221
1 INTRODUCTION
1.1 Studymotivation
Thetestpresentedinhereisapartofastudyheading
towards a design of an autonomous navigation
systemforanice‐probe. Destinationof theice‐probe
is ice exploration on Enceladus, one of the Saturn’s
moon.Thereisawill,drivenbyast
robiologyscientific
community,toexploretheicyshellofthemoonand
toreachtheunder‐icewatersource.Tocaterforthis
will, the German Aerospace Centre, (DLR), took an
initiative of assessing the feasibility of an Enceladus
exploration mission. The first phase of the project,
which concluded in 2015, resulted in a design of a
demonstratorofanice‐probe.Theprobecharact
erizes
withlengthofaround2meters,weightofaround60
kgandpowerconsumptionatthelevelof2kW.The
probe’s main designed features were the
maneuverability in the ice, precise location and
navigation in the ice without usage of the GNSS
system nor optical instruments, targeting the water
reservoirandself‐decont
aminationabilityinorderto
not to contaminate the recovered under‐ice water
samples. The final test mission was a scientific field
survey in Antarctica, where the under‐ice iron‐rich
hypersaline water samples, which supply the
outflowingBloodFalls,waresuccessfullycollected.
The navigation system design of the probe was
ba
sedonfollowingtechnologies:inertialrotationand
accelerationmeasurementsforattitudedetermination;
magnetometryforheadingestimation;ultrasoundsin
positioningaswellasreconnaissancesubsystem.All
subsystems were integrated into a position and
attitudenavigationsystemwithtra
jectoryplanning.
The Institute of Space Technology and Space
Applications, (ISTA), contributed to the navigation
system design with attitude determination system.
Having the availability of the space and sufficient
power supply within the ice‐probe, the Northrop
Grumman LN‐200, tactical grade Inertial
Measurement Unit (IMU) with Fiber Optic
Gyroscopes(FOG),wasused.Atti
tudedetermination
was of high accuracy, although the environmental
conditions were not trivial. The key factors playing
thesignificantroleintheoverall performanceof the
attitude determination system‐only were: very low
ice‐probedynamics(velocityatthelevelof1m/hour),
axialrotation rateof the ice‐probeduring therunat
Efficiency of MEMS Inertial Sensors Used in Low-
dynamics Application
A.Szumski&B.Eissfeller
BundeswehrUniversityofMunich,Neubiberg,Germany
ABSTRACT: The analysis presents the performance o
f
navigation application driven with MEMS and FOG
inertial sensors. The inertial sensors were working under conditions simulating a potential robotic mission,
whichreduceaccuracyofsomeofthenavigationapplications.Empirical resultsofthetestconfirmdegradation
ofthenavigationsystemperformanceinthepresenteddemandingmission.Influenceofthetestingcondit
ions
andoftheinertialsensortechnologyispresentedanddiscussedinthepaper.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 2
June 2017
DOI:10.12716/1001.11.02.02
222
the level of the Earth rotation rate, testing at high
latitudes,andverylong,over24hours,testduration
time.
1.2 Requirementsoftheexperiment
Currently, the development of the attitude
determination systembased on the inertial
measurement technologycontinues with new
requirements. The study focuses strongly on
miniaturization and
energy consumption
optimization. Neither of these belongs to the
characteristicsof previously used LN‐200 in view of
thestudiedexplorationmission.Inordertomeetthe
requirements, Microelectromechanical systems
(MEMS)IMUtakespartofthetestedsystem.Forthis
purposethe LITEFμIMUhasbeen chosenasone of
the best performing MEMS‐based inertial sensor
commerciallyavailable.
Anotherimportantfocusofthecurrentstudyisthe
environment of the studied mission destination,
Enceladus. From the inertial measurements point of
view,the inertiaand gravityof Enceladusare much
smaller than the ones of the Earth, and at the same
time not so well and accurate known. The most
influential on the inertial subsystem Enceladus
characteristicsare small moon gravity field of about
0.01 g on the surface and small rotation period of
around1.37days.
Both, the less performant IMU and the
characteristicsofEnceladusaresettobe
requirements
oftheexecutedinertialattitudedeterminationtest.
2 TESTINGSCENARIO
2.1 Gyrocompassing
Thepurposeofthetestwasassessingtheeffectiveness
of the attitude determination system during the
Enceladus ice exploration mission. The mission
characteristics results with a very long exploration
time, even several weeks long. During long
navigation time
the inertial subsystem require
multiple realignments. Realignment, as well as the
initial alignment, requires a certain time, when the
probe, together with an inertial sensor inside, stays
still.The only movement,which should at that time
bedetectedbytheinertialsensor,isthemovementof
themoon.Insuch
situationitispossibletodetermine
twocharacteristictothemoonvectors:rotationofthe
moonandgravity.
