Airborne Topographic Mapper Calibration Procedures and 

Accuracy Assessment

NASA/TM–2012-215891

February 2012

Chreston F. Martin, WIlliam B. Krabill, Serdar S. Manizade, Rob L. Russell, John G. Sonntag, 

Robert N. Swift, and James K. Yungel

National Aeronautics and 

Space Administration 

Goddard Space Flight Center

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Airborne Topographic Mapper Calibration Procedures and 

Accuracy Assessment

NASA/TM–2012-215891

February 2012

Chreston F. Martin 

Sigma Space, Inc., Lanham, MD 

William B. Krabill

Sigma Space, Inc., Lanham, MD 

Serdar S. Manizade 

URS, Inc., San Francisco, CA 

Rob L. Russell 

Sigma Space, Inc., Lanham, MD 

John G. Sonntag 

URS, Inc., San Francisco, CA 

Robert N. Swift 

Sigma Space, Inc., Lanham, MD 

James K. Yungel

URS, Inc., San Francisco, CA
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Contract No. NNG09HP18C with the National Aeronautics and Space Administration. 

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i

Table&of&Contents

Table!of!Contents......................................................................................................................................iv

List!of!Tables...............................................................................................................................................iv

List!of!Figures..............................................................................................................................................!v!

1.0!Introduction..........................................................................................................................................!1!

2.0!ATM!System!Description!.................................................................................................................!4!

3.0!ATM!Calibration!and!Accuracy!Assessment!...........................................................................!7!

3.1!ATM!Calibration!from!Ramp!Pass!Overflights!..................................................................!7!

3.2!Crossing!Pass!Accuracy!Assessment!...................................................................................10

4.0!Trajectory!Computation!and!Accuracy!...................................................................................15

5.0!Attitude!Errors!and!Their!Effects!on!Surveys......................................................................22

6.0!Error!in!Knowledge!of!Horizontal!Footprint!Positioning...............................................26

6.1!Laser!Pulse!Timing!Errors!.......................................................................................................27

6.2!Scan!and!Date!Timing!Errors!.................................................................................................!27

6.3!Scan!Azimuth!Bias!Error!..........................................................................................................28

6.4!Heading!Bias!Error .....................................................................................................................28

6.5!Pitch!and!Roll!Error....................................................................................................................29

6.6!Heading!Error ...............................................................................................................................29

6.7!GPS!Positioning!Error................................................................................................................29

6.8!Total!Horizontal!Error ..............................................................................................................30

7.0!Error!Analysis!Summary!...............................................................................................................30

8.0!References...........................................................................................................................................32

List&of&Tables

Table!1.!Parameter!Estimates!from!Punta!Arenas!Ramp!Passes!from!Fall!2009!..........!7!

Table!2.!Measured!Range!Calibration!for!ATM!T3!Laser!..........................................................!8!

Table!3.!Estimated!Range!Biases!from!Ramp!Passes.!α!Fixed!at!11.062°.!........................!9!

Table!4.!Summary!of!Crossover!Differences!from!ATM!Campaigns.!.................................!21

Table!5.!Summary!of!Estimated!Pitch!and!Roll!Errors!for!ATM!Missions.!......................26

Table!6.!Summary!of!Estimated!Pitch!and!Roll!Errors!for!ATM!Missions!(converted!

into!vertical!error). .................................................................................................................................!26

Table!7.!Characteristics!and!Accuracies!of!ATM!Ice!Sheet!Surveys.!..................................31
ii

List&of&Figures

Figure!1.!Northern!Hemisphere!ATM!Operations.!......................................................................!1!

Figure!2.!Southern!Hemisphere!ATM!operations.!.......................................................................!2!

Figure!3.!Depiction!of!ATM!survey!mission!over!Greenland!following!previously!

surveyed!terrain.........................................................................................................................................!3!

Figure!4.!Primary!instrumentation!components!of!the!Airborne!Topographic!

Mapper. ..........................................................................................................................................................!4!

Figure!5.!Aircraft!layout!of!ATM!components.!Measurements!of!dX,!dY!(not!shown)!

and!dZ=dZ1+dZ2!are!made!with!tape!measure!and!plumb!bob.!............................................!6!

Figure!6.!Devicq!Glacier!ATM!crossing.!..........................................................................................11

Figure!7.!Crossing!pass!ATM!elevations.!.......................................................................................12

Figure!8.!Estimated!corrections!for!crossing!point!elevation!differences.!.....................14

Figure!9.!Computed!corrections!for!crossing!pass!along!latitude!band!a74.92625°.!.!14

Figure!10.!Groundtracks!for!2009!Antarctica!campaign.!.......................................................17

Figure!11.!Groundtracks!for!2010!Greenland!campaigns.!.....................................................18

Figure!12.!Mean!and!RMS!differences!between!Applanix!and!gitar!trajectory!heights!

for!2009!Antarctica!campaign.!...........................................................................................................19

Figure!13.!Mean!and!RMS!differences!between!Applanix!and!gitar!trajectory!heights!

for!2010!Greenland!DC8!campaign.!.................................................................................................!20

Figure!14.!Pitch!and!roll!errors!estimated!for!the!2008!DC8!deployment!to!

Antarctica.!...................................................................................................................................................23

Figure!15.!Pitch!and!roll!errors!estimated!for!the!2010!DC8!deployment!to!

Greenland....................................................................................................................................................24

Figure!16.!Pitch!and!roll!errors!estimated!for!the!2010!P3!deployment!to!Greenland.

.........................................................................................................................................................................25
1

1.0&Introduction

Late! in! 2008,! recognizing! that! ICESata1! was! near! its! end! of life! and! that! ICESata2!

would!not!be!launched!until!2015!or!2016,!NASA!initiated!a!program!using!aircraft!

to! “fill! this! gap”! in! critical! Polar! measurements.! The! purpose! of! this! project! was!

initially to! collect! aircraft!laser! altimeter! data! under! the! failing! ICESat!in! order! to!

assess! the! quality! of! data! from! the! currently! very! low! power! transmitter,! and! to!

acquire! data! to! bridge! the! gap! between! ICESata1! and! ICESata2.! ! IceBridge! data!

collection!began!with!the!ATM as!the!prime!sensor in!late!March 2009!by!combining!

with!the!onagoing!Arctic!Ice!Mapping!component!of!the!PARCA!program,!initiated!by!

the! Cryospheric! Sciences! Program! at! NASA! in! the! early! 1990’s.! IceBridge! has!

evolved!into!a!multiaaircraft!multiaremote!sensor!program,!built!on!a!decade!and!a!

half of! highly! successful! flight! experience! by! the! Airborne! Topographic! Mapper!

(ATM)!team!with!previous!operations!in!Greenland,!Arctic!Canada,!Svalbard,!Alaska,!

Patagonia,!and!Antarctica!(Figures!1!and!2).

Figure'1.'Northern'Hemisphere'ATM'Operations.
2

Figure'2.'Southern'Hemisphere'ATM'operations.

The!ATM!is!a!conicallyascanning!laser!altimeter!that!accurately!measures!the!surface!

topography!of!a!swath!of!terrain!directly!beneath!the!path!of!the!aircraft!(Krabill!et!

al.!2002).!!It!comprises!the!scanning!laser!with!associated!optics!and!data!system,!a!

differential!GPS!system!for!accurate!positioning!of!the!aircraft,!and!inertial!sensors!

(accelerometers!and!gyros)!to!measure!aircraft!roll,!pitch,!and!heading.!Using!these!

three!systems,!each!laser!pulse,!or!“shot”,!is!assigned!threeadimensional!geographic!

coordinates.!With!thousands!of!these!shots!per!second,!the!result!is!a!topographic!

survey!of!a!swath!of!width!ranging!between!0.4!and!1.2!km,!depending!on!aircraft!

height!(generally!500!– 1500!m)!and!offanadir!scan!angle.!!Elevation!accuracy!is!

typically!about!10!cm!(Krabill!et!al.,!2002),!with!one!measurement!for!every!few!sq.!

m.!!ATM!surveys!alone!can!be!used!for!change!detection,!with!laser!swaths!rea

surveyed!after!a!few!years,!and!differences!between!the!two!surveys!yielding!

estimates!of!elevation!change!during!the!interim.!!ATM!surveys!can!also!be!used!for!

comparison!with!satellite!altimeter!measurements,!again!yielding!elevation!change!

rates!provided!the!altimeter!measurements!are!compatible!with!the!ATM!laser!

measurements.!!The!ATM!has!collected!high!quality!topographic!data!from!a!wide!

variety!of!platforms,!including!the!NASA!P3,!a!Chilean!Navy!P3,!a!US!Navy!P3,!the!

NASA!DC8,!the!NCAR!Ca130,!and!a!halfadozen!Twin!Otters.
3

The!accuracy!of!ATM!surveys!has!been!assessed!previously!(Krabill!et#al.!1995,!

2002).!!!In!this!paper!we!consider!the!accuracy!that can!be!and!has!been!achieved!

using!updated instrumentation!and!techniques,!with!the!primary!application!the!

surveying!of!Greenland!and!Antarctic!ice!sheets!in!recent!years.!!Section!2!describes!

the!instrumentation!currently!used.!Section!3!describes!the!techniques!used!for!

analyzing!ATM!ramp!passes!at!the!base!airport,!and!crossing!passes!at!the!science!

target!sites,!to!determine!accuracy!in!ATM!measurements.!!Section!4!describes!the!

procedures!used!for!producing!aircraft!trajectories,!compares!trajectories!computed!

using!two!entirely!different!techniques,!and!assesses!trajectory!accuracy!for!several!

