research article real-time hardware-in-the-loop...

Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2013 Article ID 505720 13 pageshttpdxdoiorg1011552013505720

Research ArticleReal-Time Hardware-in-the-Loop Tests ofStar Tracker Algorithms

Giancarlo Rufino1 Domenico Accardo1 Michele Grassi1 Giancarmine Fasano1

Alfredo Renga1 and Urbano Tancredi2

1 Department of Industrial Engineering (DII) University of Naples ldquoFederico IIrdquo Piazzale Tecchio 80 80125 Napoli Italy2 Department for Technologies University of Naples ldquoParthenoperdquo Centro Direzionale Isola C4 80143 Napoli Italy

Correspondence should be addressed to Giancarlo Rufino giancarlorufinouninait

Received 15 May 2013 Accepted 7 August 2013

Academic Editor Paolo Tortora

Copyright copy 2013 Giancarlo Rufino et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper deals with star tracker algorithms validation based on star field scene simulation and hardware-in-the-loop testconfiguration A laboratory facility for indoor tests based on the simulation of star field scenes is presented Attainable performanceis analyzed theoretically for both static and dynamic simulations Also a test campaign is presented in which a star sensor prototypewith real-time fully autonomous capability is exploited Results that assess star field scene simulation performance and show theachievable validation for the sensor algorithms and performance in different operating modes (autonomous attitude acquisitionattitude tracking and angular rate-only) and different aspects (coverage reliability and measurement performance) are discussed

1 Introduction

Many spacecraft with accurate 3-axis control requirementsare equipped with a star sensor to support attitude deter-mination In recent years star tracker technology has had aremarkable evolution In particular these sensors have gainedsignificant improvements in their autonomy and capabilities[1 2]Modern star sensors are expected to offer new advancedfunctionalities in addition to the assessed capability of high-precision pointing determination during low angular ratemission phases They are conceived [3]

(i) to produce high-accuracy high-reliability attitudeangle and rate estimates without external support

(ii) to operate in a wide range of mission conditions(iii) to solve the lost-in-space problem autonomously and

in short time(iv) to deliver angular rate information also when attitude

determination is not feasible as during platformdetumbling or slewing

The ultimate goal is the achievement of performancefunctionality and reliability allowing star sensors to be the

only attitude sensor onboard the spacecraft [4] Latest gener-ation star sensor novel and advanced functionalities shouldbe achieved via additional software routines rather thanby hardware enhancements and different operating modesshould control sensor operation As a result software forsystem control and management becomes very complex

Due to the widened range of functionality and novelhardware characteristics new problems arise in testingmodern star trackers both for calibration and performanceassessment Angular and photometric calibration can still beoperated following the procedures that have been successfullyapplied up to now [5 6] Differently all the functions relatedto processing real star field scenes to platform dynamicseffects and estimation and to control logic robustness needthe introduction of new techniques

Specialized laboratory facilities and procedures must bedeveloped to this aim in order to integrate data coming fromtrue-sky tests The latter in fact cannot be avoided [5] Buteven if they must be performed for final system validationthey are not adequate for fine calibration of the sensorLikely they are also more expensive and time-consumingthan indoor procedures because ad hoc external campaignsto adequate locationsmdashtypically far sitesmdashare needed and in

2 International Journal of Aerospace Engineering

addition dedicated hardware setup must be realized In factatmospheric effects (refraction scintillation light absorptionand background light caused by light pollution) must beminimized which is achieved thanks to high-altitude sitesfar from urban areas and near-zenith sensor pointing [9]Valid tests for angle measurement stability require long-time (hours) sequences of measures with firmness of sensorinstallation Often these tests are carried out at astronomicalobservatories installing the sensor on the structure of atelescope thus taking advantage of its tracking system to keepa fixed inertial pointing during the test [10]

In the following some problems related to laboratory val-idation of modern star trackers are studied In particular it isconsidered the solution of testing hardwaremodels in end-to-end configuration by acquiring and processing simulated starfield scenes that extend over the whole sensor FOV True-skyscene simulation is analyzed Specifically a high-resolutionLCDdisplay is adopted to simulate star fields Aspects dealingwith design realization and operation of such a facilityare presented Hence the achievable performance of suchsimulation is discussed from a theoretical point of viewFinally a test campaign is presented It was carried outwith twofold objective firstly to validate the theoreticalperformance analysis of the star field simulation system andsecondly to show the kind of validation that can be achieved

2 Test Facility Architecture

The tests of modern star trackers cannot be limited tocalibration and measurement performance assessment forsingle star-like light source The algorithms presently inuse in fact exploit star field scenes that can be acquiredunder different operatingmodes and during differentmissionphases with operation capability in a range of dynamicalconditions from stabilized attitude to high rate rotationsRelevant performance assessment as well as themanagementof the operating modes typically autonomous requires vali-dation under realistic input conditions and end-to-end testconfiguration including the hardware model of the sensorIn particular the former issue is to be preferred even at thepreliminary stage of algorithm testing Also extensive testcampaigns must be foreseen for adequate validation Afterthese considerations the architecture of a laboratory facilityto carry out indoor testing of modern star trackers has beendefined in order to meet the following objectives

(i) ability to support end-to-end tests with hardwaresensor models or functional prototypes

(ii) realistic simulation of star field scenes to allow starfield scene acquisition as during in-orbit operation ofthe sensor and consequent processing

(iii) ability of simulating the orbital and attitude dynamicsof a spacecraft carrying the sensor to carry out testsreproducing specific mission phases of interest

The facility architecture proposed and analyzed by RufinoandMoccia [11 12] has been selected since it meets the aboveobjectives and it is quite flexible to carry out the mentionedvariety of tests It is presented in Figures 1 and 2 The basic

Sensor optical head

Sensor processing unit

Ethernet

DVI

Display control processing unit

Experiment control processing unit

Sensor

Optical radiation

RS-232

Hi-res display

Figure 1 System block diagram of the star field simulation labora-tory facility

idea is that the LCD screen stimulates the sensor under testIt shows the star field scene that would be viewed in the sensorFOV for the assigned orientation

Two kinds of simulations are considered static anddynamic A static simulation consists of one star field scenecorresponding to a given pointing without attitude dynamicsin the inertial reference frame (where sky stars are stillneglecting long timescale proper motion effects) A dynamicsimulation accounts for orbit and attitude dynamics of theplatform carrying the sensor during a finite time interval It isrealized by means of a sequence of star field scene reportingthe apparent motion in the sensor FOV exhibited by theviewed stars The sequence is characterized by the frequency119891119904119891

at which it is updated which is necessarily limited butbenefits of technology advance

A single pixel of the LCD screen is exploited to simulatea single star of a star field if a static pointing is consideredor in the case of a low rate dynamics of the orbiting platform(Figure 3) Differently when high rate attitude dynamics areaccounted for in the simulation a single star is represented bythe strip of pixels reproducing its apparent trajectory in thesensor FOV during the scene update time 1119891