Consideringalocalframe,definedhereasNorth‐
East‐Down,as theone usedin thenavigation of the
probe, the moon gravity and rotation vectors may
almostdirectlydefinethatframe.Three
equations(1)
areconsideredforderivationoftheNEDframefrom
themeasuredvectors.
g
Dgn
ED n
N
ED





 (1)
whereN,E,D=unitybasevectorsoftheNEDframe;
g=gravityvector;ω=moonrotationvectorn
g=unity
vectorofthegravityvectorg;n
ω=unityvectorofthe
rotation vector ω. This way of finding the North
directionmaybealsonamedasgyrocompassing.The
realization of the equations (1) in formation of the
NEDframeinthefirstEnceladusExplorerprojectare
describedin(Niedermeieretal.2014).
Measureofthegravity
androtationvectorsisnot
error free, especially when the measured values are
smallenoughtobecomparablewithnoisegenerated
bythesensor.Inthedescribedapplicationthegravity
measuredonthesurfaceofEnceladusisexpected to
beequalto0.114m/s
2
andtheaveragerotationrateis
equal to 5.3e
‐5
rad/s (3e
‐3
°/s). As can be seen in the
equations (1) accuracy of the g and ω vectors
determineaccuracyoftheNEDframederivation.The
gravityvectorisusuallyleadingtoaverylittleerror
providingthe down‐angle estimation onaccuracy of
severalmradslevelorbetter.Evenfor such
reduced
gravityavailableonEnceladusitshouldn’timplicate
insignificantlevelingerror.Thesituationisdifferent
whenusingmeasures oftherotationrateω.Asforan
example,consumergradegyroscopesarenot ableto
measure effectively the rotation of the Earth.
Eventuallyinthiscase,theNorthandEast
directions
cannotbefound.Therefore,thisaspectoftheinertial
sensing is the most sensitive in the navigation
systems. It becomes a focus of the test to check the
influences of the rotation rate vector on the North
finding. The IMU were rotated w.r.t. the inertial
frame with the angular velocity
expected being
observed on Enceladus. In order to simulate such
condition, the sensors have been rotated on a turn
tablewithanangularvelocityequalto0.00112°/sin
theopposite direction totheEarth rotation.Attitude
determinationwasperformedusingthemeasurement
recording. The results were juxtaposed with the
counterpart calculations for the Earth conditions. In
thiscasethesensorsstoodstillsensingEarthrotation
only. A detailed description of Enceladus on the
inertialmeasurementarepresentedin(Szumskietal.
2016).
2.2 IMUperformance
Accuracyoftherotationandgravityvectorestimation
depends as much on the strength of
the vector
mentioned above as on the noise coming from the
sensor. Estimation of the inertial sensor noise is not
straight forward to be obtained since it depends on
many different aspects. One of the most convenient
way of the inertial sensor noise estimation is to
measure it using the
Allan Variance methodology.
Observingtheoutcomesignalfora longenoughtime
one obtain, with a quite good reliability, a
dependence of the sensor noise on the samples
averaging time. The dependency is not linear and
therefore must be performed for many different
integration times, which usually is time consuming.
In
areward,theobtainedvarianceiseasytointerpret.
Choosing an optimal averaging time leads to
minimization of the sensor noise. The following
equation(2)(Hoveetal.1981)wasused.
223



2
2
21
2
1
1
2
22
N
kkk
k
t
N



(2)
where σ = Allan standard deviation τ = time of the
integration cluster; N = number of clusters; θ =
incrementsofangle/velocityduringintegrationtime.
This analysis was done for each of the sensors
separately.Assumingthatthereisnorestrictioninthe
alignment procedure duration,
for each sensor there
has been chosen an optimum averaging time
accordingtotheminimumgyroscopenoise.
3 EXPERIMENTIMPLEMENTATION
3.1 Sensorsplatform
In total three sensors have been used in the testing.
Aforementioned LN‐200E IMU from Northrop
Grumman played in the test the role of reference
IMU. The FOGs
of this IMU characterizes with bias
stabilityof1°/hr,randomwalkof0.08°/√hrandscale
factorof100ppm.Thissensorhasarobusthousingof
avolumeofaround0.7landweights700g.
