Methodology and Case Studies of Signal-in-Space Error Calculation - - PowerPoint PPT Presentation
Methodology and Case Studies of Signal-in-Space Error Calculation Top-down Meets Bottom-up Grace Xingxin Gao * , Haochen Tang * , Juan Blanch * , Jiyun Lee + , Todd Walter * and Per Enge * * Stanford University, USA + KAIST, Korea September 23,
Grace Xingxin Gao*, Haochen Tang*, Juan Blanch*, Jiyun Lee+, Todd Walter* and Per Enge*
* Stanford University, USA + KAIST, Korea
Research funded by Federal Aviation Administration
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Ionosphere Delay Troposphere Delay
Signal in space error
Propagation error
Receiver and local environment error
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– signal-in-space, propagation and receiver errors have been well studied, but better understanding is still required – Essential for GPS integrity
4.42*URA (User Range Accuracy)
– KAIST, Jiyun Lee. GEAS presentations since early 2009 – Ohio Univ., Frank Van Grass. GEAS presentation 2009 – FAATC, Tom McHugh for WAAS PAN report – IIT, Boris Pervan, et al. GEAS presentation in Sept. 2008 – Aerospace, Karl Kovach, presented at SCPNT in Nov. 2008 – David L. M. Warren and John F. Raquet, Broadcast vs. precise GPS ephemerides: a historical perspective, GPS Solutions, 2004 – Jefferson D, Bar-Sever Y (2000) Accuracy and consistency of broadcast GPS ephemeris data. Proc ION-GPS-2000
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Ionosphere Troposphere
Signal in space error
Propagation error
User receiver error
Signal in space error
Signal in space error = total pseudo-range error
Signal in space error satellite position error + clock error
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Pick proper broadcast ephemerides based on the time of the truth Propagate broadcast satellite positions to the time of the truth Propagate broadcast satellite clock error to the time of the truth Calculate the difference between the propagated broadcast ephemerides and the truth Project the ephemeris error to a certain receiver on Earth
Start End
Signal in space error
Signal in space error = satellite position error + clock error
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Data Source: Wide Area Augmentation System (WAAS) / National Satellite Test Bed (NSTB) Network
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http://earth-info.nga.mil/GandG/sathtml/StationMap.gif
Broadcast ephemeris: International GNSS Service (IGS) network Precise ephemeris: National Geospatial-Intelligence Agency (NGA) network
http://igscb.jpl.nasa.gov/network/netindex.html
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No Yes Include all SIS errors Yes No Remove all non SIS errors Yes No Depend on post-processed truth Available Difficult to retrieve past data Data availability Worldwide, but not even Limited (CONUS) Receiver coverage Yes No for WAAS Receiver glitches Low, 15 min High, every 1 sec Data update rate No Yes Control of data source IGS & NGA WAAS & NSTB Data Source Bottom-up Top-down
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Worst projected ephemeris error ( )
, , , X Y Z b ∆ ∆ ∆ ∆
Zoom in Planned Outage PRN 10, Day 39 of 2007
SV set unhealthy SV set unhealthy
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Atlantic City NJ, 39.44º N 74.56º W 100-sec smoothing PRN 10 Day 39
17 17.5 18 18.5 19 19.5 20 20.5 21
10 20 30 40 50 UTC (hour) Projected Ephemeris Error (m) 100-sec smooth Actual Error Calculated Error
Top-down Bottom-up
Top-down Bottom-up
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Atlantic City NJ, 39.44º N 74.56º W
17 18 19 20 21 22 23 24
1 2 3 UTC (hour) Discrepancies of projected ephemeris error (meters) 100-sec smooth
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Atlantic City NJ, 39.44º N 74.56º W 15-min smoothing PRN 10 Day 39
17 17.5 18 18.5 19 19.5 20 20.5 21
10 20 30 40 50 UTC (hour) Projected Ephemeris Error (m) 15-min smooth Actual Error Calculated Error
Top-down Bottom-up
Top-down Bottom-up
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Atlantic City NJ, 39.44º N 74.56º W
17 18 19 20 21 22 23 24
1 2 3 UTC (hour) Discrepancies of projected ephemeris error (meters) 15-min smooth
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Anomaly
Worst projected ephemeris error ( )
, , , X Y Z b ∆ ∆ ∆ ∆
PRN 07, Day 229 of 2007
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5 10 15 20 25 UTC time (hours) Worst projected ephemeris error (meters) Projected ephemeris error URA 4.42*URA Actual projected ephem error