119904119891(Figure 4)

Pixel brightness control is used to reproduce star apparentbrightness as explained in the following

Star positions in the FOV are computed as a function ofthe simulated orientation on the basis of a sky star catalogassumed as reference which must be completed at least upto the sensitivity limit of the sensor under test for correctrealistic simulation For the realized facility the SKY2000 starcatalog was selected [13]

At the stage of generation of simulated star field scenesother effects can be introduced As an example space radia-tion can be accounted for by adding activated pixel besidesthose representing real stars [10] In fact radiation maydetermine star-like features in the images acquired by thesensor Occurrence of the phenomenon shall be based onmodels taking account of orbit and epoch

The realization of the facility presented here has beenbased on commercial-off-the-shelf (COTS) products Themain components are

(i) a high-resolution computer-controlled LCD displaythat shows the simulated star field scenes constituting

International Journal of Aerospace Engineering 3

Hi-res LCD display Darkroom Star

sensor Collimating optics

Optical table

Large-scale longitudinal translation stage

Collimator support (orientation and height adjustment)

DVI link

fc

Experiment and display controlprocessing unit RS-232 link

Translationand

rotationstages

Figure 2 Schematic of the star field simulation laboratory facility

(a) (b)

Figure 3 Static simulation Simulated star field displayed by the LCD screen (a) and corresponding acquisition carried out by the sensor (b)

Figure 4 Simulated star field scene displayed in the facility in adynamic simulation with high rate of rotation along boresight

the input to the sensor under test With respect tothe original solution by Rufino and Moccia here anLCD is adopted instead of a CRT display which guar-antees improved simulation performance thanks to itssuperior characteristics in terms of image geometryand thanks to its flatness [12] Specifically the selectedunit is a 3010158401015840-wide (16 9 format) highresolution LCDdisplay by EIZO (Table 1)

(ii) an Intel-Quad-based single-board computer equi-pped with 1-GB-RAM and a high-resolution videocard In the presented realization of the facility itis in charge of both the functions of experimentcontrol (EC) and display control (DC) processingunits (Figure 1)

(iii) a collimating optics that makes the scene on theLCD display appear as if at infinite distance fromthe sensor The collimator focal length 119891

119888is to be

selected so that the LCD screen covers the wholeFOV of the sensor under testThe lens support allowsvertical position and orientation adjustment For therealization of the facility119891

119888= 13meters was adopted

determining the features in Table 2(iv) a set of high-precision translation and rotation stages

that constitute the basis of the mechanical interfacefor installation of the sensor in the test chamberTheyallow fine adjustment of position and orientationwith respect to the LCD screen In particular large-scale adaptation of the distance from the screenis common to both the collimator and the sensorwhilst micrometric adjustment of orientation andtransversal position is available for the sensor

(v) a darkroom that covers the sensor the collimator andthe LCD screen In particular its side opposite to thesensor is constituted by the LCD screen closely andstably fixed to the darkroom structure to guaranteethat no light contaminates the darkroom inside

(vi) an optical bench with pneumatic vibration isolationthat supports the facility guaranteeing alignmentstability

Some additional details about the above processing unitsare necessary to the aim of a clear description


Table 1 Main features of the LCD display in use (EIZOMX300W) [7 8]

Diagonal (m) 0756 (3010158401015840 169 format)Active area H times V (m) 0641 times 0401Dot pitch (mm) 0250Resolution H times V (pixel) 2560 times 1600Refresh frequency (Hz) 60Luminance (fL) 87Pixel brightness control DICOM calibration curve

Table 2 Facility features relevant to sensor FOV matching

Collimator focal (m) 13Collimator diameter (mm) 50Display apparent angular size (deg) 277 (H) times 175 (V)Pixel apparent angular size at screen centre (arcsec) 40 (H) times 40 (V)Overall magnification ratio (with 16 mm focal sensor optics) 123 times 10minus2

The DC processing unit is in charge of controlling thevisualization of sequences of simulated star field scenes onthe LCD screenWhen a specific dynamics is to be simulatedthis must be accomplished respecting a severe timing As aconsequence for this unit a real-time operating system maybe taken in consideration A DVI link is used to control thedisplay

The EC processing unit is in charge of experiment man-agement control of the tasks of the DC unit and of the sensorunder test logging of experiment data (both simulation andsensor IO) and experiment database preliminary (off-line)simulation data computation (orbit and sensor pointing sim-ulated scene sequence) These tasks require less strict timingthan display control hence a standard operating system hasbeen envisaged The link to the sensor is serial to supportthe same format as the typical one used to communicatewith an onboard data handling unit The latter requirementis significant if testing engineering or flight models In thecase of a different communication link it can be easily metby reconfiguring the port of the EC processing unit

DC and EC tasks were conceived to be implementedpossibly and preferably in separate hardware units in orderto guarantee the best performance in dynamical simulationsas described in the following Communication between themis based on Ethernet link and TCPIP protocol In the testfacility realization presented here a simplified solution hasbeen validated they are two virtual units that is two distinctsoftware tasks running in the same processing unit thataddress two distinct Ethernet network ports both available atthe hardware processing unit hosting the two tasks and areconnected to each other

Specific software procedures were developed for the twotasks Besides the already mentioned functionalities the ECunit software allows synchronization of display control andcommands to the sensor under test to carry out simulationof specific mission phases both in terms of star field scenesin the sensor FOV along with operation and on board IO ofthe sensor With reference to the mentioned function of sim-ulation data computation any arbitrary sequence of sensor

orientations can be processed from external input files to gen-erate the LCD star field scenes to be displayed for their simu-lation Also basic simulations can be generated without inputfiles adequate to test typical star sensor operation modes

(1) static simulations to support the development andtesting of autonomous attitude acquisition routinesIn this case a series of independent star field scenesthat are uniformly distributed over the celestial sphereare generated and the sensor prototype is com-manded to perform autonomous attitude acquisitionfor algorithm first validation

(2) dynamic simulations to test attitude tracking rou-tines In this case the generated sequence of starfield scenes corresponds to a given orbit and zeroattitude during a selected orbit segment Kepleriancircular orbits can be selected by assigning radiusand inclination This mode allows real operatingconditions during a space mission to be simulated

Figure 5 shows the realized system The LCD display isthe key component of this facility Table 1 reports its maincharacteristics Star brightness simulation can be modeled interms of the apparent visual magnitude 119898V as a function ofthe display luminance 119871fl with its control scale and of thedistance 119891

119888from the screen to the collimating lens [11]

