SSATT Manual1.0

8/4/2019 SSATT Manual1.0

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Delta

Delta-Utec Space Research and Consultancy

Platschelpenbank 3

2317 ML Leiden

The Netherlands

Tel: +31 (0)71 523 0662

Fax: +31 (0)71 523 3309www.delta-utec.demon.nl

Michiel Kruijff & Erik van der Heide

SSATTDELTA-UTECS STAR SENSOR ALGORITHM TEST TOOL

VERSION 1.0 - SHAREWARE

The manual
http://www.delta-utec.demon.nl/http://www.delta-utec.demon.nl/http://www.delta-utec.demon.nl/


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Table of Contents

INTRODUCTION 4

CHAPTER 1: BACKGROUND INFORMATION 5

1.1 Development of On-board Database for Triangle recognition 51.1.1 Conversion of star magnitudes and Star Catalogue 5

1.1.2 Calculation of triangles 7

1.1.3 Uniformization of the triangle set 10

1.2 Image processing, Star identification and Attitude determination algorithms 131.2.1 Centroiding and image simulation 13

1.2.2 Apparent multiples model 14

1.2.3 Identification & validation 15

1.2.4 Attitude determination 15

CHAPTER 2: TEST TOOL START-UP WINDOW 16

2.1 Start-up window buttons and I/O screens 16

2.2 Start-up window: detailed information 17

2.3 SSATT I/O 18

CHAPTER 3: SETTINGS FOR SPATCAT WINDOW 20

3.1 Settings for Camera and Spatcat window buttons and i/o screens 20

CHAPTER 4: DATABASE STATISTICS WINDOW 27

CHAPTER 5: ADVANCED SETTINGS WINDOW 29

5.1 Advanced Settings window buttons and i/o screens 29

CHAPTER 6: TAKE PICTURE AND IDENTIFY STARS WINDOW 33

6.1 Take picture and identify stars window buttons and i/o screens 33

6.2 Reporting 37

6.2.1 Summary file 376.2.2 Monte Carlo report 40


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CHAPTER 7: NOTES 42

CHAPTER 8: TEST RESULTS 43

8.1 Background 43

8.2 Triangle selection algorithm results 45

REFERENCES 48


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Introduction

Welcome to the SSATT ShareWareVersion!

This manual contains background information on the Delta-Utec Star Sensor Algorithm Test Tool

V1.0 ShareWareSSATT. Additional information is given in the program itself by pointing the

mouse to any specific item. This pop-up information is generally given in the format:

UnitRangeDescription

SSATT has been performed under the Delta-Utec R&D program 98, as well as under funding by

the Dutch government and ESA/ESTEC.

The purpose of the program is two-fold:

to help gain insight in the influence of camera parameters on star sensor images investigate the influence of various settings on the performance of the Douma and Delta-Utec

Douma Extension star initial recognition, validation and identification algorithms, memory

requirements and computation time.

The Douma algorithm is defined in the thesis work of S.R. Douma [11]. A short description of the

algorithm and the changes/additions to it performed under this studies is given in the chapter 1.

This chapter contains some overall background information to help the reader better understand the

following chapters where the pop-up windows of the test tool are explained. In chapter 7 some

additional notes on features of the program are given. Chapter 8 reports some preliminary tests.


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Chapter 1: Background information

The actual star recognition from a CCD image is performed by extracting a combination of

features (pattern) for each selected star from the observed star positions and magnitudes. Wehave restricted ourselves to the triangular pattern, as it is more distinctive than a star pair [9], and

still quite simple.

Fig. 1.1: A triangle pattern plus feature definitions

A feature has to be independent from the camera attitude and can be a magnitude or a great-circleangular distance between two stars (see Fig. 1.1). The selection of the type of features that is used

is based on a statistical analysis of a star catalogue to yield a uniform pattern distribution of

distinctive features. The triangles that are selected for storage in the database are obtained using a

method based on Douma [11]. Douma selects triangles with high likeliness of detection by a camera.

The method was further developed to DUDE (Delta-Utec Douma Extension).