ATM!campaigns.!!Section!5!analyzes!the!performance!of!INS!systems!on!these!

campaigns!and!computes!the!trajectory!height!errors!due!to!INS!errors.!!Section!6!

assesses!the!various!contributions!to!horizontal!survey!errors.!!Section!7!then!

summarizes!the!overall!error levels!that would!be!expected!from!ATM!surveys.

Figure'3.'Depiction'of'ATM'survey'mission'over'Greenland'following'previously'surveyed'terrain.
4

2.0&ATM&System&Description

The!ATM!measures!ground!topography!by!determining the!distance!and!direction!

from!an!aircraft!to!a!laser!spot!on!the!ground.!!The!system!components!fall!into!four

categories:!GPS!(global!positioning!system)!components!that!are!used!to!determine!

the!location!of!the!aircraft;!INS1 components!that!determine the attitude!of!the!

aircraft;!the!LiDAR component!that!measures!the!slant!range!to!the!surface;!and!the!

scanner!component!which!steers!the!direction!of!the!optical!path!out!of!the!aircraft.!!

Figure!4 shows!these!components!in!a!block!diagram.!!There!is!some!duplication!

among!the!components,!providing!some!redundancy!and!also!allowing!equipment!

intercomparisons.

Figure'4.'Primary'instrumentation'components'of'the'Airborne'Topographic'Mapper.

GPS!receivers!from!Javad!and!Applanix (POS!AV!510!&!610)!accept!signals!from!a!

GPS!antenna!mounted!on!the!top!of!the!aircraft!fuselage.!!GPS!data!from!ground!

receivers!are!combined!with!airborne!data!to!produce!a!trajectory!at!a!2Hz!rate!for!

the!phase!center!of!the!aircraft!antenna.!!Aspects!of!trajectory!determination!are!

discussed!is!Section4.!!!The!location!of!the!antenna!phase!center!is!thereby!specified!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 Inertial!Navigation!System!(INS)!is!the!term!used!to!describe!the!apparatus!used!to!

measure!the!aircraft!attitude.!!Inertial!Measurement!Unit!(IMU)!is!equivalent!to!INS!for!the!

purpose!of!this!document.
5

in!the!most!recent!ITRF,!i.e.!the!Terrestrial!Reference!Frame!defined!by!the!

International!Earth!Rotation!and!Reference!Systems!Service.

Attitude!is!provided!by!the!Applanix!units!and!by!a!Litton!LNa100G!INS/GPS.!!

Specifically,!these!units!measure!the!heading,!pitch,!and!roll!angles!of!the!units!

themselves,!which!may!differ!slightly!from!the!aircraft!frame!or!from!the!ATM!

frame.!!The!primary!(and!most!accurate)!INS!measurement!is!the!Applanix!Model!

610!system.!Factory!specifications!for!the!610!are

(http://www.applanix.com/media/downloads/products/specs/POSAV_SPECS.pdf,!

version!issued!June!2009):

Applanix!GPS!trajectory!accuracy:

POS!AV!Absolute!Accuracy (RMS)!Model!610!Post!Processed

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!Position:!0.05!to!0.30!meters

Applanix!POS!AV!INS

POS!AV!Absolute!Accuracy (RMS)!Model!610!Post!Processed

Roll!and!Pitch 0.0025°

True!Heading 0.0050°

In!order!to!meet!the!attitude!specifications,!the!aircraft!must!make!180° maneuvers!

periodically,!so!the!numbers!are!somewhat!optimistic!for!realistic!mapping!

missions.!!A!detailed!discussion!related!to!aircraft!attitude!determination!and!

correction!is presented!in!Section!5.

The!LiDAR contains!a!pulsed!green!laser!that!is!directed!downward!from!the!

aircraft,!nominally!at!a!5!kHz!rate.!!A!telescope!coaligned!with!the!laser!receives!the!

signal!backscattered!from!the!ground!below,!and,!if!the!input!signal!exceeds!a!set!

threshold, sends!it!through!a!photodetector!to!an!Acqiris!8!bit!waveform!digitizer!

that!captures!typically!160!samples!at!0.5!nsec!resolution.!!A!portion!of!the!

transmitted!laser!pulse!is!also!sent!to!the!photodetector!and!digitizer!via!an!optical!

fiber.!!The!delay!between!laser!pulse!transmission!and!the!detection!of!the!reflection

from!the!ice!surface is extracted!from!the!digitized!waveforms during!post!flight!

processing.!!Applying!a!75%!constantafraction!leading!edge!tracking!algorithm!to!

both!transmit!and!receive!pulses!with!an!empirically!derived!adjustment!for!

saturated!waveforms!refines!the!elapsed!time!between!the!two!waveforms.!The!

time!delay!multiplied!by!the!speed!of!light!through!the!atmosphere!yields!slant!

range.!!Accuracy!of!correlating!transmitted!and!received!pulses!is!around!0.2!nsec,!

leading!to!a!noise!floor!of!around!3!cm!in!range.!!Atmospheric!refraction!correction!

is!applied!to!the!range!at!a!later!stage!of!processing!with!consideration!of!the!

aircraft!altitude!and!a!quadratic!model!of!refraction!versus!altitude.!

The!scanner!is!a!mirror!rotating!about!an!axis!which!is!slightly!offset!from!the!

mirror!normal.!!The!scanner!typically!rotates!at!20!Hz.!!The!instantaneous!position,!

called!the!scan!azimuth,!is!determined!from!a!pulse!generated!once!per!revolution.!!

The!high!frequency!errors!in!azimuth!measurement!will!be!discussed!in!Section!6!

and!the!azimuth!bias!error!will!be!discussed!in!Section!3.1.
6

Two!ATM!systems!have!operated!on!most!Operation!IceBridge!missions,!each!

scanner!having!a!different!scan!angle!(maximum!offanadir!angle).!!For!several!years,

scanners!having!a!22° and!15° angle!have!been!operated,!and!a!2.5° scanner!was!

flown!during!the!spring!2009!campaign.!!!At!a!nominal!altitude!of!500m!above!

ground!level,!the!22° scanner!sweeps!the!LiDAR!footprint!across!a!400m!wide!

swath.!!The!scanners typically!spin!at!a!20!Hz!rate.!!In!the!following!sections,!the!

LiDAR transceiver with!the!22° scanner!may be!referred!to!as!the!T3!laser!and the!

15° one!as!the!T2!laser.

The!geometric!relationship!of!the!ATM!components!on!the!aircraft!is!shown!in!

Figure 5.!!The!separation!between!the!GPS!antenna!and!the!scan!mirror!on!an!

aircraft!can!be!as!much!as!4!m!horizontally!and!4!m!vertically.!!Transforming!

coordinates!from!the!GPS!to!the!scan!mirror!relies!in!part!on!tape!measure!and!

plumb!bob!measurements!(as!shown!in!the!Figure!5)!which!are!measured!once!(in!

aircraft!coordinates)!and!then!assumed!constant!for!a!campaign.!!In!addition,!

measurements!by!the!attitude!sensor!are!needed!to!account!for changing!aircraft!

orientation.

Other!parameters!needed!to!convert!laser!ranges!to!surface!coordinates!(latitude,!

longitude,!and!elevation)!are!the!orientation!(heading,!pitch,!and!roll)!of!the!scan!

mirror!and!the!two!angles,!α!and!β,!shown!in!Figure!5.!!The!estimation!of!these!

parameters,!their!errors,!and!their!effects!will!be!discussed!in!Section!3.1.

Figure'5.'Aircraft'layout'of'ATM'components.'Measurements'of'dX,'dY'(not'shown)'and'dZ=dZ1+dZ2 are'

made'with'tape'measure'and'plumb'bob.
7

3.0&ATM&Calibration&and&Accuracy&Assessment

The!ATM!system,!as!discussed!in!the!previous!section,!includes!a!number!of!

components!and!also!requires!the!calibration!of!a!number!of!parameters.!!This!

calibration!is!normally!performed!around!a!base!site!which!includes!a!ground!GPS!

receiver!and!a!surveyed!surface!against!which!to!compare!the!ATM!ranging!

measurements.!!The!surveyed!surface!is!usually!a!ramp!surface!at!an!airbase.!!For!

assessment!of!performance!during!a!mission,!crossings!of!mission!flight!paths!are!

the!primary!tools!for!measuring!consistency!and!inferring!accuracy.!!Ramp!passes!

and!crossing!passes!are!discussed!separately!below.

3.1&ATM&Calibration&from&Ramp&Pass&Overflights

The!ATM!(along!with!associated!inertial!measuring!instruments)!is!almost!always!

installed!on!the!aircraft!a!few!days!or!weeks!prior!to!a!campaign!and!is!then!rather!

promptly!uninstalled!after!the!campaign.!!In!order!to!obtain!the!desired!survey!

accuracy,!the!ATM!must!be!appropriately!aligned!with!the!INS!system.!!We!refer!to!

the!ATM!mounting!angles!relative!to!the!INS!orientation!as!heading,!pitch,!and!roll!

mounting!biases.!!In!addition!to!these!three!mounting!angles,!there!are!several!other!

angles!associated!with!the!scanning!laser!system:!!the!angle!beta!(β shown!in!