119898V = minus2512 log [119891119904 (10764

120587

119871fl 119860pix

119891119888

)] + 14 (1)

where 119891119904lt 1 is the attenuation accounting for atmosphere

absorption (to be assumed in the order of 075 according to[14]) and 119860pix is the area of a single display pixel activated tosimulate a star of apparent visual magnitude 119898V Assuming119891119888as large as 13 meters the achievable 119898V simulation range

is minus15 (brightest star) to 57 (dimmest star) thanks to thedisplay maximum luminance of 87 footlamberts Consider-ing that sky star distribution is larger for low brightness andthat consequently to gain sky coverage ability typical star


tracker sensitivity is up to visualmagnitude of 657 the aboverange of magnitude can be shifted towards fainter values byreducing the LCD brightness level thus scaling the entirerange downwards As an example 50 reduction changes the119898V simulation range to minus0764 A higher reduction may bepreferable in order to simulate also stars not observable bythe sensor under test but that contribute to the backgroundacquisition noise in true-sky operation on the other handthis makes larger the number of bright stars which aresimulated fainter than they are Also it is worth noting that indynamic simulationswith high rate of rotation the brightnesslevel of the pixel strip representing a single star is determinedby the constraint that the overall radiation from the stripequals the one of the simulated star

Finally also star radiation spectral characteristic in thevisible band could be accounted for in such a kind of LCD-based simulation It can be accomplished by modifying theratio between the red green and blue pixel color compo-nents but a color display must be adopted of course Thishas not been implemented yet in the realized facility sincethe most common sensor algorithms do not make use ofsuch information even if this issue is being discussed in thepublished literature [15] However it must be pointed outthat such technique for star color simulation is not straight-forward but it must be studied before implementation Infact certainly the mentioned solution cannot completelysimulate the spectrum of a star emission similar to a blackbody radiation Rather it should exploit the LCD peakedemissions at redgreenbluefrequencies with respect to starvisible spectrum and sensor photodetector spectral responseTo conclude in this case more than one pixel should beused to simulate a single star since in color displays eachpixel emits in a single color band and different color pixelsare arranged in patterns this requires additional study toguarantee correct simulation of star fields in terms of starapparent angular size angular separation between stars andapparent star motion in dynamic simulations

3 Simulation PerformanceTheoretical Analysis

Star field simulation operated by means of the presentedfacility has limitations arising from the discrete nature of thestar field scenes displayed by the LCD screen

(i) the angular size of the simulated stars is larger thanthe one of true-sky stars because of the size of theLCD pixels exploited for their simulation

(ii) star position in the simulated star field is approxi-mated because of the finite number of pixels availableon the LCD

(iii) dynamical scenes suffer fromdiscretization problemsbecause of the consideration at the previous pointand in addition due to the discrete and finite numberof scenes that can be displayed on the screen per unittime

In terms of the above issues the quality achieved in thesimulation of star fields has been evaluated preliminarily

Figure 5 Darkroom interior volume sensor installation and posi-tionorientation control system for sensor and collimator (left side)LCD screen (right side partial view) Base antireflection panels wereremoved to show the optical table and the large-scale translationtracks for LCD distance adaption of both collimator and sensor

from a theoretical point of view with special reference tothe application being considered that is functionality testsof a modern star tracker With this objective the achievedperformance of star field simulation is expressed in terms ofthe effects on attitude measures operable by the sensor undertest In other words simulation performance is expressed bymeans of the uncertainty induced in the measured attitudefollowing a conservative worst-case approachThis approachpresented by the authors in [11] where it was applied toa CRT-based test facility has been reviewed and used tocharacterize the presented test facility that takes advantage ofstate-of-art technologies

31 Static Simulation Performance In this case the displayresolution determines the accuracy of the star field simula-tion In particular its dot pitch 119889pix gives the minimum angu-lar separation 120575pix between adjacent positions of simulatedstars On the optical boresight it is

120575pix = 2tanminus1119889pix2

119891119888

(2)

Then the maximum angular error resulting from starposition approximation at pixel location is plusmn120575pix2 and thiserror is expected to be uniformly distributedThe same valuecan be regarded also as the maximum approximation for thechange of the apparent position of a single simulated starwhen reproducing a pitch-only or yaw-only attitude rotation(ie along axes perpendicular to the sensor boresight)In both cases after uniform distribution assumption thecorresponding standard deviation value of 120575pixradic12 can beregarded as single star position uncertainty in the mentionedangular terms Figure 6 shows 120575pix as a function of theoff-boresight angle computed for the adopted display andcollimating optics (Table 2) It results that 120575pix has verylimited variations keeping in the order of 40 or 55 arcsecsrespectively in H or V direction of the display and in thepixel diagonal direction It is worth mentioning that in gen-eral LCD displays may have rectangular pixels so differentdimensions can be considered in horizontal vertical andpixel diagonal directions Since LCD display single pixel have


Table 3 Simulation accuracy with reference to multiple star-based measures

120590119901119910

(arcsec) (Nstars 21540) 120590119903(arcsec) (Nstars 21540)

Boresight stars 983622 560205125 (1-deg off-boresight)Mid-range off-boresight stars 963521 803020FOV-border-off-boresight stars 923320 401510

30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V

Off-boresight angle (deg)

120575pi

x(a

rcse

c)

Figure 6 Angular separation of adjacent pixels as viewed from thesensor installation position in the test camera (12 of this quantityrepresents the maximum error in the simulation of the positionchange in sensor FOV for one star after any pith-only or yaw-onlyrotation)

practically size as the display dot pitch the above valuesrepresent also the apparent angular size of the pixel They aremuch larger than a real-sky star [16] but arewithin the typicalIFOV ofmodern star trackers which also adopt defocusing toget subpixel accuracy [1] hence this is still a valid simulationsolution

The separation between two positions on the displayscreen can be expressed also as the angle 120575pix119903 with vertexat the screen centre which is a function of the off-boresightseparation 120572offb of the considered star positions

120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)

as shown in Figure 7 for the adopted display and collimatingoptics The angle 120575pix119903 represents the roll rotation (ie alongthe boresight axis) that determines a 1-pixel position changefor a simulated star viewed at 120572offb from the FOV axis As forpitch and yaw plusmn120575pix1199032 represents in terms of roll rotationthe maximum approximation in the simulation of either theposition or the apparent motion in the sensor FOV and120575pix119903radic12 is the corresponding uncertainty

The above single-star position uncertainties can be turnedinto estimates of simulation accuracy with reference to themeasures that the star tracker under test carries out afterconsidering that such measures are based on the observationof several stars at least two [17] Assuming uncorrelatederrors in the position of the simulated stars for pitch oryaw rotations and for roll rotations the resulting attitude

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse

c)Figure 7 Angular separation of adjacent pixels as angle with vertexin FOV centre (12 of this quantity represents the maximum errorin the simulation of the position change in sensor FOV for one starafter any roll-only rotation)

uncertainties 120590119901119910

and 120590119903 respectively can be obtained

as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)

where 119873stars is the number of viewed stars exploited for thecomputation Table 3 reports the values for the presented testfacility In this table for each considered off-boresight angleH or V average values of 120575pix and 120575pix119903 with respect to H or Vdirection and pixel diagonal (Figures 6 and 7) are exploited