Another sensor is built entirely in MEMS
technology. TheμIMU from
LITEF contains
gyroscopeswithbiasstabilityof6°/hr,randomwalk
of0.3°/√hrandscalefactorof1400ppm.Asa MEMS
technology sensor, its characteristics are gravity
dependent. It is important to mention it because
makingthe sametestin10 mggravityof Enceladus
would probably give
slightly different output. The
μIMUisnotmuchsmallerthantheLN‐200EIMU.It
doesnotdefinetheminiaturization.Itwas,however,
chosenforthetestasoneofthebestrepresentativeof
theIMUsmadeinMEMStechnology.
Exclusively for the comparison purpose also the
XsensMTi‐G710
hasbeentested.Thissensorbelongs
togroupofconsumergradesensorsandhaven’tbeen
consideredtobeusedinsuchdemandingapplication
astheice‐probenavigation.Itsgyroscopeshavebias
stabilityof10°/hr.
All sensors were connected to a common data
logging platform build on a programmable
board
myRIO‐1900 from National Instruments. This board
runs on a Linux on ARM system and contains an
FPGAchip. Thesensorswerereadandcontrolledina
deterministic way. They were also referred to a
common clock assuring that the measurements are
comparable.Therecordedsampleswereavailablefor
post
‐processing.
3.2 Testingenvironment
Realization of a very precise rotation of the sensors
waspossiblewithaprecisetwo‐axisratetable build
by Contraves Goery Corporation. The rate table
characterizes with position accuracy better than
5arcsec, position resolution of 0.36 arcsec, rotation
rangestartingfrom0.0001°/s.
Setup
of this rate table played a crucial role in
simulatingrotationoftheEnceladus.Theouteraxisof
theratetablewassetduringthemeasurementinsuch
aposition,thattheinneraxisofthetablewasparallel
totherotationaxisoftheEarth.Theinneraxisofthe
tablewasrotatingthesensorswithamentionedrate
of 0.00112°/s in the opposite direction to the Earth
rotation. The cumulative, absolute rotation of the
sensors measured with respect to the inertial frame
was0.003°/s(revolutionperiodequalto33hours).A
special care was taken on the
correct weight
distributionandbalancinginordertoavoidajitterof
the rate table motor which are balancing the given
attitude.
Thestatic,nomovementtestwasrealizedwiththe
sensors attached to the foundation and at the same
time being completely isolated from the building
structure.
4 TESTINGRESULTS
4.1 IMUperformance
The analysis of the test results begins with the
comment on the Alan variance analysis. The plots
presentedinthepapershowsrecalculatedintoAllan
standard deviation relation to the averaging time.
Two plots for each sensor are given, one with the
accelerometers’standarddeviation and one
withthe
gyroscopes’.
Beginning with our reference sensor, LN‐200E
IMU, its standard deviation of the accelerometers’
noisereachesminimumafter20secondsofaveraging
(seeFigure1.).Untiltheintegrationtimeof1second
the dominant noise source isthe quantization noise.
Thisisquitealongdominanceandthe
reasonforthat
isthattheLN‐200EIMUuses16‐bitrepresentationof
thevaluespreservingbroadoperatingrangeof20g.
Thisnoiseiseasytobefilteredout,especiallyinthe
presentedapplication, wherelonger averaging times
areallowedtobeused.
Figure1. Allan standard deviation of the accelerometers
measuredintheLN‐200IMU.
Velocity random walk of the accelerometers
dominatesforonly 2to20 sofaveragingtime.This
showsthattheaccelerometerareofthegoodclass.At
the 20 s averaging it can be filtered out down to
σ=0.2m/s/hr. The accelerometer bias instability and
correlated noise defines the
minimum variance in a
widerangeof20toover1000saveragingtime.
ThegyroscopesoftheLN‐200EIMU,aspresented
in a Figure 2., are very well performing. In a
difference to the behavior of the accelerometers the
quantizationnoiseistobewellobserveduntil30ms
of integration. Very quickly,the angle random walk
224
contributestothedeviationofthemeasurement.This
may be problematic for some applications, because
filtering the random walk noise out takes ten times
longerasfilteringthequantizationnoiseout.Ittakes
300sofmeasurementtoobservereducednoisedown
toσ=0.15°/hr.
Figure2. Allan standard deviation of the gyroscopes
measuredintheLN‐200IMU.
TheμIMU from LITEF has both, accelerometers
and gyroscopes; implemented in MEMS technology.
The quantization noise in the accelerometers is
dominant for only approximately 20ms, what is
probably a result of longer, 32‐bit representation of
samples. The minimum noise at the level of
σ=0.3m/s/hr is obtained
for a 100 s measurement
representation. After that time, the correlated noise
andbiasinstabilityaremorepowerfulthanthenoise
causedbyvelocityrandomwalk.(seeFigure3.)