Figure3)!between!the!entering!laser!beam!and!the!spin!axis!of!the!scan!mirror;!the!

angle!alpha!(α'shown!in!Figure!3)!between!the!scan!mirror!spin!axis!and!the!normal!

to!the!scan!mirror;!and!the!bias!in!the!measured!azimuth!of!the!scan.!!!To!one!degree!

or!another,!all!these!parameters!can!be!estimated!from!passes!over!surveyed!airport!

ramps.

Table'1.'Parameter'Estimates'from'Punta'Arenas'Ramp'Passes'from'Fall'2009

Parameter Name Parameter 

Value

Change Sigma

Scan Azimuth Bias 1 257.445508 0.008008 0.026952

Alpha 11.063178 -0.000922 0.004842

Beta 44.503711 -0.023689 0.031430

INS Lag -0.007712 -0.007712 0.005469

Scanner Head Bias 179.644490 -0.250610 0.107223

Scanner Pitch Bias -0.401050 0.005950 0.004028

Scanner Roll Bias -0.068854 0.011046 0.030808

Scanner Range Bias -25.940646 -0.015646 0.027136

The!basic!geometry!of!a!ramp!pass!is!similar!to!that!shown!in!Figure!1!except!that!

the!surface!underneath!the!aircraft!is!not!ice!but!rather!a!surveyed!ramp.!!The!ATM!

provides!measurements!of!range!and!scan!angle;!the!INS!provides!heading,!pitch,!

and!roll;!and!the!GPS!(aircraft!and!ground)!receivers!provide!position!of!the!aircraft!

GPS!receiver.!!From!these!measurements,!the!above!six!biases!need!to!be!estimated.!!

Table 1!shows!the!summary!of!the!results!of!processing!eight!ramp!passes!from!the!
8

2009!Antarctic!mission!based!out!of!Punta!Arenas,!Chile.!!The!table!also!includes!INS!

lag!(included!because!INS!lags!have!been!a!problem!for!older!INS!systems!but!here!

adjusting!to!a!value!which!is!not!significant)!and!the!range!bias!parameter!which!we!

will!discuss!prior!to!discussing!Table!1.

Laser!range!measurements!must,!of!course,!be!calibrated!since!any!error!in!range!

bias!goes!almost!1!to!1!into!elevation!error.!!ATM!ranges!are!calibrated!in!ground!

tests!in!which!a!target!board!is!set!up!150m!or!more!from!the!aircraft!(or!from!the!

scanner!if!the!system!is!not!installed!in!an!aircraft)!and!several!minutes!of!ranging!

measurements!are!made!to!it,!with!the!“true”!range!measured!by!an!Electronic!

Distance!Measuring!(EDM)!system.!!The!ATM!ranges!are!averaged!and!the!range!

bias!determined!by subtracting!the!EDM!measurement.!!Since!range!biases!have!

been!quite!stable!over!the!years,!ATM!bias!measurements!have!been!somewhat!

infrequently made.!!Table!2!shows!a!summary!of!some!of!the!range!measurements!

for!the!“T3”!laser!normally!deployed!with!the!22° scanner.!!There!is!considerable!

scatter!in!the!measurements,!although!there!is!no!clear!trend!over!the!multiayear!

period.!One!explanation!for!the!scatter!is!that!the!measurements!are!sometimes!

difficult!to!make,!especially!in the!survey!regions,!due!to!high!winds,!limited!survey!

ranges,!and!a!number!of!other!factors.

Table'2.'Measured'Range'Calibration'for'ATM'T3'Laser

Date!of!

Calibration

Mean!Calibration

060610 a26.02!m

070410 a25.96!m

070430 a25.91!m

070525 a26.02!m

070824 a25.99!m

070830 a25.98!m

071004 a25.96!m

080402 a25.95!m

090324 a25.97!m

Average a25.973!m!±!3.4!cm

It!should!be!noted!that!the!range!bias!measured!in!ground!tests!is!the!error!made!in!

the!measurement!from!the!scan!mirror!to!the!target.!!In!ramp!passes,!however,!the!

range!bias!estimates!the!endatoaend!contribution!from!several!error!sources.!!The!

range!calculated!to!the!surveyed!surface!starts!with!the!trajectory!determination!of!

the!aircraft!GPS!antenna!phase!center!position!which!must!then!be!transferred!to!

the!scan!mirror!over!a!distance!of!5a6!m!or!so.!!As!has!been!pointed!out!in!Section!2,!

this!transfer!involves!tape!measure!determination!of!GPS!antenna!to!scan!mirror!

relative!positions!in!aircraft!coordinates.!!In!flight,!these!coordinates!have!to!be!

transferred!to!earth!fixed!Cartesian!coordinates!using!INS!measurements!– which!

are!made!by!a!system!which!is!probably!installed!tilted!relative!to!the!aircraft!floor!
9

by!a!few!tenths!of!a!degree!(as!is!typically!observed!by!comparing!different!INS!

systems).!!Finally,!the!vertical!separation!of!the!GPS!antenna!and!scan!mirror!is!

measured!to!the!base!of!the physical!antenna.! An!attempt!was!made!to!estimate!the!

relative!positions!of!the!aircraft!antenna!L1!and!L2!phase!centers!using!an!~3.5!

hour!GPS!data!set!taken!during!a!takeoff!delay!while!mechanical!problems!were!

being!corrected!on!November!16, 2009!at!Punta!Arenas,!Chile!during!the!Antarctic!

campaign.!!The!estimated!L2!phase!center!was!1.6!cm!below!the!L1!phase!center,!

which!would!lead!to!an!L3!phase!center!some!2.5!cm!above!the!L1!phase!center.!!

Unfortunately,!the!physical!location!of!the!L1!phase!center!is!unknown.!!From!NGS!

measurements!on!an!antenna!range!

(http://www.ngs.noaa.gov/ANTCAL/images/ant_info.abs),!the!L1!phase!center!is!

2.5!mm!above!the!antenna!base!and!the!L2!phase!center!37.8!mm!above!the!base,!

leading!to!an!L3!phase!center!4.6!cm!below!the!base.!!But!the!antenna!installed!in!an!

aircraft!is!expected!to!have!quite!different!phase!characteristics!than!those!observed!

from!antenna!range!tests,!so!both!measurements!could!be!correct!for!their!

environments.!!So!the!lack!of!an!antenna!phase!center correction,!along!with!several!

other!error!sources,!can!propagate!significant!uncertainty!into!the!transformation!of!

coordinates!from!GPS!phase!center!to!the!scan!mirror.!!However,!since!these!effects!

are!compensated!for!in!the!ramp!pass!range!bias!estimate,!ramp!pass!results!can!

correct!for!the!combination!of!these!effects.!!Further,!the!compensation!is!carried!

over!to!survey!data!processing!since!the!same!processing!procedures!are!used.

Turning!now!to!the!consistency!of!ramp!passes,!Table!3!shows!the!Punta!Arenas

range!bias!estimate!along!with!estimates!from!two other!ramp!pass survey!

campaigns.!!As!noted in!the!Table!caption,!the!value!of!α!(see!Figure!5)!is!fixed.!!(In!

Table!1,!α!is!allowed!to!adjust!and!its!slight!adjustment!leads!to!a!slightly!different!

range!bias.)!!The!mean!value!of!these!three estimates!is!a25.926!m.!!If!2.5!cm!of!

phase!center!correction!had!been!applied,!the!average!would!be!a25.951!m,!differing!

from!the!ground!calibration!average!value!by!only!2.2!cm.

Table'3.'Estimated'Range'Biases'from'Ramp'Passes.'α'Fixed'at'11.062°.

Location Date Estimated!Range!Bias

Wallops!Island,!VA April!4,!2007 a25.931!m

Ilullisat,!Greenland July!2008 a25.912!m

Punta!Arenas,!Chile OctaNov!2009 a25.935!m

In!practice,!the range!bias!used!in!ATM!data!processing!is!chosen!to!be!within!1a2!

cm!of!the!ramp!pass!measured!range!bias!but!always!within!reasonable!agreement!

with!ground!calibrations.!!Based!on!this!procedure!and!the!fact!that!the!ramp!pass!

calibrations!compensate!in!principle!for!a!number!of!small!errors,!we!estimate!an!

uncertainty!of!2!cm!which!will!be!adopted!as!a!systematic!error!for!elevation!errors!

common!to!all!missions!in!a!campaign.

The!data!processing!summarized!in!Table!1!was!made!with!an!assumed!range!

measurement!noise!level!of!1!m.!!The!sigmas!for!the!estimated!parameters!in!the!
10

table!(units!for!range!are!meters!and!degrees!for!angles)!should!thus!be!

conservative!considering!that!the!RMS!data!fits!are!better!than!10!cm.!!The!

parameter!with!the!largest!uncertainty!is!scanner!heading!bias,!but!the!estimate!

should!still!be!better!than!0.1°.!!Sigmas!for!beta!and!roll!mounting!bias!look!much!

larger!than!the!sigma!for!pitch!bias.!!However,!the!correlation!between!the!two!is!

very!high!(0.988)!so!the!combined!effect!on!a!scan!position!should!be!comparable!to!

that!for!pitch.!!The!correlation!between!alpha!and!range!bias!(0.85)!also!looks!high.!!