32 Dynamic Simulation Performance To carry out tests ofthe advanced functionalities of a modern star tracker itis necessary to display a sequence of stellar scenes to thesensor as it would observe them in orbit during real oper-ation This aspect of star field simulation is addressed hereconsidering the effects of finite resolution of the simulationin terms of both star positions in the simulated scene andupdate frequency of the star field scenes (ie the number ofsimulated scene displayed per second) Both of these factsimply that the simulated star apparent motion displayedon the screen cannot be rigorously continuous that issimulated star apparent motion continuity is limited becauseof spatial and temporal discretization of the synthetic scenesthat simulate the evolving star field This limitation can bemade little thanks to technology improvements (more LCDpixels higher frequency of simulated scenes) but cannot


Table 4 Minimum angular rates for continuous motion simulation (ie 1-LCD pixel simulated star position change between subsequentsensor acquisitions)

120596min119901119910 (arcsecs) 120596min 119903 (arcsecs)Boresight stars 190 10800 (1-deg off-boresight angle)Mid-range off-boresight stars 188 1550FOV-border-off-boresight stars 180 765

be canceled The resulting effects in terms of quality ofsimulation are discussed and analyzed quantitatively in thefollowing introducing some figures of merit and evaluatingthem for the presented test facility

The settings of the test facility and of the sensor undertest affect simulation performance analysis In the presentedanalysis it is assumed that the simulation display frame rate is119891119904119891= 10Hz In general it must be119891

119904119891ge 119891upd where the latter

one is the sensor update rate that is the frequency at whichthe sensor generates its measures In the following 119891upd =4Hz is assumed

321 Minimum Angular Rate To perform angular ratemeasurements even if the viewed star apparent motion isnot continuous it is necessary that the simulated scenesshow changes in presence of nonzero attitude dynamics Inparticular this means that the position of the simulated starsshall change at least one display pixel in Δ119905upd = 1119891upd(continuous-motion constraint) The resulting minimumangular rate is obtained after turning the 1-pixel motion intoangular terms It can be derived for pitch or yaw and for roll as

120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)

The resulting values based on the data in Figures 6 and 7are summarized in Table 4

322 Accuracy of Angular Rate Simulation As describedin [11] this performance parameter can be split into twocontributions the first one 120590

120596 Δ120579 is related to the accuracy of

simulation of each single star field and the second one 120590120596 Δ119905

is related to timing accuracy of sequence display Based on thefollowing model of angular rate computation

120596 =Δ120579

Δ119905 (6)

where 120596 and Δ120579 are respectively the computed angular rateand the rotation realized during the time interval Δ119905 it is

120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)

the wc label with standing for ldquoworst-caserdquo Finally for uncor-related contribution the overall performance can be ex-pressed as

120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)

Quantitative results from this model are obtained aftersome choices

(i) 120590Δ120579

is assumed equal to 120590119901119910

and 120590119903for pitch or yaw

rotations and for roll rotations (Table 3) respectively

(ii) Δ119905 is related the frame rate of the star field sequenceas 1119891

119904119891 and its uncertainty 120590

Δ119905 depends on the

timing capability of the DC computer The latteruncertainty can be significantly reduced by adoptinga real-time operating system (RT os) for the DCcomputer that guarantees event execution control atmicroseconds whilst standard (non-RT) operatingsystems guarantee lower timing performance Hencesignificant difference of performancemay result in thetwo cases

However in the present case where the DC computerdoes not run any additional task other than frameupdating it can be assumed that 120590

Δ119905is in the order

of 001ms as confirmed experimentally (see nextsection)

Under the above assumption for 120590Δ119905and for Δ119905 in the

order of 01 s in the worst case condition (ie non-RT os) the contribution to 120590

120596from (8) is lower than

10 arcsecs even for 120596max larger of 25 degs whilst theone from equation is much larger hence the latterone is dominant

Table 5 presents the results for Δ119905 = 01 s and mid-range off-boresight angles of observed star positions Evenif these values may be not completely satisfactory it mustbe mentioned that there is not any different test solutionto perform such kind of end-to-end tests that is with thesensor under test operated in its complete configuration (starsin attitude out) The only viable alternative is representedby processing simulated acquisitions of the sensor thus by-passing image forming and image acquisition but this maynot be desirable True-sky test may offer source scene withbetter characteristics even if atmospheric and environmentalartifact must be taken into account but they cannot simulatemission phases or maneuvers and they are certainly moreexpensive and time-consuming


Table 5 Angular rate simulation performance estimated for the laboratory facility (Δ119905 = 01 s119873stars = 15)

Angular rate accuracy (arcsecs)Pitch yaw Roll

Boresight stars 36 2050Mid-range off-boresight stars 35 300FOV-borderoff-boresight stars 33 150

Table 6 Star sensor specifications

Field of view (deg) 2248 times 1702Focal length (mm) 16F-number 14Star sensitivity Up to visible magnitude 7Image sensor (12)10158401015840 CCD progressive scanImage size (pixel) 1280 times 1024Instantaneous field of view (arcsec) 61 times 61

4 Test Campaign and Validation

A test campaign was carried out based on the operationof a star sensor hardware model and it is presented herewith twofold purpose Firstly the various simulated orbitandor attitude cases are presented discussing the relevantstar field simulation in terms of performance parameters toassess the theoretical analysis Secondly sensor test results arepresented to show how its functionality and performance canbe analyzed by means of the presented laboratory facility

41 Sensor Hardware Model A hardware model of advancedstar tracker was developed It is based on COTS hardwarecomponents and original software routines that implementthe typical operation modes required for modern advancedsensors [3]

(1) Cartography at each acquisition this mode returns alist of observed stars and the relevant unit vectors inthe sensor reference frame

(2) Autonomous attitude tracking in this mode the sen-sor is able to perform inertial attitude measurementwith a selected data rate without need of externalinformation as soon as it receives input about thestarting initial inertial attitude from an externalsource This function is carried out by exploitingstar unit vectors measured in the sensor referenceframe and the relevant star unit vectors in the inertialreference frame that are contained in a star databaseinstalled in the sensor processing unit

(3) Autonomous attitude acquisition when this modeis commanded the star sensor acquires the initialattitude without need of external information Thisfunction is carried out by comparing star field featuresextracted from observations and models that arecontained in a star feature catalog installed in thesensor processing unit

In order to ensure that the sensor can operate in any ofthe above reported operating modes the sensor itself had to

be designed so that its physical and software characteristicsallow one to implement the mentioned modes The criteriafor selecting these characteristics are reported in [18] Thefollowing list summarizes the sensor specifications to beassessed