Figure3. Allan standard deviation of the accelerometers
measuredintheLITEFμIMU.
Figure4. Allan standard deviation of the gyroscopes
measuredintheLITEFμIMU.
The plots of the Allan standard deviation of the
gyroscopesinμIMUpresentedinFigure4showthat
these MEMS sensors are very well performing.
Dominant quantization noise is observed until
approximately 70ms of integration. Further
integration until 400s reduces the noise down to
σ=0.4°/hr.This
levelofnoiseisverysmallasforthe
MEMSgyroscope.Itisobtainedhoweverafteralong
integrationtime.
The Xsens MTi‐G710 is a very small factor
integrated inertial navigation system. The noise
characteristics of accelerometers and the gyroscopes
ofthissystemweretestedandpresentedrespectively
inFigures
5.and6.
In general, in the Xsens gyroscopes and
accelerometers, the quantization noise is not
observable at any time. The measured values are
represented in 64‐bit floating‐point numbers, which
givesasufficientmarginforrepresentingaverywide
dynamicsofthemeasurement.Theintegrationofthe
accelerometers’
measurementmakesitprofitableonly
until1s.Afterthattimethevelocityrandomwalkis
buried in the electronic noise, interpreted as bias
instabilty.At1sintegrationtheaccelerometer’sAllan
standarddeviationisreducedtoσ=6m/s/hr.
Very quickly, after 10 seconds of integration, the
acceleration random walk
becomes a dominating
componentinthesensornoisecharacteristics.
Figure5. Allan standard deviation of the accelerometers
measuredintheXsensMTi‐G710.
Figure 6. Allan standard deviation of the gyroscopes
measuredintheXsensMTi‐G710.
The optimum integration time for the Xsens
gyroscopesis30s,accordingtothemeasurements.At
that time the most contributing angle random walk
dropstoσ=17°/hr.
The final comparison of the minimum standard
deviation of the tested accelerometers is shown in
Table1.
225
Table1. Accelerometers’ minimum Allan standard
deviation
_______________________________________________
SensorMinimumσ(τ) Integrationtime
m/s/hrs
_______________________________________________
LN‐200EIMU 0.220
μIMU0.3100
MTi‐G710610
_______________________________________________
TheaccelerometersoftheLN‐200EIMUaremost
stable within the set of the tested sensors. Their
velocityrandomwalkmaybeobservedonlyuntilthe
20th second of integration. It also operates with the
smallest, among the tested sensors, noise level. Not
much less performant are accelerometers
of the
μIMU. They generated at tiny bit more of velocity
random walk, but it was observed not until 100th
second of averaging time. The optimum observation
time for the MTi‐G710 accelerometers was the
shortest, i.e. only 10s, but after that time the
significant, in comparison, 6m/s/hr
standard
deviationisobserved.
Theperformanceofalltestedgyroscopesareonce
morepresentedintheTable2.
Table2.Gyroscopes’minimumAllanstandarddeviation
_______________________________________________
SensorMinimumσ(τ) Integration
time
°/hrs
_______________________________________________
LN‐200EIMU0.15300
μIMU0.4400
MTi‐G7101730
_______________________________________________
AsitwasexpectedfromtheFOG, itoutperforms
the MEMS gyroscopes. The best minimum σ(τ) is
obtainedafterrelativelyshorttime,whencomparing
totheμIMU.TheLITEFsensorisalsomeasuringwith
slightpollution of the measurements. The minimum
σ(τ) is obtained after much
longer time but it is
important to underline, this was achieved with a
MEMS technology gyroscope. Representing the
consumer grade IMU MTi‐G710 generates the
minimumnoiseatthelevelofσ(τ)=17°/hrandisnot
capabletocompetewiththeothertwosensors.Infact
this
valueisgreaterthantheEarthrotationrate=15
°/hr.
Itisimportanttoinformherethattheauthorsdid
not compare the results with the factories product
specificationduetolackofcompleteinformationand
differentforeachproducttestingprocedure.Thatwas
alsoareasonofperformingthe
relativecomparisonof
the units, what complements the sensors
specifications
4.2 Gyrocompassing
Thefollowingtestaimedanestimationoftheattitude
determinationofthe sensor withrespect tothe local
frame. As described in a previous chapter, the
vulnerable are the rotation measurements, because
the meas ured values are on the
level of the sensors
inaccuracies. Therefore, in order to get the best
gyroscope measurements, each sensor’s best
integrationtimeofthesamplespresentedintheTable
2.,wasusedinthispartoftesting.