For!a!single!pass,!the!correlation!would!be!near!1.0!because!the!aircraft!determines!

the!height,!which!is!related!to!range!and!α!by!the!approximate!relation

Height!≈!Range!*!cos(2α) (1)

With!multiple!passes!at!different!heights!over!the!ramps,!the!correlation!becomes!

sufficiently!small!that!both!range!bias!and!α!can!be!estimated!with!reasonable!

confidence.

3.2&Crossing&Pass&Accuracy&Assessment

While!nominal!values!of!parameters!affecting!ATM!survey!accuracy!are!determined!

from!passes!over!surveyed!ramp!surfaces!normally!at!the!aircraft!base!station!and!

close!to!a!ground!GPS!site!used!as!a!reference!for!the!aircraft!trajectory,!

performance!at!the!primary!survey!site!hundreds!of!kilometers!away!can!be!quite!

different.!!The!INS!system!used!can!be!expected!to!drift!to!some!extent!and!aircraft!

trajectory!accuracy!will!be!affected!by!the!large!separation!from!the!ground!base

station!(or!stations).!!For!these!reasons,!attempts!are!made!to!validate!system!

parameters!at!the!survey!site!to!the!extent!possible.!!The!primary!technique!used!for!

this!validation!is!the!use!of!crossing!ATM!passes,!either!on!the!same!mission!day!or!

on!different!days.!!Such!passes!normally!occur!simply!due!to!the!nature!of!the!

survey!mission,!with!a!prime!example!being!detailed!glacier!surveys!in!which!

aircraft!tracks!are!performed!in!a!grid!pattern.!!The!assumption!made!in!processing!

crossing!passes!is!that!the!surface!topography!remains!unchanged!between!the!

passes.!!The!validity!of!this!assumption!varies,!of!course,!with!the!dynamics!of!the!

surveyed!terrain!and!decreases!with!time.!!However,!we!would!expect!crossing!

passes!made!on!the!same!day!to!find!very!similar!topography!and!passes!separated!

by!a!few!days!do!have!a!high!probability!of!similar!topography!except!at!very!low!

elevations.

Assuming!similar!topography,!the!primary!parameters!which!would!be!expected!to!

affect!the!differences!in!topography!measured!by!two!crossing!passes!are!aircraft!

pitch!and!roll!errors!and!trajectory!height!errors!(more!specifically,!differences!

between!the!trajectory!height!errors).!!For!same!day!crossings,!the!height!error!

differences!would!be!expected!to!be!rather!small!since!a!high!proportion!of!the!

systematic!errors!in!the!trajectories!should!be!common.!!In!general,!height!

differences!for!passes!separated!by!only!by!a!day!or!two!would!be!expected!to!be
11

Assuming!similar!topography,!the!primary!parameters!which!would!be expected!to!

affect!the!differences!in!topography!measured!by!two!crossing!passes!are!aircraft!

pitch!and!roll!errors!and!trajectory!height!errors!(more!specifically,!differences!

between!the!trajectory!height!errors).!!For!same!day!crossings,!the!height!error!

differences!would!be!expected!to!be!rather!small!since!a!high!proportion!of!the!

systematic!errors!in!the!trajectories!should!be!common.!!In!general,!height!

differences!for!passes!separated!by!only!by!a!day!or!two!would!be!expected!to!be!

larger!than!sameaday!crossing!differences,!primarily!due!to!systematic!trajectory!

errors,!although!this!depends!upon!topography!variability.!It!should!also!be!noted!

that!there!is!a!limit!to!how!rough!the!terrain!can!be!without!having!so!much!noise!

that!little!can!be!extracted!from!the!pass!differences.

Figure'6.'Devicq'Glacier'ATM'crossing.

Figure!6!shows!the!location!of!two!ATM!crossing!passes!made!on!October!16,!2009!

on!Devicq!glacier!in!Antarctica.!!The!circled!crossing!will!be!discussed!here.!!As!will!

be!noted!from!the!figure,!the!two!passes!cross!at!a!near!90° angle,!a!desirable!

characteristic!for!accurate!parameter!estimation.!!!Figure!7!shows!the!spots!whose!

locations!and!elevations!were!measured!by!each!pass.!!The!points!are!coloracoded to!

show!the!elevations!(around!250m)!along!the!two!swaths!and!are!separated!by!only!

about!30!minutes!in!time.!!It!will!be!noted!that!the!edges!of!the!earlier!pass!(the!

vertical!one)!is slightly!curved,!indicating!that!the!aircraft!is!in!a!slight!turn,!

consistent!with!the!track!shown!in!Figure!6. The!procedure!used!in!processing!the!

crossing!is!to!difference!the!elevation!of!each!point!in!the!later!pass!from!the!

elevation!of!points!in!the!earlier!pass!that!are!within!a!specified!distance!(2!m!

nominally).!!This!gives!a!residual!and!there!are!typically!some!10000!or!more!

residuals!in!a!crossover.!!An!estimation!is!then!made!of!the!elevation!difference!and!
12

pitch!and!roll!errors!for!each!pass!which!will!produce!the!minimum!value!of!the!sum!

of!squared!residuals!– standard!least!squares!estimation.!!(In!practice,!as!a!matter!of!

convenience,!the!pitch!and!roll!errors!estimated!are!the!errors!in!pitch!and!roll!

mounting!of!the!ATM!scan!mirror.)

Figure'7.'Crossing'pass'ATM'elevations.

It!should!be!emphasized!that!the!INS!data!used!in!producing!the!plot!shown!in!

Figure!7 is!based!on!a!preliminary!processing!of!the!2009!Antarctic!mission!with!

INS!data!from!the!ln100g!inertial!system!(in!order!to!maximize!the!differences!for!

illustrative!purposes)!and!is!not!from!an!operational!processing.!!Figure!8 shows!a!

color!coded!plot!of!the!change!to!the!elevation!differences!resulting!from!the!

estimated!pitch,!roll,!and!height!adjustments!which!need!to!be!applied!in!the!

crossover!area!to!obtain!the!best!agreement!between!the!two!passes.!!The!actual!

numbers!range!from!around!a30cm!to!+20cm.!!Estimated!parameters!from!the!

crossover!were:
13

Elevation!difference: a0.024m

Pitch!error,!NaS!pass: a0.0618°

Roll!error,!NaS!pass: a0.0359°

Pitch!error,!EaW pass: a0.0238°

Roll!error,!EaW!pass: a0.0146°

Note!that!the!elevation!difference!is!real!(i.e.,!best!trajectories!were!used)!and!is!

consistent!with!what!would!be!expected!for!a!same!day!crossover,!especially!one!

with!small!time!separation.!!The!pitch!and roll!errors,!however,!are!smaller!in!the!

operational!!processing!using!Applanix!INS!data (see!Section!5).!!Although!there!are!

bands!of!color,!primarily!about!the!left!and!right!sides,!Figure!8 appears!to!be!

somewhat!noisy,!even!though!the!computed!corrections!that!are!plotted!would!be!

expected!to!be!smoothly!varying.!!To!better!understand!the!nature!of!the!

corrections,!Figure!9 shows!the!corrections!along!a!narrow!band!of!latitude.!By!

selecting!a!latitude!band!through!the!middle!of!the!crossing,!the!points!have!

effectively!been!edited!to!include!only!directly!forward!and!aft!portions!of!the!scan!

from!the!EastaWest!pass.!!The!full!scan!of!the!NorthaSouth!pass!is!included.!!The!

graph!shows!the!correction!applied.!!More!precisely,!the!graph!shows!the!combined!

corrections!applied!to!the!two!passes.!!Since!the!EaW!pass!contributes!only!two!

points!from!each!scan!(one!fore!and!one!aft),!there!are!two!discrete!sets.!!The!two!

ellipses!correspond!to!the!correction!for!all!scan!azimuths!from!the!NorthaSouth!

pass.!!
14

Figure'8.'Estimated'corrections'for'crossing'point'elevation'differences.

Figure'9.'Computed'corrections'for'crossing'pass'along'latitude'band'^74.92625°.
15

Although!elevation!differences!estimated!from!crossing!passes!near!sea!level!do!not!

represent!trajectory!error!but!rather!geophysical!effects!such!as!tide!changes,!such!

crossings!can!still!produce!good!estimates!of!pitch!and!roll!errors!from!reasonably!

smooth!surfaces.!!It!should!be!noted!that!if pitch!and!roll!errors!are!not!of!particular!

concern,!the!above!technique!can!be!used!to!estimate!elevation!changes!at!any!

elevation!regardless!of!surface!roughness.!!In!fact,!the!program!in!which!the!

technique!is!implemented!(“altdify”)!was!specifically!developed!for!doing!elevation!

difference!computations!over!rough!surfaces.!!In!addition,!it!was!primarily!intended!

to!difference!alongtrack!passes.