(i) on board star catalog size(ii) on board star feature catalog size(iii) optics focal length 119891(iv) optics 119891-number 119865(v) minimum brightness visible star magnitudeSensor specifications derived as reported above and the

results of a market analysis of available COTS units deter-mined the sensor configuration described in the followingIt is based on the Matrox IRIS P-1200HR system [19] that iscomposed of the following

(1) sensor processing unit based on a 400MHz Intel ULPCeleron 128MB ram 128MB flash disk Ethernet10100 RS-232 andOperating SystemMicrosoftWin-dows CE 50

(2) sensor camera unit equipped with a SONYCCD 1210158401015840progressive scan photodetector model ICX267ALwith a 1280 times 1024 pixel arrayThe camera can acquireup to 15 frames per second

(3) lens system produced with 119891 = 16mm and 119865 = 14The resulting specifications are reported in Table 6

Figure 5 shows the camera head installed on racks insidethe darkroom Sensor algorithms that were adopted forthe various operating modes and relevant performances aredescribed in [18 20]

Presently the laboratory facility has been tuned foroperation with this sensor (Table 2) In particular the focallength of the collimating optics119891

119888 has been selected tomatch

the vertical size of the display to the vertical size of the startracker prototype FOV The diameter of the collimator hasbeen determined to avoid vignetting at large off-boresightwithin the displayed scene on the LCD screen [12]


Table 7 DS1 test cases characteristics

DS1 test case 1 DS1 test case 2 DS1 test case 3Orbit Equatorial Polar

Sensor boresight orientation (wrt orbit) Radial (zenith) Perpendicular to orbitplane Radial (zenith)

Inertial attitude angles (deg) (3-1-3 Euler sequence)

Rot1 Linear variation (360-degrange) 90 0


Rot3 Stepwise constant 90 minus90+90

Linear variation (360-degrange)

Stepwise constant 0minus180 0

Frame rate of simulated star fields (Hz) 10Number of stars in simulated star fields (meanstd over1 orbit) 138740 152604 143861

Simulated stars size (LCD display pixels) 1 rarr starimaged as a single pixel gt1 rarr star imaged as a pixelstrip(meanstd over 1 orbit)

1505 1103 1306


DS2 test case 1 DS2 test case 2 DS2 test case 3 DS2 test case 4Orbit EquatorialSensor boresight orientation (at maneuverbeginning wrt orbit frame) Radial (zenith)

Orbital rotation (sensor axis)(Yaw at maneuverbeginning) Yaw and Roll Yaw and Pitch

High-rate attitude rotation (sensor axis) Pitch Roll (boresight)Attitude rate (degs) 1 5 1 5Frame rate of simulated star fields (Hz) 10Simulated stars size (LCD display pixels) 1 rarrstar imaged as a single pixel gt1 rarr star imagedas a pixel strip(meanstd)

90046 25302 2307 7527

411 Test Cases Three main test cases were considered

(i) Static simulations random pointing 1000 randomorientations uniformly distributed over the celestialsphere were generated to carry out a test of theautonomous attitude acquisition procedure andmea-sure precision

(ii) Dynamic simulations orbit plus low-angular-rateattitude (referred to as DS1 in the following) threedifferent combinations of orbit and sensor pointingwith no attitude dynamic in addition to orbit wereconsidered to test sensor operation from autonomousattitude acquisition to tracking during dynamic sim-ulations Two different orbits (equatorial for case 1and 2 and polar for case 3) both are circular withradius of 7178 km (800 kmaltitude 0059 degs orbitalangular rate) and ascending node on the 119883-axis ofthe earth-centered inertial reference frame sensorpointing is along orbit radius toward zenith for case1 and 3 and perpendicular to orbit plane for case 2Table 7 summarizes orbit characteristics and inertialattitude angles for the sensor-fixed reference frame for

each case A sequence of star field scene at119891119904119891= 10Hz

and lasting a complete orbit has been considered in allthe three cases The relevant statistics of the numberof simulated stars per frame are in Table 7

(iii) Dynamic simulations orbit plus high-angular-rateattitude (referred to as DS2 in the following Table 8)a single orbit (circular 500 km altitude and equato-rial 0062 degs orbital angular rate) is consideredwith four cases of additional attitude dynamics thatconsist in the combination of two angular rates(1 degs and 5 degs) and two orientation of therotation axis (perpendicular to and along sensorboresight in both cases in the orbit plate) Sequencesof star field scenes at 119891

119904119891= 10Hz and with time

extension of 18 to 300 seconds were considered inthese cases In these simulations rate-only algorithmswere tested In particular the validated algorithmsare not installed yet in the sensor in use but theywere tested off-line The sensor was operated inthe simulation facility to acquire and save star fieldscenes


Table 9 Statistics of the parameters characterizing static frames

Single star position error (arcsec) Max (abs value) 198Std 115

Average number of stars Mean 176Std 60

Table 10 Star field frame timing performance of the display control processing unit equipped with nonreal-time operating system

DS1 test case 1 DS1 test case 2 DS1 test case 3Frame construction time (ms)

Mean 78 42 808Std 22 12 27

Frame duration (ms)Nominal 100Mean 100008 100001 100009Std 033 059 039

412 Simulation Performance Assessment The quality of thesimulation has been analyzed considering the data describingthe simulated frames and their presentation on the screenduring tests This was done by comparing frame data (acti-vated pixels and their apparent angular position at the sensorunder test) and star catalog data and analyzing log datasaved during test execution to derive figures of merit of thesimulated star field and satellite dynamics

First of all data of the static simulation have beenexploited to validate the theoretical estimation of single starposition accuracy On the basis of the pixel activated tosimulate each star the apparent angular position in the facilityhas been computed and compared to the desired one In termsof angular separations from FOV planes of symmetry theresults (Table 9) are in perfect agreement with the estimateduniform distribution in the range from minus120575pix2 to +120575pix2Also the average number of stars displayed on the LCD is inthe order of 175

Dealing with dynamic simulations the main concernwas checking the adopted solution for the DC processingunit with special regard to scene sequence timing understandard operating systemThis could determine serious lossof performance as already highlighted It is worth notingthat both real-time and nonreal time operating systemshave the same ability to measure time but it is not so fortask planning following a time schedule The latter task isoperated always very accurately only by real-time systemssince they are designed to have deterministic response timepredictability minimum interrupt latency and minimal taskthread switching latency Nonreal-time systems differentlydo not base task thread switching on (time) deadlines Afterthese considerations during dynamic simulations the savedlog data included the times at which the star field scenes wereprocessed In particular two aspects have been analyzed

(i) the duration of the time interval required to ldquosubsti-tuterdquo displayed scenesThis quantity must be as low aspossible with respect to the scene display time 1119891