Bottom-up Top-down
Arcata CA, 40.97º N 124.11º W
Top-down Bottom-up
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4 5 6 7 8 9 10 11
1 2
UTC Time (hour) worst projected ephemeris error discrepancies (m)
Arcata CA, 40.97º N 124.11º W
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– Top-down: strips off all other errors from the pseudo-range errors, leaves alone signal-in-space errors – Bottom-up: builds up signal-in-space errors from satellite position errors and clock errors
No Yes Include all SIS errors Yes No Remove all non SIS errors Yes No Depend on post-processed truth Available Difficult to retrieve past data Data availability Worldwide, but not even Limited (CONUS) Receiver coverage Yes No for WAAS Receiver glitches Low, 15 min High, every 1 sec Data update rate No Yes Control of data source IGS & NGA WAAS & NSTB Data Source Bottom-up Top-down
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– Inaccurate estimate of iono/tropo/multipath/receiver clock errors – Other error sources, e.g. code-carrier incoherence, signal deformation, Inter- signal errors, satellite antenna phase center variation, satellite antenna group delay center variation, relativistic correction errors, etc – Inaccuracies in precise ephemerides – Incorrect choice of active broadcast ephemeris
Arcata, CA Atlantic City, NJ Site investigated Satellite clock Satellite position Outage type No Yes Planned outage? PRN 07, Day 229 of Year 2007 PRN 10, Day 39 of Year 2007
The authors acknowledge Tom McHugh from the FAA Tech Center for providing the WAAS/NSTB data of the 2007 outages.
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Dual-frequency iono-free combination:
2 2 1 2 1 2 2 2 2 2 1 2 1 2 2 2 1 2 1 2 2 2 2 2 1 2 1 2
, ,
L L IF L L L L L L L L IF L L L L L L
f f f f f f f f f f f f ρ ρ ρ = − − − Φ = Φ − Φ − −
Code measurement Carrier measurement Iono-free combination of code measurements Ionosphere Troposphere
Signal in space error
Propagation error
User receiver error
: : :
IF
ρ ρ Φ
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Estimate and removal of troposphere error based on WAAS Minimum Operational Standard (MOPS) :
Troposphere delay for satellite Troposphere
Signal in space error
Propagation error
User receiver error
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i tropo TVE i
i
Troposphere mapping function for satellite i Troposphere Vertical Error
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Carrier smoothing using a recursive filter of length M:
1 1 1 1
1 ( 1) ( ) ( ) [ ( ) ( ( ) ( ))], ( ) ( ).
i i i i i
M t t t t t M M t t ρ ρ ρ ρ ρ
− −
− = + + Φ − Φ =
Code measurement Carrier measurement Smoothed pseudo-range measurement
Signal in space error
Propagation error
User receiver error
( ) : ( ) : ( ) : t t t ρ ρ Φ
Carrier smoothing:
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Carrier smoothing using a recursive filter of length M: Signal in space error
Propagation error
User receiver error
error for pseudo-ranges from all satellites
space error is zero-mean i.i.d.
from those healthy satellites cancels out satellite in space errors and leaves alone the user clock bias
Common among satellites, remains after averaging Different among satellites, cancels out after averaging
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(IGS) network
measurements and navigation data in RINEX format
Agency (NGA) network
ephemeris
clock information
http://earth-info.nga.mil/GandG/sathtml/StationMap.gif http://igscb.jpl.nasa.gov/network/netindex.html
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Pick proper broadcast ephemerides based on the time of the truth Propagate broadcast satellite positions to the time of the truth Propagate broadcast satellite clock error to the time of the truth Calculate the difference between the propagated broadcast ephemerides and the truth Project the ephemeris error to a certain receiver on earth
Start End Choose the most recent TTOM Use Kepler’s equations Based on the clock drift and the drift rate The broadcast and true ephemerides are of the same time stamp for fair comparison Project along line-of-sight between the satellite and the receiver
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Ephemeris error ( )
, , X Y Z ∆ ∆ ∆
The ephemeris anomaly of PRN 10 on Day 39 is due to satellite position errors. Zoom in PRN 10, Day 39 of 2007
SV set unhealthy SV set unhealthy
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PRN 07, Day 229 Year 2007