4.0&Trajectory&Computation&and&Accuracy

Traditionally,!trajectories!to!support!ATM!missions!have!been!computed!by!the!

gitar&program!which!uses!double!difference!techniques!based!on!ground!GPS!

receiver!data!along!with!the!aircraft!GPS!receiver!data.!!Ambiguities!are!resolved!

where!feasible,!as!they!generally!are!when!there!is!a!ground!receiver!at!the!aircraft!

base!station.!!The!major!source!of!error!in!such!trajectories!is!tropospheric!

refraction!modeling!error,!with!a!major!component!of!such!error!due!to!the!lack!of!

atmospheric!data.!!The!current tropospheric!correction!makes!use!of!NOAA!National!

Center!for!Environmental!Prediction!(NCEP)!High!Resolution!Global!Forecast!

System!data!sets!(web!site!

http://nomads.ncdc.noaa.gov/data.php#hires_weather_datasets).!!For!Greenland!and!

Antarctica,!data!are!obtained!on!a!1° grid!at!3!hr!intervals,!with!the!selection!of!

pressure,!temperature,!and!relative!humidity!down!to!an!atmospheric!pressure!of!

250!mb.!The!gitar estimation!process!allows!the!estimation!of!scale!factors for!both!

aircraft!refraction!corrections!and!for!ground!corrections.!!The!aircraft!corrections!

can!also!be!scaled!with!height!to!eliminate!inconsistent!refraction!modeling!when!

the!aircraft!is!on!the!ground!near!the!reference!GPS!site.!!For!long!baselines,!such!as!

for!Antarctic!missions,!additional!software!is!used!to!effectively!estimate!the!aircraft!

trajectory!with!the!simultaneous!use!of!two!or!more!ground!GPS!sites.

Figure!10 shows!the!groundtracks!and!reference!ground!sites!for!the!2009!Antarctic!

campaign.!!Most!trajectories!were!based!on!data!from!Palmer!(PAL2)!and!Rothera!

(ROTH).!!For!Oct.!16,!no!Rothera!data!was!available!so!data!was!substituted!from!the!

South!Pole!(AMU2)!site.!!Three!station!trajectories!were!estimated!for!some!days!

but!did!not!differ!significantly!from!the!twoastation!solution.!!The!Antarctic!missions!

all!required!long!transit!times!from!the!base!station!in!Punta!Arenas,!Chile.!!The!

gitar trajectories!were!estimated!only!for!the!portion!of!the!trajectories!near!the!

mission!areas.!!No!attempts!were!made!to!resolve!GPS!ambiguities.

Figure!11 shows!the!groundtracks!and!reference!ground!sites!for!the!two!2010!

Greenland!campaigns,!the!first!flown!on!a!DC8!and!the!second!on!a!P3!aircraft.!!For!
16

the!DC8!campaign,!all!missions!were!based!out!of!Thule!(B898)!and!only!singlea

station!trajectories!were!estimated.!!For!the!P3!campaign,!flights!were!flown!out!of!

Kangerlussuaq!(6138)!prior!to!April!17.!!On!April!17,!the!aircraft!transited!to!Thule!

and!subsequent!missions!were!flown!out!of!Thule.!!Single!station!trajectories!were!

estimated!using!the!base!station!GPS!except!for!the!transit!mission.!!For!the!transit!

mission,!data!was!available!and!used!from!Ilulissat!(ILUL)!and!Upernavik!(UPVK)!,!

with!no!base!station!data!available.

With!the!recent!introduction!of!the!Applanix!systems,!primarily!for!improvements!

in!INS!accuracy,!an!additional!procedure!for!computing!aircraft!trajectories!is!

available.!!Using!Applanix!postamission!processing!software!(plus!various!data!sets),!

trajectories!can!be!computed!without!the!use!of!any!ground!sites (a!mode!exists!also!

to!use!ground!sites,!but!this!mode!has!not!been!extensively!exercised).!!For!recent!

ATM!campaigns,!trajectories!have!been!computed!using!the!Applanix!software!and!

data!from!an!Applanix!510!system!for!the!2009!Antarctic!campaign,!an!Applanix!610!

system!for!the!2010!Greenland!campaign,!and!an!Applanix!510!system!for!the!2010!

Greenland!P3!campaign!(610!data!is!also!available!for!a!portion!of!the!P3!campaign).!!

The!stated!accuracy!of!the!Applanix!trajectories!(see!Section!2)!is!5a30!cm,!a!rather!

wide!range.!!The!conditions are!not!clearly!defined as!to!when!a 5!cm!accuracy!can!

be!expected!and!when!a!30!cm!accuracy!is!to!be!expected.!!So!we!have!compared!

available!Applanix!trajectories!with!gitar trajectories!!to!see!how!they!compare!for!

different!regions,!baseline!lengths!and!trajectory!lengths.!!If!the!trajectories!are!

found!to!be!robust!(not!susceptible!to!gross!errors)!and!to!have!accuracies!

comparable!to!those!using!gitar we!may!adopt!the!procedure.
17

Figure'10.'Groundtracks'for'2009'Antarctica'campaign.
18

Figure'11.'Groundtracks'for'2010'Greenland'campaigns.

The!Applanix!trajectories!for!the!first!two!campaigns!have!been!compared!with!the

corresponding!gitar trajectories;!the!height!mean!and!rms!differences (as!error!

bars)!are!shown!in!Figures!12!and!13.!!The!mean!differences!for!the!2009!Antarctic!

campaign!(averaging!the!18!days)!show!the!Applanix!to!be!higher!than!gitar by!6.6!

cm.!!The!baselines!for!gitar&trajectories!for!some!of!the!Antarctic!missions!exceed!

2000!km!and,!as!can!be!seen!from!Figure!10,!the!two!ground!sites!are!along!the!

same!line!and!thus!the!second!site!does!not!add!much!additional!geometry.!!On!the!

other!hand!there!are!missions!to!the!Antarctic!Peninsula!for!which!the!baselines!are!

only!on!the!order!of!500!km,!with!Rothera!and!Palmer!having!significantly!different!
19

directions!from!the!survey!sites.!!Yet!the!mean!Applanixagitar height!difference!for!

the!Peninsula!flights!is!7.02!cm,!the!same!as!the!average!for!all!flights.!!With!two!

stations!having!(relatively)!short!distances!to!the!Peninsula!survey!region!and!being!

in!different!directions!from!the!survey!area,!it!is!difficult!to!believe!that!the!gitar

trajectory!error!constitutes!a!major!portion!of!the!7!cm!height!difference.!!

Figure'12.'Mean'and'RMS'differences'between'Applanix'and'gitar'trajectory'heights'for'2009'Antarctica'

campaign.
20

Figure'13.'Mean'and'RMS'differences'between'Applanix'and'gitar'trajectory'heights'for'2010'Greenland'

DC8'campaign.

For!the!2010!Greenland!DC8!campaign,!the!Applanixagitar!height!differences,!as!

shown!in!Figure!13,!have!a!mean!of!+2.7!cm.!!It’s!not!clear!why!these!differences!

should!be!so!much!smaller!than!the!2009!Antarctic!differences.!!The!improvement!is!

not!sufficiently!addressed!by!the!5a30!cm!trajectory!accuracy!specification!from!

Applanix.!!The!Applanix!trajectories!for!Antarctica!were!somewhat!longer!in!time!

and!distance!(the!Applanix!trajectories!spanned from!before!takeoff!to!after!

landing),!though!the!significance!of!length!is!unclear.!!The!Applanix!instruments!

were!different!for!the!two!campaigns!– Model!510!for!Antarctica!and!Model!610!for!

Greenland.!!The!specifications!for!both!are!comparable!for!trajectory!accuracy!and!it!

is!unclear!whether!the!superior!610!specification!for!INS!accuracy!might!relate!to!

smaller!trajectory!differences.!!!At!any!rate!we!lack!extensive!experience!with!
21

utilization!of!the!Applanix!systems!and!its!postaprocessing!software!and!we!may!see!

smaller!differences!in!the!future.!!But!the!relatively!good!agreement!between!the!

ground!based!trajectories!and!Applanix!trajectories!is!an!indication!that!neither!is!

grossly!in!error,!considering!that!the!procedures!for!their!computation!are!totally!

different.

Accepting!that!the!gitar trajectories!are!the!more!accurate,!we!now!consider!their!

accuracy.!!Crossover!differences!have!been!discussed!in!Section!3,!noting!that!they!

can!produce!trajectory!difference!errors!as!well!as!pitch!and!roll!errors.!!The!2009!

Antarctic!campaign!and!the!two!2010!Greenland!campaigns!have!been!processed!in!

the!altdify program!to!estimate!their!crossover!differences!along!with!pitch!and!roll!

errors.!!The!crossover!differences!for!the!three!campaigns!were!then edited!

according!to:

Surface!elevation: >!200!m!to!minimize!rapidly!varying!surfaces

Crossover!angle: >!45° to!allow!meaningful!separation!between!roll!biases

Crossover!rms: <!1m!to!eliminate!rough!topography

Table'4.'Summary'of'Crossover'Differences'from'ATM'Campaigns.

Campaign Antarctic!

2009

Campaign

Greenland!2010

DC8!Campaign

Greenland!2010

P3!Campaign

Time!separation!(days) No.!of!

Points

RMS!

(cm)

No.!!of

Points

RMS!

(cm)

No.!of

Points

RMS!