119904119891

(ii) the stability of the star field update frequency 119891119904119891

To carry out these checks the DC software measures andlogs the time at which each star field scene processing starts(ie just before canceling the previous scene) and the time atwhich the scene is completed on the display (ie right afterthe last pixel of the scene is activated)The first figure ofmerithas been computed as the difference of the above two loggedtimes for the same frame and the second one as difference ofthe start time of subsequent frames Statistics of the results isin Table 10 Frame construction is completed in less than 5of the frame duration frame duration is stable within 06It is worth recalling that these results are obtained runningthe DC unit as a virtual machine in the same hardware unitthat hosts the EC unit software and that this processing unitwas equipped with standard nonreal-time-operating systemEven in this case which does not implement the best solutionfor time stability of LCD scene sequencing (ie a dedicatedhardware unit and hard real-time operating system for theDC Unit) the results are definitely good and support theassumption on which the theoretical assessment of dynamicsimulation performance was based

413 Sensor Performance Assessment Example The sensorunit described above was operated during all the mentionedsimulations in different modes

During static simulations for each star field scenefirstly the sensor was commanded to autonomous attitudeacquisition from unknown orientation then after attitudeidentification it was commanded to attitude tracking Ifthis mode starts successfully it is maintained for about 10seconds in the case the autonomous attitude determinationwas incorrect Tracking fails and the sensor is commandedback to another attempt for autonomous attitude acquisitionand subsequent tracking Running this test it is possible tocheck star tracker algorithm

(i) for autonomous attitude acquisition

(a) sky coverage (percentage of the celestial spherewhere autonomous attitude acquisition is car-ried out successfully)


Table 11 Test of sensor performance for stationary input (static simulations) global results over the whole celestial sphere

Autonomous attitude acquisitionSky coverage gt95Failure lt5

Efficiency821 solution at first algorithm run129 solution in more runs(281412 meanstdmax runs)

Accuracy (arcsec) 60Precision (arcsec) (yaw or pitchroll) 30gt300Number of stars used for attitude computation 2 divide 4

Attitude trackingAccuracy (arcsec) lt5Precision (arcsec) (yaw or pitchroll) 530Number of stars used for attitude computation (meanstd) 161

Table 12 Test of sensor performance for dynamic input (DS1 simulations)

DS1 test case 1 DS1 test case 2 DS1 test case 3Sensor performance

Accuracy (arcsec) (yaw or pitchroll) 2550 605 2050Precision (arcsec) (yaw or pitchroll) 5 divide 1030 530 5 divide 2050

Number of stars used for attitude computation (meanstd) 139302 1540755 148448

(b) efficiency (number of attempts to get the correctsolution)

(c) reliability (percentages of failure and of falseattitude solution)

(d) accuracy and precision of the attitude measuresproduced Accuracy and precision are estimatedas average and standard deviation respectivelyof the deviation of the measured sensor-fixedreference frame from the simulated one Inparticular this deviation is expressed in terms ofyaw pitch and roll errors that is the rotationsthat relate the above two frames

(ii) for attitude tracking

(a) accuracy and precision They were evaluatedas in the previous case in terms of mean andstandard deviation of the errors of measuresequence for fixed stationary simulated starfield this statistics was then averaged over all the1000 cases to get the overall figure of merit ofsensor performance in its FOV

Table 11 shows the results globally for sensor orientationover the whole celestial sphere variability is due to on boardstar catalog and sky star distribution density as analyzedin detail in [18] Different precision in the two modes(autonomous attitude acquisition and tracking) is due tothe different number of stars exploited for reconstructingattitude In detail accuracy and primarily precision esti-mates for Autonomous Attitude Acquisition are stronglyaffected by the algorithm strategy that aims at fast solution

and does not exploit stars uniformly distributed over theFOV in large number Differently tracking data is definitelymore reliable because of the larger number of exploited starscovering almost the complete FOV and in fact they are inagreement with the presented theoretical analysis and meetusual performance assessment for modern star sensors [17]

During dynamic simulation DS1 each test started inIA mode and successfully turned to TR mode which waskept for the whole orbit simulation Sensor inertial attitudewas successfully reconstructed by the TR algorithm and theachieved performance is reported in Table 12 in terms ofattitude angle error statistics for yaw pitch and roll rotations(ie rotations along sensor-fixed axes) Table 12 shows sensorperformance in terms of the measure of error statisticsComplete agreement with TR operation in static tests isaccomplished with slight loss due to the dynamic evolutionof the input scenes

During dynamic simulations DS2 innovative algorithmsfor angular rate determination were examined In thesepeculiar test conditions (specifically high rate of rotation)the stars acquired by the sensor are imaged as strips due totheir apparent motion in the sensor FOV during the imageintegration time adopted by the sensor focal plane subsystemConsequently inertial attitude determination is not feasiblesince star field patterns cannot be identified but angularrates can be estimated on the basis of the apparent motionby examining the length of the imaged star strips [21] orcomparing subsequent acquisitions of a sequence [22] Theapplication of the latter approach to the images acquiredin the described DS2 simulations was carried out by theauthors [23] These tests and their results are briefly reportedhere to show range and variety of tests and validations


Table 13 Test of sensor performance for dynamic input in highrate rotations (DS2 simulations)

DS2 test case 1 DS2 test case 2 DS2 test case 3 DS2 test case 4Accuracy (arcsecs) (yaw or pitchroll) 364179 323461 808240 345286Precision (arcsecs) (yaw or pitchroll) 461439 3964970 224200 408436

possible by means of the presented facility Key point andinnovation of the applied algorithm is the optical-flow-basedestimation of the apparent motion of the imaged star field[23] as displacement field of the imaged stars in subsequentacquisitions This is exploited to compute the time derivativeof the unit vectors to the viewed stars and hence to inertialangular velocity estimation in least-square sense

Table 13 reports the measurement performance exhibitedin these tests in terms of accuracy and precision that ismean and standard deviation of the measure errors duringthe considered mission segment As in the previous casesas expected measures of rotations along the boresight axisare one order of magnitude worse and precision in all thethree components (pitch yaw and roll) is compatible withthe presented theoretical analysis in most cases In particularlarger errors are exhibited only in test case 2 due to thesignificant strip length and the consequent diminution ofthe signal-to-noise ratio in each frame which reduces thenumber of valid star measurements and degrades accuracyin estimating star centroids and their displacement

