Doppler Shift from Satellite Moving Toward Aircraftδf(sat) + δf(AFC)Unit Vector from Aircraft Toward Vertical Upward = Vector from Center of Earth Toward AircraftRange Rate from Aircraft Toward Satellite Due to ROCUplink Doppler Shift from Rate of ClimbRange Rate from Aircraft to Satellite Due to Horizontal Ground SpeedUplink Doppler Shift from Aircraft Moving (Horizontally) toward Actual SatelliteNominal Satellite Location
@ 0 Latitude 64.5 Longitude
Unit Vector from Aircraft to Nominal Satellite PositionRange Rate from A/C to Nominal Satellite location due to horizontal ground SpeedΔf comp = Uplink Doppler Shift from Aircraft Moving Toward Nominal SatellitePredicted BFO
2
Notes:
1. Version 1.0 Beta issued October 31, 2017.
2. Make manual input entries in yellow cells.
3. The green and gold cells show the model outputs.
4. The measured data and 2-
σ error values must be copied manually from the list on the second worksheet "BTO & BFO Data" to the blue cells on this worksheet depending on the time entered.
5. See the notes in the "BTO & BFO Data" worksheet for a description of the 2-
σ error values.
6. Version 1.1 (1 November 2017): Added 23:14 BFO calculation.
7. Version 1.2 (6 November 2017): Slightly modified BFO error statistics.
TimeAircraft Latitude (Geodetic)Aircraft LongitudeFlight LevelΔSAT
≡ SAT
- SAT
ISA
True CourseGround SpeedRate of ClimbDrB's Model Predictions2-σ Error
(from DSTG)
Inmarsat CBTO DataError

Model
- Data
DrB's Model Predictions2-σ Error
(from DSTG)
Inmarsat CBFO DataError

Model
- Data
SATISA
at
Flight Level
SAT
at Flight Level
Density Altitude Correction for TemperatureTrue Altitude
(Density Altitude)
ECEF XYZ (in km)
of Satellite Inmarsat F-1
from ATSB Table 3
Range from Perth to Satelliteh = True Aircraft AltitudeN(Φ)
= Range along normal at Earth surface to Z-axis
X Coordinate of Aircraft in ECEFY Coordinate of Aircraft in ECEFZ Coordinate of Aircraft in ECEFRange from Aircraft to satellitePredicted BTO for Aircraft LocationNorth SpeedEast SpeedX dotY dotZ dotX dotY dotZ dotXYZXYZXYZXYZXYZ
3
Parameter ListUTCdeg Ndeg EhftCdegktsfpmμsμsμsμsHzHzHzHzKKftftX (km)Y (km)Z (km)kmkmkmkmkmkmkmμsm/sm/sm/sm/sm/skm/skm/skm/s------km/sHz------km/sHzHz------m/sHzm/sHzkmkmkm------m/sHzHz
4
NameValueUnitsDescription2014/3/7 16:30:002.745101.71009.70.00#NAME?5814,907#NAME?#NAME?687#NAME?288.2297.91,1271,127#NAME?#NAME?#NAME?#NAME?0.3446,378.2-1,293.096,238.61303.47#NAME?#NAME?0.000.000.00.00.0#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.20270.97810.0476#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52050.8538-0.00800.000.00#NAME?
5
wb_light_speed299,792,458m/sSpeed of light in vacuum2014/3/7 16:44:002.860101.670269.7343.2166#NAME?#NAME?283.0292.71,1253,725#NAME?#NAME?#NAME?#NAME?1.1356,378.2-1,288.776,239.68316.17#NAME?#NAME?81.71-24.7125.01.081.6#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.20200.97810.0496#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52040.8539-0.008413.2072.48#NAME?
6
wb_BTO_bias-495,679μs"Offset" in BTO calculation2014/3/7 17:06:435.299102.8133509.325.0423#NAME?5815,610#NAME?#NAME?6132#NAME?218.8228.11,07636,076#NAME?#NAME?#NAME?#NAME?10.9966,378.3-1,410.906,203.59586.16#NAME?#NAME?197.1592.05-85.7-38.2196.3#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.22080.97100.0917#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52230.8526-0.0155-80.36-441.38#NAME?