(cm)

0 45 5.65 70 5.44 132 7.76

1a2 27 7.33 0 N/A 141 6.19

3a5 10 14.71 0 N/A 162 13.3

>5 84 19.61 51 8.76 16 13.81

The!results!are!summarized!in!Table!4.!!Crossovers!are!based!on!two!trajectories,!

each!of!which!has!both!shortaterm!(sameaday)!errors!!and!systematic!errors!which!

are!different!from!one!day!to!the!next.!!In!the!row!of!the!table!for!0!days!separation,!

only!short!term!errors!contribute!to!the!RMS.!!For!the!other!time!separations,!the!

systematic!errors!also!contribute.!!But!as!the!separation!gets!longer!and!longer,!true!

surface!changes!also!contribute.!!Indeed,!there!are!a!number!of!relatively!rapidly!

changing!elevations!(later!elevation!is!almost!always!smaller!than!the!earlier!one).!!

So!we!adopt!the!1a2!day!separation!row!as!best!representing!true!trajectory!errors!

with!a!minimum!amount!of!true!surface!elevation!change.!!In!addition,!we!assume!

that!the!systematic!errors!in!the!trajectories!are!independent!from!one!day!to!the!

next!and!that!the!error!levels!(expected!errors)!are!the!same!from!one!day!to!the!

next.!!(The!surface!elevations!do!have!systematic!errors!due!to!range!bias,!which!

will!be!added!in!later.)!Then,!if!a!crossover!difference!is!the!difference!between!

independent!errors!each!having!the!same!sigma!(σ),!then!the!uncertainty!of!a!

crossover!εc can!be!expressed!as
22

εc =!!ε2!!a!!ε1 (2)

which!says!only!that!the!crossover!error!is!the!difference!of!the!errors!from!each!

pass.!!But,!given!the!independence!of!the!errors!from!one!pass!from!another,!the!

expected!value!of!the!square!of!the!crossover!error!is

E(εc)2!!=!E(ε2)2 +2E(ε1 ε2)!+!E(ε1)2 =!2!σ2 (3)

Since!the!errors!are!independent!from!one!day!to!the!next!and!the!expected!error!

for!each!day!is!the!same.!!It!follows!that!the!individual!pass!trajectory!uncertainty!is

!!!σ'''='(crossover!rms)/√2 (4)

From!Table!4,!we!get!the!following!estimates!for!the!1a2!day!separation!crossovers:

Antarctica 2009 5.18!cm

Greenland!2010!DC8 no!data

Greenland!2010!P3 4.38!cm

We!note!that!even!for!the!>5!day!crossovers!for!the!Greenland!DC8!mission,!we!

would!get!6.19!cm.!!An!average!of!the!3!numbers!is!5.25!cm.!!Considering!that!one!

number!is!based!on!passes!which!probably!include!some!surface!change,!we!adopt!

the!5!cm!number!for!the!expected!value!of!trajectory!uncertainty,!not!including!

range!bias!uncertainty.!!When!we!add!in!the!2!cm!estimated!in!Section!3.1,!we!arrive!

at!a!total!surface!elevation uncertainty!of! √29=5.4!cm.

It!may!be noted!in!Table!4!that!the!sameaday!rms!crossover!differences!for!the!2010!

Greenland!P3!mission!was!larger!than!the!1a2!day!rms.!!The!reason!for!this!has!not!

been!extensively!investigated.!!However,!having!a!large!number!of!crossings!on!the!

same!day!suggests!that!a!glacier!was!being!surveyed!in!a!grid!pattern!and!at!a!lower!

elevation!than!for!1a2!day!crossings!a with!rougher!terrain!and!accordingly!more!

noise!in!the!estimated!crossovers.

5.0&Attitude&Errors&and&Their&Effects&on&Surveys

Aircraft!attitude!errors!are!one!of!the!more!significant!contributors!to!ATM!survey!

errors.!!Accordingly,!the!most!accurate!instruments!available!have!been!used!on!

recent!deployments.!!As!stated!in!the!previous!section,!the!Applanix!Model!!510!

system!was!used!on!deployments!to!Antarctica!in!the!Fall!of!2009!and!in!the!Spring!

deployment!to!Greenland!on!the!P3!aircraft.!!On!the!2010!Greenland!deployment!on!

the!DC8!aircraft,!the!most!advanced!Applanix!system,!Model!610!was!used.!!
23

Accuracy!specifications!for!these!systems!are!0.005° (pitch!and!roll)!for!the!510!

system!and!0.0025° (Section!2)!for the!610!system.!!These!numbers,!however,!are!

couched!with!a!number!of!caveats,!such!as!the!need!to!do!180° turns!every!20a30!

minutes!to!maintain!INS!accuracy.!!For!most!ATM!missions,!and!especially!for!

Antarctic!missions!flown!out!of!Chile,!these!maneuvers!for!maintaining!optimum!

accuracy!are!not!feasible.!!Fortunately,!the!use!of!crossing!passes!as!discussed!in!

Section!3,!along!with!mission!trajectories!inherently!having!a!large!number!of!

crossing!tracks,!allow!the!determination!of!pitch!and!roll!errors!while!at!the!survey!

site.!!!For!these!estimations,!the!same!crossing!edits!on!elevation,!crossing!angle,!and!

surface!roughness!were!used!as!were!discussed!in!the!previous!section!for!

trajectory!height!error!analysis.!!Lower!elevations!could!be!allowed!but!the!

possibility!of!surface!topography!changes!between!passes!is!considerably!greater,!

particularly!for!pass!separations!of!many!days.

Figure'14.'Pitch'and'roll'errors'estimated'for'the'2008'DC8'deployment'to'Antarctica.
24

Figure'15.'Pitch'and'roll'errors'estimated'for'the'2010'DC8'deployment'to'Greenland.

Figures!14,!15,!and!16!show,!respectively,!the!estimated!errors!for!the!2009!

Antarctic!deployment,!the!2010!Greenland!DC8!deployment,!and!the!2010!

Greenland!P3!deployment.!!A!major!characteristic!of!pitch!and!roll!errors!of!

particular!interest!is!the!stability!of!the!errors!from!day!to!day.!!Considering!the!long!

transit!time!for!deployment!from!Chile!to!Antarctica,!significant!drifts!might!be!

expected!for!the!Antarctic!deployments.!!The!questions!then!are,!how!stable!are!the!

drifts!from!day!to!day!and!how!variable!are!they!during!a!survey!mission?!!After!we!

learn!the!answers!to!these!questions,!we!can!determine!what!procedures!we!need!to!

follow!to!compute!and!apply!corrections!to!INS!measurements.

Assessment!of!the!errors!begins!by!calculating!the!mean!errors!and!their!rms!about!

the!means.!!These!have!been!calculated!for!pitch!and!roll!for!each!of!the!three!
25

deployments!and!are!shown!in!Table!5.!!The Applanix!system!used!is!also!included!

in!the!table!because!it!may!be!significant.!!It!should!be!noted!that,!in!order!to!

compensate!for!some!INS!drift,!pitch!and!roll!offsets!of!0.005a0.01° have!already!

been!applied!in!the!processings!from!which!Figures!14a16 were!plotted.!!!Such!mean!

drifts!are!easy!to!compute!from!crossing!passes!and!simple!to!apply.!!The!concern!is!

for!the!errors!that remain!after!these!drifts!are!applied.!!As!Table!5!shows,!residual!

means!are!small,!the!largest!being!0.0061°.!!Additional!processing!could!reduce!all!

of!them!to!zero.! However,!even!adding!(in!an!RSS!sense)!the!mean!and!RMS errors,!

the!largest!errors!are!0.011° for!the!610!system!and!0.0154° for!the!510!system.

Figure'16.'Pitch'and'roll'errors'estimated'for'the'2010'P3'deployment'to'Greenland.

Table!6!shows!the!INS!errors!transformed!into!elevation!errors!assuming!a!mission!

height!above!the!surface!of!500!m!and!the!scanner!used!for!the!mission.!!We!note!

that!for!a!scanner!the!pitch!and!roll!errors!both!produce!elevation!errors!but!

basically!not!at!the!same!time.!!So!we!pick!worstacase!errors,!which!would!be!pitch!
26

for!the!610!system!and!roll!for!the!510!system.!!From!Table!6,!we!obtain!elevation!

errors!of!3.8!cm!for!the!610!system,!though!those!would!be!5.4!cm!for!the!510!

system!if!a!22° scanner!had!been!used.!!Since!the!Applanix!610!is!our!adopted!INS!

system,!the!RMS!error!that!we!calculate!for!elevation!error!from!INS!errors!is!3.8!

cm.

Table'5.'Summary'of'Estimated'Pitch and'Roll'Errors'for'ATM'Missions.

Campaign Applanix

System

No.!of

Measurements

Pitch

mean

Pitch

Rms

Roll

mean

Roll

rms

2009!Antarctic 510 235 a0.0014 0.0092 a0.0061 0.0105

2010!Greenland!DC8 610 334 a0.0059 0.0089 a0.0003 0.0054

2010!Greenland!P3 510 824 a0.0020 0.0094 a0.0030 0.0154

Table'6.'Summary'of'Estimated'Pitch'and'Roll'Errors'for'ATM'Missions'(converted'

into'vertical'error).

Campaign

Applanix

System

Scanner!