5 Conclusion

This paper presented a laboratory prototype designed andrealized to carry out tests of software-based functionalitiesof modern star trackers and a laboratory facility to carryout such tests indoor Star field scenes are simulated bymeans of a high-resolution large-size LCD display con-trolled by a computer so that star tracker operation duringa generic mission phase or maneuver can be reproducedand tested Components of both sensor and test facilitywere detailed selected among Commercial-Off-The-Shelfproducts Also their software components were describedThen the performance achieved by the star field simulationsystem was derived They are in the order of 3 arcsecs and30 arcsecs for pitch or yaw rotations and for roll rotationsrespectively in static simulations in dynamic simulationsthey are 200 arcsecs and 1500 arcsecs for pitch or yawrotation rates and for roll rotation rates respectively Eventhough the attained values may not be fully satisfactory thistest solution allows one to simulate a variety of operationconditions static and dynamic that cannot be offered by anyother solution Finally a test campaign is presented basedon a modern star tracker prototype Facility design solutionand the discussed performance analysis were validated Inaddition it was shown that sensor operation can be testedin all the operation modes typical of the latest generationsensors (autonomous attitude acquisition attitude trackingand rate-only) to assess various performance aspects (skycoverage reliability autonomous mode management andmeasurement performance)

Nomenclature

119860pix LCD screen pixel area119889pix dot pitch119865 optics 119891-number119891 sensor optics focal length119891119888 collimating optics focal length

119891119904 atmosphere attenuation factor

119891119904119891 frame rate of simulation display

119891upd update rate of the sensor119871fl LCD display luminance in footlamberts119898V star apparent visual magnitude119873stars number of viewed stars119903 distance between display and collimator120572offb off-boresight separationΔ pix pixel size of the LCDΔ pixD displacement in the direction of the pixel

diagonalΔ119905 time intervalΔ119905upd time interval between two subsequent

acquisitionsΔ120579 rotation realized in Δ119905120575pix angular separation between adjacent

positions of simulated stars120590119901119910

estimate uncertainty on pitch and yawangles

120590119903 estimate uncertainty on roll angle

120590Δ119905 estimate uncertainty on Δ119905


120590120596 estimate uncertainty on 120596

120590120596Δ119905

timing accuracy of sequence display120590120596Δ120579

accuracy of a single star field simulation120596 angular rate120596min119901119910 minimum pitch and yaw rates120596min 119903 minimum roll rate

References

[1] M M Birnbaum ldquoSpacecraft attitude control using star fieldtrackersrdquoActa Astronautica vol 39 no 9-12 pp 763ndash773 1996

[2] C C Liebe L Alkalai G Domingo et al ldquoMicroAPS based startrackerrdquo in Proceedings of the IEEE Aerospace Conference vol 5pp 2285ndash2300 2002

[3] European SpaceAgency ldquoStars sensors terminology and perfor-mance specificationrdquo document ECSS-E-ST-60-20C EuropeanCooperation for Space Standardization ESA-ESTEC Noord-wijk The Netherlands 2008

[4] T B Shucker ldquoA ground-based prototype of a CMOS naviga-tional star camera for small satellite applicationsrdquo in Proceedingsof the 15th AIAAUSU Conference on Small Satellites 2001

[5] V C Thomas R C Blue and D Procopio ldquoCassini stellarreference unit performance test approach and resultsrdquo in


CassiniHuygens A Mission to the Saturnian Systems Proceed-ings of SPIE pp 288ndash298 August 1996

[6] S N Gullapalli D J Flynn F J Kissih A G Gauthier and TMKenney ldquoASTRA1 solid state star trackers for Martin Mariettarsquosmodular attitude control system modulerdquo in Proceedings of theSociety of Photo-Optical Instrumentation Engineers vol 1949pp 127ndash137 1993

[7] EIZO Inc ldquoManual of EIZO MX300Wrdquo httpwwweizocomglobalsupportdbproductsmanualFlexScan+MX300Wtab-03

[8] ldquoBrightnessControlwith aBacklight Sensorrdquo EizoNanaoCorpdoc no 04-002 2004 httpwwwradiforcenlpoolfilesnlWP Backlightpdf

[9] T Bank ldquoCharacterizing a star tracker with built in attitudeestimation algorithms under the night skyrdquo in Proceedings of theSociety of Photo-Optical Instrumentation Engineers vol 3086pp 264ndash274 April 1997

[10] A Eisenman and C C Liebe ldquoOperation and performance ofa second generation solid state star tracker the ASCrdquo ActaAstronautica vol 39 no 9ndash12 pp 697ndash705 1996

[11] G Rufino and A Moccia ldquoLaboratory test system for per-formance evaluation of advanced star sensorsrdquo Journal ofGuidance Control and Dynamics vol 25 no 2 pp 200ndash2082002

[12] G Rufino and A Moccia ldquoStellar scene simulation for indoorcalibration of modern star trackersrdquo Space Technology vol 21no 1-2 pp 41ndash51 2002

[13] J R Myers C B Sande A C Miller W H Warren Jr andD A Tracewell ldquoSKY2000mdashMaster Star CatalogmdashStar CatalogDatabaserdquo Bulletin of the American Astronomical Society vol191 article 12812 1997

[14] H R Condit ldquoNatural phenomenardquo in SPSE Handbook ofPhotographic Science and Engineering T Woodlief Jr Ed pp9ndash30 John Wiley and Sons New York NY USA 1973

[15] J Enright and G McVittiey ldquoStar tracking using colour CMOSdetectorsrdquo in Proceedings of the AIAA Guidance Navigationand Control Conference paper no AIAA 2010-8449 TorontoCanada 2010

[16] M Fracassini L E Pasinetti-Fracassini L Pastori and RPironi ldquoCatalog of Apparent Diameters and Absolute Radii ofStars (CADARS)rdquo in Bulletin DrsquoInformation pp 121ndash123 Centrede Donnees astronomiques de Strasbourg 2nd edition 1988

[17] C C Liebe ldquoAccuracy performance of star trackersmdasha tutorialrdquoIEEE Transactions on Aerospace and Electronic Systems vol 38no 2 pp 587ndash599 2002

[18] D Accardo and G Rufino ldquoBrightness-independent start-uproutine for star trackersrdquo IEEE Transactions on Aerospace andElectronic Systems vol 38 no 3 pp 813ndash823 2002

[19] Matrox Inc Datasheet of Matrox IRIS P series httpwwwmatroxcomimagingproductsiris pserieshomecfm

[20] G Rufino and D Accardo ldquoEnhancement of the centroidingalgorithm for star tracker measure refinementrdquo Acta Astronau-tica vol 53 no 2 pp 135ndash147 2003

[21] D Accardo and G Rufino ldquoA procedure for three-dimensionalangular velocity determination using a star sensor in high-raterotation modesrdquo Acta Astronautica vol 48 no 5ndash12 pp 311ndash320 2001

[22] J L Crassidis ldquoAngular velocity determination directly fromstar tracker measurementsrdquo Journal of Guidance Control andDynamics vol 25 no 6 pp 1165ndash1168 2002

[23] G Fasano G Rufino D Accardo and M Grassi ldquoSatelliteangular velocity estimation based on star images and opticalflow techniquesrdquo submitted to Sensors 2013