7
wb_a_km6,378.137kmSemi-major axis of Earth in WGS-84 model2014/3/7 17:20:356.937103.5853509.825.5468#NAME?#NAME?218.8228.61,12836,128#NAME?#NAME?#NAME?#NAME?11.0126,378.4-1,489.826,165.24766.52#NAME?#NAME?217.21103.64-94.6-49.8215.6#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.23320.96500.1200#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52330.8519-0.0202-96.32-529.03#NAME?
8
wb_b_km6,356.752kmSemi-minor axis of Earth in WGS-84 model2014/3/7 17:20:506.954103.6143509.858.8481#NAME?#NAME?218.8228.61,12836,128#NAME?#NAME?#NAME?#NAME?11.0126,378.4-1,492.866,164.26768.44#NAME?#NAME?128.15211.68-202.1-64.9127.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.23370.96480.1203#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52330.8519-0.0203-163.63-898.74#NAME?
9
wb_f0.003352810665--Flattening of Earth in WGS-84 model = (a-b)/a2014/3/7 17:22:077.043103.7603509.858.8481#NAME?#NAME?218.8228.61,13036,130#NAME?#NAME?#NAME?#NAME?11.0136,378.5-1,508.336,159.26778.18#NAME?#NAME?128.15211.68-201.9-65.6127.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.23610.96410.1218#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52360.8517-0.0205-164.19-901.82#NAME?
10
wb_e_sq0.006694380--First eccentricity squared of Earth in WGS-84 model2014/3/7 17:24:027.260103.68035011.8339.7497#NAME?#NAME?218.8230.61,35436,354#NAME?#NAME?#NAME?#NAME?11.0816,378.5-1,499.016,158.52802.07#NAME?#NAME?240.09-88.6193.3-8.5238.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.23460.96390.1255#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52340.8518-0.021236.51200.56#NAME?
11
wb_up_freq1,646.6525MHzAES uplink frequency2014/3/7 17:36:156.285102.2783608.7235.2501#NAME?#NAME?216.8225.51,00537,005#NAME?#NAME?#NAME?#NAME?11.2796,378.4-1,350.586,206.01694.84#NAME?#NAME?-147.10-211.52203.360.7-146.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.21140.97130.1088#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.52110.8533-0.0184160.41881.10#NAME?
12
wb_down_freq3,615.1525MHzAES downlink frequency2014/3/7 17:52:355.180100.2603609.0241.3505#NAME?#NAME?216.8225.81,04237,042#NAME?#NAME?#NAME?#NAME?11.2906,378.3-1,133.446,261.75573.04#NAME?#NAME?-124.69-228.03222.451.7-124.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.17740.98000.0897#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.51760.8555-0.0152161.22885.50#NAME?
13
wb_BFO_bias149.86"Offset" in BFO calculation2014/3/7 18:02:355.66098.9403609.4289.9504#NAME?#NAME?216.8226.21,08437,084#NAME?#NAME?#NAME?#NAME?11.3036,378.3-988.116,281.25625.98#NAME?#NAME?88.47-243.81242.229.388.0#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.15470.98310.0980#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.51500.8570-0.0167148.35814.82#NAME?
14
nomsatradius42,588kmDistance of satellite from center of Earth2014/3/7 18:22:126.56496.3673609.7295.5498#NAME?5812,687#NAME?#NAME?6138#NAME?216.8226.51,11637,116#NAME?#NAME?#NAME?#NAME?11.3136,378.4-703.976,308.69725.53#NAME?#NAME?110.40-231.45231.413.1109.7#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.11020.98740.1136#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50970.8602-0.0194127.11698.16#NAME?
15
wb_nomsatlon64.5degLongitude of nominal sub-satellite point2014/3/7 18:28:157.10395.7433609.7295.7513#NAME?5812,480#NAME?#NAME?6143#NAME?216.8226.51,11537,115#NAME?#NAME?#NAME?#NAME?11.3136,378.5-634.456,308.92784.84#NAME?#NAME?114.44-237.79238.09.7113.6#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.09930.98740.1228#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50830.8609-0.0210126.95697.29#NAME?
16
wb_nomsatlat0.00degLatitude of nominal sub-satellite point2014/3/7 18:38:417.74594.4063609.9295.7509#NAME?#NAME?216.8226.71,14237,142#NAME?#NAME?#NAME?#NAME?11.3216,378.5-486.416,312.84855.38#NAME?#NAME?113.48-235.79236.32.9112.4#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.07610.98810.1339#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50540.8626-0.0230119.29655.22#NAME?