Width

Pitch

Mean

Ht!effect

Pitch

Rms

Ht!effect

Roll

Mean

Ht!effect

Roll

Rms

Ht!effect

2009!Antarctic 510 22° 0.5!cm 3.24!cm 2.15!cm 3.70!cm

2010!Greenland!DC8 610 22° 2.08!cm 3.14!cm .11!cm 1.90!cm

2010!Greenland!P3 510 15° 0.47!cm 2.20!cm 0.70!cm 3.60!cm

It!may!be!noted!that!the!Applanix!610!roll!errors!are!particularly!stable!and!that!

ATM!surveys,!due!to!the!conical!scanner,!contain!forward!scans!and!backward!scans!

for!which!the!effects!of!pitch!errors!largely!cancel.!!So!the!INS!contribution!of!3.8!cm!

to!vertical!error!is!actually!quite!conservative.

6.0&Error&in&Knowledge&of&Horizontal&Footprint&Positioning

In!sharp!contrast!to!our!approach!to!vertical!errors,!we!have!not!made!a!robust!effort!to!

experimentally!quantify!errors!in!the!horizontal!positioning!of!ATM!laser!footprints.!!

This!stems!from!our understanding!that!for!ice!sheet!applications,!horizontal!positioning

errors!are!small!enough!to!be!unimportant,!compared!with!vertical!errors,!since!such!

targets!tend!to!be!relatively!smooth!and!flat.!!So!here!we!adopt!an!analytical!approach!

to!quantify!the!expected!horizontal!error.!!Several!error!sources!contribute!to!error!in!

knowledge!of!the!latitude!and!longitude!of!each!laser!footprint.!!These!are!timing!error,!

scan!azimuth!bias!error,!heading!bias!error,!pitch!and!roll!error,!heading!error!and!GPS!

positioning!error.!!We!consider!each!of!these!in!turn!below,!and!finally!sum!their!

contributions!into!an!overall!horizontal!footprint!error.!!For!the!purposes!of!this!error!

analysis,!we!model!the!target!surface!as!a!flat,!horizontal!plane.
27

6.1&Laser&Pulse&Timing&Errors

Waveform!analysis!can!produce!timing!errors,!as!a!point!of!the!waveform!corresponding!

to!the!target!must!be!selected!according!to!the!algorithm!described!in!Section!2.0.!As!

mentioned!in!that!section,!an!atmospheric!refraction!correction!is!added.!Typical!laser!

range!timing!measurements!to!a!stationary!target!corrected!for!atmospheric!refraction!

and!systemHtiming!biases!result!in!ATM!range!RMS!values!of!approximately!5!cm.

6.2&Scan&and&Date&Timing&Errors

Timing!errors!arise!because!each!laser!shot!is!imperfectly!timeHtagged!under!the!

influence!of!two!predominant!kinds!of!motion.!!These!are!the!forward!motion!of!the!

aircraft!in!flight,!and!the!motion!of!the!scanner!mechanism!as!it!slews!successive!laser!

spots!around!the!scan!pattern.!!An!error!in!timeHtagging!means!that!the!laser!spot!on!

the!ground!is!misplaced!by!an!amount!proportional!to!the!speed!of!the!motion.!!We!

show!below!that!the!dominant!effect!of!timing!errors!is!on!the!knowledge!of!scanner!

position.

All!timing!in!the!ATM!system!is!driven!by!a!1!pulseHperHsecond!(1!PPS)!strobe,!which!is!

produced!by!surveyHgrade!GPS!receivers.!!Prior!to!the!2010!ATM!field!season!this!1!PPS!

strobe!was!provided!by!Ashtech!ZH12!receivers,!which!had!a!stated!1!PPS!accuracy!of!1!

microsecond.!!During!the!2010 field!season!the!ATM!switched!its timing!source!to!newer!

Javad!surveyHgrade!GPS!receivers,!which!have!a!rated!1!PPS!timing!accuracy!of!25!

nanoseconds.!!Between!these!1!PPS!strobes,!all!events,!including!scanner!position,!are!

timed!using!an!internal!crystal!oscillatorHbased!timing!circuit,!which!has!a!rated!stability!

of!50!ppm,!or!50!microseconds!per!second.!!The!25Hnanosecond!1!PPS!error!is!negligible!

in!comparison.

We!do!not!directly!measure!the!angular!position!of!the!scan!mirror.!!Instead,!a!HallH

effect!sensor!triggers!a!strobe!when the!scanner!rotates!past a!fixed!position!at!one!

point!around!each!scan.!!We!timeHtag!this!strobe,!and!compute!the!angular!position!of!

the!scanner!for!each!similarly!timeHtagged!laser!pulse!by!linearly!interpolating!the!360°

scan!between!these!strobes.!!Thus,!the!maximum!timing!error!for!an!individual!laser!

pulse!occurs!at!the!end!of!each!scan,!just!prior!to!the!HallHeffect!sensor!being!tripped!to!

signal!the!beginning!of!a!new!scan.!!With!20!scans!per!second!and!the!above!50!

microseconds!per!second!timing!drift,!this!yields!a!maximum!timing!error!during!a!scan!

of!2.5!microseconds,!and!an!average!timing!error!of!half!that,!or!1.25!microseconds.!!

The!resulting!average!error!in!scanner!position!angle!is!0.009°.
28

For!the!scanning!motion!on!the!ground,!for!this!purpose!we!model!the!scan!as!a!perfect!

circle!with!a!diameter!proportional!to!the!sensor!altitude!above!ground!level!(AGL).!!In!

truth!the!scan!pattern!is!somewhat!elliptical!and!slightly!eggHshaped,!but!any!error!

introduced!by!the!circular!approximation!is!small.!!In!typical!operations,!the!ATM!is!

operated!at!an!AGL!altitude!of!500!m!with!a!scan!rate!of!20!Hz,!and!the!resulting!scan!

swath!width!for!our!wideHswath!22° scanner!is!404 m.!!The!corresponding!

circumference!of!the!approximate!circular!scan!is!1296 m,!and!the!speed!of!the!scan!

across!the!ground!is!25,386 m/s.!!Given!the!average!expected!timing!error!above!of!1.25!

microseconds!and!resulting!scanner!position!angle!error!of!0.009°,!this!yields!a!footprint!

position!error!of!3.2 cm. We!neglect!the!timingHinduced!error!due!to!forward!motion!of!

the!aircraft,!which!at!~120!m/s!is!negligible!compared!to!the!25,386 m/s!scan!motion.

6.3&Scan&Azimuth&Bias&Error

Scan!azimuth!bias!error!is!a!constant!offset!in!knowledge!of!current!angular!position!

along!the!scan.!!It!is!a!parameter!that is!estimated!(along!with!pitch,!roll!and!range!

biases)!as!part!of!the!overall!scanner!calibration!process.!!The!combined!leastHsquares!

determination!of!scanner!parameters!for!the!fall!2009!IceBridge!deployment!shown!in!

Table!1!yields!a!formal!uncertainty!for!the!scan!azimuth!bias!determination!for!that!

campaign!as!0.027°.!!!Since!the!leastHsquares!process!cannot!formally!model!all!

potential!sources!of!error,!we!conservatively!double!this!formal!uncertainty!to!an!error!

estimate!in!scan!azimuth!bias!of!0.05°.!!A!displacement!of!a!laser!spot!of!0.05° along!the!

scan!described!above!on!the!ground!yields!a!horizontal!position!error!of!18.0 cm.

6.4&Heading&Bias&Error

Heading!bias!error!is!the!fixed!difference!between!the!aircraft's!true!heading!and!the!

heading!indicated!by!the!ATM's!inertial!navigation!system.!!Like!scan!azimuth!bias,!

heading!bias!is!estimated!as!part!of!the!overall!scanner!calibration!process.!!It!is!similar!

to,!and!mathematically!correlated!with,!scan!azimuth!bias.!!However,!since!scan!azimuth!

bias!represents!an!error!in!the!determination!of!where a!spot!lies!along!the!scan!while!

heading!bias!represents!an!angular!displacement!of!the!entire!scan,!the!slightly!nonH

circular!shape!of!the!scan!helps!to!partially!decorrelate!the!two!parameters!and!allow!

their!independent!estimation.!!As!before,!the!scanner!parameter!estimation!process!for!

Fall!2009!IceBridge!shown!in!Table!1!yields!a!formal!uncertainty!in!heading!bias!of!0.11°,

which!we!again!double!to!0.2° for!a!conservative!estimate!of!heading!bias!error.!!This!

relatively!large!displacement!of!the!laser!scan!yields!a!horizontal!position!error!of!72.0

cm.
29

6.5&Pitch&and&Roll&Error

Errors!in!knowledge!of!aircraft!pitch!and!roll!contribute!to!errors!in!horizontal!footprint!

location!by!shifting!the!footprint!location!laterally!according!to!the!following!

trigonometric!relationship:!

dS!=!h*tan(theta+dtheta)H(w/2) (5)

where!dS!is!the!horizontal!positioning error,!h!is!AGL!altitude,!theta!is!the!nominal!offH

nadir!scan!angle,!dtheta!is!the!error!in!knowledge!of!offHnadir!angle,!and!w!is!the!width!

of!the!full!scan!on!the!ground.!!Table!5 shows!RMS!pitch!and!roll!errors!for!three!