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



addition dedicated hardware setup must be realized In factatmospheric effects (refraction scintillation light absorptionand background light caused by light pollution) must beminimized which is achieved thanks to high-altitude sitesfar from urban areas and near-zenith sensor pointing [9]Valid tests for angle measurement stability require long-time (hours) sequences of measures with firmness of sensorinstallation Often these tests are carried out at astronomicalobservatories installing the sensor on the structure of atelescope thus taking advantage of its tracking system to keepa fixed inertial pointing during the test [10]

In the following some problems related to laboratory val-idation of modern star trackers are studied In particular it isconsidered the solution of testing hardwaremodels in end-to-end configuration by acquiring and processing simulated starfield scenes that extend over the whole sensor FOV True-skyscene simulation is analyzed Specifically a high-resolutionLCDdisplay is adopted to simulate star fields Aspects dealingwith design realization and operation of such a facilityare presented Hence the achievable performance of suchsimulation is discussed from a theoretical point of viewFinally a test campaign is presented It was carried outwith twofold objective firstly to validate the theoreticalperformance analysis of the star field simulation system andsecondly to show the kind of validation that can be achieved

2 Test Facility Architecture

The tests of modern star trackers cannot be limited tocalibration and measurement performance assessment forsingle star-like light source The algorithms presently inuse in fact exploit star field scenes that can be acquiredunder different operatingmodes and during differentmissionphases with operation capability in a range of dynamicalconditions from stabilized attitude to high rate rotationsRelevant performance assessment as well as themanagementof the operating modes typically autonomous requires vali-dation under realistic input conditions and end-to-end testconfiguration including the hardware model of the sensorIn particular the former issue is to be preferred even at thepreliminary stage of algorithm testing Also extensive testcampaigns must be foreseen for adequate validation Afterthese considerations the architecture of a laboratory facilityto carry out indoor testing of modern star trackers has beendefined in order to meet the following objectives

(i) ability to support end-to-end tests with hardwaresensor models or functional prototypes

(ii) realistic simulation of star field scenes to allow starfield scene acquisition as during in-orbit operation ofthe sensor and consequent processing

(iii) ability of simulating the orbital and attitude dynamicsof a spacecraft carrying the sensor to carry out testsreproducing specific mission phases of interest

The facility architecture proposed and analyzed by RufinoandMoccia [11 12] has been selected since it meets the aboveobjectives and it is quite flexible to carry out the mentionedvariety of tests It is presented in Figures 1 and 2 The basic

Sensor optical head

Sensor processing unit

Ethernet

DVI

Display control processing unit

Experiment control processing unit

Sensor

Optical radiation

RS-232

Hi-res display

Figure 1 System block diagram of the star field simulation labora-tory facility

idea is that the LCD screen stimulates the sensor under testIt shows the star field scene that would be viewed in the sensorFOV for the assigned orientation

Two kinds of simulations are considered static anddynamic A static simulation consists of one star field scenecorresponding to a given pointing without attitude dynamicsin the inertial reference frame (where sky stars are stillneglecting long timescale proper motion effects) A dynamicsimulation accounts for orbit and attitude dynamics of theplatform carrying the sensor during a finite time interval It isrealized by means of a sequence of star field scene reportingthe apparent motion in the sensor FOV exhibited by theviewed stars The sequence is characterized by the frequency119891119904119891

at which it is updated which is necessarily limited butbenefits of technology advance

A single pixel of the LCD screen is exploited to simulatea single star of a star field if a static pointing is consideredor in the case of a low rate dynamics of the orbiting platform(Figure 3) Differently when high rate attitude dynamics areaccounted for in the simulation a single star is represented bythe strip of pixels reproducing its apparent trajectory in thesensor FOV during the scene update time 1119891

119904119891(Figure 4)

Pixel brightness control is used to reproduce star apparentbrightness as explained in the following

Star positions in the FOV are computed as a function ofthe simulated orientation on the basis of a sky star catalogassumed as reference which must be completed at least upto the sensitivity limit of the sensor under test for correctrealistic simulation For the realized facility the SKY2000 starcatalog was selected [13]

At the stage of generation of simulated star field scenesother effects can be introduced As an example space radia-tion can be accounted for by adding activated pixel besidesthose representing real stars [10] In fact radiation maydetermine star-like features in the images acquired by thesensor Occurrence of the phenomenon shall be based onmodels taking account of orbit and epoch

The realization of the facility presented here has beenbased on commercial-off-the-shelf (COTS) products Themain components are

(i) a high-resolution computer-controlled LCD displaythat shows the simulated star field scenes constituting




Optical table



DVI link

fc


Translationand

rotationstages


(a) (b)






119888is to be






















119898V = minus2512 log [119891119904 (10764

120587

119871fl 119860pix

119891119888

)] + 14 (1)

















119891119888

(2)




120590119901119910



30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

x(a

rcse

c)




120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)



0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse




as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)











120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Optical table



DVI link

fc


Translationand

rotationstages


(a) (b)






119888is to be






















119898V = minus2512 log [119891119904 (10764

120587

119871fl 119860pix

119891119888

)] + 14 (1)

















119891119888

(2)




120590119901119910



30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

x(a

rcse

c)




120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)



0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse




as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)











120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation























119898V = minus2512 log [119891119904 (10764

120587

119871fl 119860pix

119891119888

)] + 14 (1)

















119891119888

(2)




120590119901119910



30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

x(a

rcse

c)




120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)



0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse




as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)











120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation






















119891119888

(2)




120590119901119910



30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

x(a

rcse

c)




120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)



0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse




as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)











120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120590119901119910



30

35

40

45

50

55

60

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

x(a

rcse

c)




120575pix119903 = 2tanminus1 (

Δ pix2

119891119888tan120572offb

) cong119889pix

119891119888tan120572offb

(3)



0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

DiagH V


120575pi

xr(a

rcse




as

120590119901119910=120575pixradic12

radic119873stars

120590119903=120575pix119903radic12

radic119873stars

(4)











120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

















120596min119901119910 =120575pix

Δ119905upd

120596min 119903 =120575pix119903

Δ119905upd

(5)






120596 =Δ120579

Δ119905 (6)


120590120596Δ120579

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ120579

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ120579=120590Δ120579

Δ119905

120590120596Δ119905

= (10038161003816100381610038161003816100381610038161003816

120597120596

120597Δ119905

10038161003816100381610038161003816100381610038161003816)119908119888

120590Δ119905= (

Δ120579

Δ1199052)119908119888

120590Δ119905= 120596max

120590Δ119905

Δ119905

(7)


120590120596= (1205902120596Δ120579

+ 1205902120596Δ119905)12

(8)


(i) 120590Δ120579



















































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












































1505 1103 1306





90046 25302 2307 7527















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Mean 78 42 808Std 22 12 27






119904119891































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































5 Conclusion


Nomenclature













120590120596Δ119905



References




























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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