17
Perth_X_km-2,368.8kmECEF XYZ coordinates of
Inmarsat Ground Station at Perth
2014/3/7 18:40:327.63394.2253609.9180.0491#NAME?#NAME?216.8226.71,14237,142#NAME?#NAME?#NAME?#NAME?11.3216,378.5-466.576,316.01843.02#NAME?#NAME?-252.390.00-2.533.4-250.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.07300.98860.1319#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50500.8628-0.022633.26182.70#NAME?
18
Perth_Y_km4,881.1km2014/3/7 19:41:00-0.01793.72736010.2183.7454#NAME?5811,500#NAME?#NAME?6111#NAME?216.8227.01,17537,175#NAME?#NAME?#NAME?#NAME?11.3316,378.1-415.316,375.96-1.85#NAME?#NAME?-232.84-15.2215.20.9-232.8#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.06500.9979-0.0003#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50480.86320.00008.4546.42#NAME?
19
Perth_Z_km-3,342.0km2014/3/7 20:41:02-7.58993.16036010.5184.3450#NAME?5811,740#NAME?#NAME?6141#NAME?216.8227.31,20637,206#NAME?#NAME?#NAME?#NAME?11.3406,378.5-349.166,324.24-838.28#NAME?#NAME?-230.73-17.3319.0-29.5-228.7#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.05460.9898-0.1312#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.50270.86410.0226-21.08-115.79#NAME?
20
degperrad57.2957795degConversion factor for degrees to radians2014/3/7 21:41:24-15.16292.84536010.1182.4450#NAME?5812,780#NAME?#NAME?6168#NAME?216.8227.01,16937,169#NAME?#NAME?#NAME?#NAME?11.3296,379.6-306.146,160.87-1,660.34#NAME?#NAME?-231.25-9.4912.5-59.9-223.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.04790.9644-0.2599#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.49960.86510.0445-55.55-305.10#NAME?
21
2014/3/7 22:41:19-22.56192.8833609.1179.7440#NAME?5814,540#NAME?#NAME?6204#NAME?216.8225.91,05537,055#NAME?#NAME?#NAME?#NAME?11.2946,381.3-296.935,895.90-2,436.21#NAME?#NAME?-226.241.123.3-86.7-208.9#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.04650.9232-0.3815#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.49580.86600.0648-87.06-478.17#NAME?
22
2014/3/7 23:14:20-25.470093.78753908.0180.0480.5#NAME?#NAME?6217.3#NAME?216.7224.792839,928#NAME?#NAME?#NAME?#NAME?12.1706,382.1-381.335,760.20-2,731.40#NAME?#NAME?-247.190.007.0-106.1-223.2#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.05970.9020-0.4277#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.49570.86550.0723-104.46-573.79#NAME?
23
2014/3/8 0:11:00-33.14693.9753606.1174.8397#NAME?5818,040#NAME?#NAME?6252#NAME?216.8222.971136,711#NAME?#NAME?#NAME?#NAME?11.1906,384.5-371.235,342.11-3,473.67#NAME?#NAME?-203.4918.62-10.9-112.3-170.4#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.05820.8369-0.5442#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.49000.86700.0910-118.17-649.07#NAME?
24
2014/3/8 0:19:29-34.01094.1413002.6170.9339-4,485#NAME?12418,400#NAME?#NAME?6179#NAME?228.7231.331030,310#NAME?#NAME?#NAME?#NAME?9.2386,384.8-382.735,286.47-3,552.52#NAME?#NAME?-172.0127.64-20.6-98.0-142.6#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.06000.8285-0.5568#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.48950.86700.0929-108.27-594.69#NAME?
25
2014/3/8 0:19:37-34.01094.1413002.6170.9300-15,015#NAME?8618,410#NAME?#NAME?6-5#NAME?228.7231.331030,310#NAME?#NAME?#NAME?#NAME?9.2386,384.8-382.735,286.47-3,552.52#NAME?#NAME?-152.3824.48-18.3-86.8-126.3#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?-0.06000.8285-0.5568#NAME?#NAME?#NAME?#NAME?18,334.638,439.30.00.48950.86700.0929-95.91-526.83#NAME?
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100