IceBridge!campaigns!to!be!approximately!0.01° in!almost!every!case,!with!mean!errors!

considerably smaller.!!Based!on!that,!we!adopt!0.01° as!the!error!in!our!knowledge!of!

attitude.!!This!yields!a!resulting!horizontal!positioning!error of!10.2!cm.

6.6&Heading&Error

Heading!error!is!distinct!from!heading!bias!error.!!It!is!the!error!in!realHtime!knowledge!

of!aircraft!heading!from!the!ATM's!inertial!navigation!system.!!Where!heading!bias!error!

remains!fixed!as!long!as!the!ATM!transceiver!and!INS!are!themselves!fixed!to!the!

airframe,!heading!error!drifts!in!time!as!the!INS!drifts.!!Heading!error!is!difficult!to!

characterize!from!realHworld!ATM!measurements!simply!because!they!are!not!very!

sensitive!to!it,!particularly!given!the!relatively!smooth!topography!usually!measured.!!

However,!we!know!that!the!Applanix!510!INS!specifies!pitch!and!roll!error!as!0.005° and!

heading!as!0.008°.!!We!also!know!from!the!above!discussion!of!pitch!and!roll!error!that!

our!realHworld!measurements!of!these!are!worse!than!these!specifications!by!a!factor!of!

2.!!Thus!it!seems!reasonable!to!inflate!the!heading!specification by!a!factor!of!2!as!well,!

then!conservatively!round!up!to!0.02°.!!Using!the!same!geometrical!argument!as!in!

sections!6.2!and!6.3,!this!yields!a!resulting!horizontal!error!of!6.5!cm.

6.7&GPS&Positioning&Error

Errors!in!horizontal!GPS!positioning!of!the!aircraft!translate!directly!into!errors!in!

horizontal!laser!spot!positioning.!!In!Section!4,!the vertical!GPS!accuracy!was!shown!to!

be!<6!cm.!!GPS!horizontal!positioning!is!typically!more accurate than vertical!positioning

for!several!reasons.!!For!the!current!analysis,!a!value!of!6 cm!is!adopted!as!the expected!

GPS!horizontal!accuracy,!which!is!also!the!GPS!contribution!to!horizontal!laser!spot!

positioning.
30

6.8&Total&Horizontal&Error

The!errors!described!above!contribute!to!the!overall!horizontal!error!in!footprint!

locations!in!an!additive!manner.!!Thus!we!compute!the!total!error!as!the!square!root!of!

the!sum!of!the!squares!of!these!errors.!!Based!on!the!above!results,!the!overall!

horizontal!error!is!74 cm.!!It!is!dominated,!by!far,!by!the!heading!bias!error,!while!timing,!

GPS!and!attitude!errors!are!fairly!insignificant!in!comparison.

The!precision!of!the!horizontal!spot!locations!is!much!better!than!this,!however,!

because!the!largest!error!sources!discussed!above!are!constant!biases.!!The!remaining!

variable!errors!are!the!2.9!cm!timing!error,!the!6.5!cm!heading!error,!the!9.3!cm!

pitch/roll!error,!and!the!6 cm!GPS!positioning!error.!!The!square!root!of!the!sum!of!the!

squares!of!these!is!14 cm.

7.0&Error&Analysis&Summary

The!various!error!components!which!affect!the!accuracy!with!which!the!ATM!can!

perform!topographic!surveys!for!ice!sheet!elevation!measurement!have!been!

discussed!in!some!detail!in!previous!sections!and!various!accuracies!estimated.!!

Although!sea!ice!tracks!were!not!analyzed!in!the!same!way!as!ice!sheets,!because!of!

the!tide!effects!and!lack!of!track!crossings,!they!have!been!analyzed!for!attitude!

errors!and!the!accuracies!for!them!are!expected!to!be!comparable!to!those!obtained

for!the!ice!sheets.!The!survey!characteristics!for!the!current!primary!ATM!system,!

and!the!accuracies!which!have!been!estimated,!are!shown!in!Table!7.!!Perhaps!the!

most!significant!accuracy,!or!at!least!the!one!with!the!most!effort!made!to!improve

it,!is!vertical!accuracy,!which!has!3!major!contributors!to!its!uncertainty:!!

● trajectory!error,!

● range!bias!error,!and

● pointing!errors

Trajectory!error!is!currently!the!largest!component.!!The!attitude!component!is!the!

next!largest,!and!assumes!that!the most!accurate!currently!available!INS!instrument!

will!be!employed.!!Even!with!this!system,!it!is!assumed!that!data!taken!during!

survey!missions!will!be!used!for!attitude!verification!and!used,!if!necessary,!to!

remove!INS!drifts!that!occur!during!transit!from!a!base!airbase to!the!survey!region.
31

Table'7.'Characteristics'and'Accuracies'of'ATM'Ice'Sheet'Surveys.

*!The!vertical!accuracy!value!was!calculated!from!a!data!ensemble!containing!comparison!pairs!of!

elevation!measurements!from!the!overlap!of!ATM!swaths!at!the!intersection!of!two!aircraft!tracks.!!

The!ATM!22° scanner!operating!at!a!500!m!altitude!for!2!tracks!intersecting!at!right!angles!collects!

elevation!measurements!from!an!area!of!about!400m!x!400m!containing!about!14,000!ATM!

measurements!for!each!track.!!This!is!the!approximate!number!of!pointatoapoint!comparisons!used!in!

analyzing!an!intersection!for!the!estimation!of!a!height!difference!and!aircraft!pitch!and!roll!errors.!!

With!this!number!of!measurements,!the!effects!of!measurement!noise!average!to!near!zero.!!The!

dominant!contributors!to!height!error!are!systematic,!primarily!trajectory!errors!(but!contributions!

from!others!such!as!attitude!and!range!bias),!as!the!document!discusses!elsewhere.!!

**The!number!for!vertical!precision!in!Table!7,!on!the!other!hand,!is!our!estimate!of!the!ATM!pointa

toapoint relative!accuracy.

Survey'Parameter ATM'– 22° scanner'

Operating!Altitude 500!to!750!m!above!the!ice!surface

Horizontal!Accuracy 74!cm

Horizontal!Precision 14!cm

Vertical!Accuracy* 6.6!cm

Vertical!Precision** !!3!cm.

Swath!Width ~400!m

Area!Coverage!/!Flight!Hour ~180!km2

Shot!Density ~1!/!10!m2

Laser!Footprint!Size ~1!m

Spacing!Along!Track ~3!m

Spacing!Across!Track 5!m!at!center!of!swath,

<!1m!at!edge!of!swath

Data!Products georeferenced!spot!elevations

georeferenced!!80!m!nadir!platelet!+!

5!equally!spaced platelets!spanning!

swath!width,!all!with!center!

elevation!and!local!slope!values
32

8.0&References

Krabill,!W.!B.,!R.!H.!Thomas,!C.!F.!Martin,!R.!N.!Swift,!E.!B.!Frederick,!1995.!Accuracy!

of!airborne!laser!altimetry!over!the!Greenland!ice!sheet,!International#Journal#of#

Remote#Sensing,!16(7)!1211a1222.!!DOI: 10.1080/01431169508954472

Krabill,!W.,!E.!Frederick,!S.!Manizade,!C.!Martin,!J.!Sonntag,!R.!Swift,!R.!Thomas,!W.!

Wright,!and!J.!Yungel,!1999.!Rapid!Thinning!of!Parts!of!the!Southern!Greenland!Ice!

Sheet,!Science 283 (5407),!1522.![DOI:10.1126/science.283.5407.1522]

Krabill,!W.,!W.!Abdalati,!E.!Frederick,!S.!Manizade,!C.!Martin,!J.!Sonntag,!R.!Swift,!R.!

Thomas,!W.!Wright,!and!J.!Yungel,!!2000.!Greenland!Ice!Sheet:!HighaElevation!

Balance!and!Peripheral!Thinning,!Science#289,!428a430![DOI:!

10.1126/science.289.5478.428]

Krabill,!W.!B.,!W.!Abdalati,!E.!B.!Frederick,!S.!S.!Manizade,!C.!F.!Martin,!J.!G.!Sonntag,

R.!N.!Swift,!R.!H.!Thomas,!J.!K.!Yungel,!2002.!!Aircraft!laser!altimetry!measurement!of!

elevation!changes!of!the!Greenland!ice!sheet:!technique!and!accuracy!assessment,!

Journal#of#Geodynamics 34 357–376.![doi:10.1016/S0264a3707(02)00040a6]

Martin,!C.!F.,!R.!H.!Thomas,!W.!B.!Krabill,!and!S.!S.!Manizade,!2005.!ICESat!range!and!

mounting!bias!estimation!over!preciselyasurveyed!terrain,!Geophys. Res.#Lett.,!32,!

L21S07,!doi:10.1029/2005GL023800.

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Airborne Topographic Mapper Calibration Procedures and Accuracy 

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Chreston F. Martin, WIlliam B. Krabill, Serdar S. Manizade, Rob L. Russell, 

John G. Sonntag, Robert N. Swift, and James K. Yungel 

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Description of NASA Airborn Topographic Mapper (ATM) lidar calibration procedures including analysis of the accuracy and 

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elevations measurements from a nominal operating altitude 500 to 750 m above the ice surface was found to be: Horizontal Accuracy 

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