The identical test procedure of attitude
determinationwasperformedfortwoscenarios:non‐
rotatingsensorsforthe
attitudedeterminationinthe
Earth conditions; rotating sensors what simulated
Enceladusenvironment.
Theresultsofthattestingpartaregatheredinthe
Table3. Thevalues inthe table arerepresenting the
standard deviation from the actual attitude of the
sensors. σ
leveling is depends on the accelerometer
measurements and they are the same for every test
run,sinceonlynominal1ggravityaccelerationwas
available to be measured. σ
North articulates the
standarddeviationoftheNorthfinding.Itisdifferent
fortheEarthandsimulatedEnceladusconditions.
Thepresentederrorsofnorthestimationhavetheir
origin in the bias instability and correlated noise of
the gyroscopes. A bias or scale factor of the sensors
have had negligible influence on
the accuracy
presentedinthetable.Thiswasalsoa purposeofthe
testtoexposetheerrors,whichcannotbecorrectedin
a stand‐alone inertial attitude determination system
andcanbemodelledonlywithstatistics.
Table3. Attitude estimation error: comparison between
North‐findingontheEarthandonEnceladusandleveling
accuracy.
_______________________________________________
Sensorσleveling σNorthEarth σNorthEnceladus
deg degdeg
_______________________________________________
LN‐200EIMU 3.24e
‐3
 0.180.26
μIMU4.71e
‐3
 0.420.77
MTi‐G71027.2e
‐3
 n/an/a
_______________________________________________
The leveling error caused by the accelerometer
noiseisonthesimilarlevel,tensofarcseconds,inthe
LN‐200E andμIMU. The same error caused by the
MTi‐G is almost ten times bigger. North finding is
morechallengingforallsensors.Thisistheresultof
a
small rotation measurement. The FOG was best
performingamongthetested gyroscopes. TheNorth
findinguncertaintycausebythegyroscopenoisewas
almost0.2°fortheEarthconditionsandincreased44
%incaseofrotationofEnceladus.
TheμIMUwasover twiceworsecomparingtothe
tested FOG.
This happened after a longer by 100 s
integrationtime.ThedegradationofNorthfindingin
theEnceladusconditionalmostdoubled.
TheMTi‐G710wasnotreasonablyclosetothereal
Northpointing.
5 CONCLUSIONS
Thetestansweredtotwoquestionsofthestudy.The
firstwasifitis
possibletoestimatetheattitudeofthe
inertial sensors on Enceladus, and if yes, what
degradation of such estimation should be expected.
The obtained degradation w.r.t. the previous
generationoftheattitudedeterminationsystemforan
iceprobe, that is performance of theμIMU tested in
Enceladus conditions w.r.t. the LN‐200
tested in the
Earthconditions,hasbeenmeas uredtobearound430
%.Thistestconcentratedonrandombehaviorofthe
gyroscopesandconstanterror,likemisalignmentand
biasrepeatabilitywerenotinthetestconsidered.The
226
obtained result may be interpreted as the minimum
for course alignment algorithms. The drop of
accuracy is significant but not critical for the
presented,higherdemandingapplication.
Thisstudyhaven’tansweryetthequestionwhatis
the minimum accuracy of the attitude estimation in
the subpolar regions, which is one
of the mission
assumptions. It seems however that yet, there is a
justifiedpresumptionthatthemoredemanding,low‐
dynamic application may be realized with MEMS
technologyinertialsensorsinthenearestfuture.This
may drive significant costs reduction in the
navigation systems implementation. This is an
advantage which may
be taken in the exploration
applications, space or terrestrial, as well as in the
maritime application, which characterizes with very
lowfrequenciesmovements.
REFERENCES
Hove,D.A.,Allan,D.W.&Barnes,J.A.,1981.Propertiesof
signalsourcesandmeasurementmethods. Proceedingsof
the 35th Annual Symposium on Frequency Control, (DOI:
10.1109/FREQ.1981.200541):669‐716.
Niedermeier, H. et al., 2014. Navigation system for a
research ice probe for antarctic glaciers. Position,
Location and Navigation Symposium‐PLANS 2014,
2014IEEE/ION,(DOI:10.1109/PLANS.2014.6851461)
Szumski, A. et al., 2016. Enceladusʹ environment and the
design of the Enceladus ice‐probe navigation system.
AIAASPACE2016,AIAASPACEForum,(10.2514/6.2016‐
5536).