The Star Sensor Algorithm Test Tool SSATT- supports all these characteristics and applies theQUEST algorithm

[4,6]to obtain an attitude estimate and investigate performance. With SSATT

whole-sky simulations in large quantities were performed. From these simulations performance

can be compared to principles of Liebe and Quine and results published by Van Bezooijen.

1.1 Development of On-board Database for Triangle recognition

The key part of the autonomous star sensor S/W is the on-board database and its structure to

facilitate efficient search. The database has to be created on-ground by the following steps, that are

automated in SSATT:

Conversion of star magnitudes from catalogued visual value to instrumental magnitude; Calculation of triangles to be stored; Selection and uniformization of triangle features for storage.

1.1.1 Conversion of star magnitudes and Star Catalogue

A database of stars needs to be produced from the instrumental magnitude of the catalogued stars1

.However, the magnitude of stars is catalogued in visual frequency domain. Such a magnitude can

differ up to 2 from the magnitude as observed by the instrument, depending on its optical

characteristics.

1 Star catalogues are available from www.cdsweb.u-strasbg.fr (Bright Star Catalogue) or at low cost from e.g. ESA/ESTEC [Hipparcos]

or NASA [Hubble Guide Star]. This study has considered the Bright Star catalogue.

C

B

A

Base star


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To model the star camera, of each specific star the amount of energy needs to be known that will

be absorbed and transformed into a readable current by the instruments CCD array. This amount

can be calculated by integrating the convolution between the responsivity of the camera R instr ()and the spectral density of the star light as it reaches the instrument, Sat earth ().

A fair estimation of a star spectral density S() (the amount of emitted energy as function of thewavelength) is given by Plancks law. In this, the shape of the spectrum depends only on the starseffective temperature Teff. The advantage is that Teff can be derived from the spectral type/

luminosity class of each star. Both properties can be found in catalogues.

The ideal Planck approximation would be sufficient if energy transportation through space were

unhindered. In reality however, clouds of interstellar dust can absorb and scatter a fair amount of

the starlight before it enters the optical head of a star camera near the Earth. The combined effect

of absorption and scattering on radiation transport is known as extinction. Radiation on the blue

side of the spectral density (having smaller wavelengths) is dimmed more than that on the red side,

which makes the star appear too reddish and is called reddening. It is difficult to include extinctioninto the radiation transport equations analytically [19]. However, as empirical methods have shown,

a good approach is to assume a magnitude correction A that would be measured without

interstellar extinction [20]:

A cst eff

1 2.

The effective wavelength eff is an instrument property that follows from its responsivity. Theconstant is a function of colour indices (B-V) and (B-V)0 and depends on the amount of extinction.

The step by step instrument magnitude estimation process

1. Find a calibration set of stars for which are available: magnitudes mcal, the associated

responsivity curve Rcal(), colour (B-V) and spectral type [Teffand (B-V)0].

2. Convert the calibration magnitudes into unreddened values mcal,unred through reddening

correction factor Acal (Rcal(), (B-V), (B-V)0).

3. Determine the spectral density at the star surface, Sat star (Teff, ) by inserting the effectivetemperature Teffinto Plancks law.

4. A convolution between Rcal and Sat earth yields mcal, unred (step 2). Sat earth can thus be derived whenassuming Sat earth = cst * Sat star

5. Now Sat earth can be convoluted with the responsivity Rinstr() of the camera to give an estimationfor the unreddened instrument magnitude minstr, unred.

6. Add reddening influence to minstr, unred that has been subtracted in step 2 with a new correction

factor Ainstr (Rinstr(), (B-V), (B-V)0). This step results in the instrument magnitude estimationminstr that was looked for.

(7) Optional step: if the size of the calibration set found in step 1 is not sufficient, it is possible toplot for all stars available the magnitudes minstr against (B-V) and fit trough these points a

suitable polynomial minstr = P(B-V). With P, the estimated magnitude can be found for all stars

of known (B-V), although with a somewhat decreased accuracy compared to the original set[3]

.


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Step 3 Step 4 Step 5

Sat star Sat star

Sat earth

Rcal

Sat earth

Rinstrument

Fig. 1.2: Visualisation of step 3, 4 and 5

By steps 1-7, the instrumental magnitudes were determined for the catalogued stars. Stars weaker

than the instrumental magnitude threshold plus 3 sigma are unlikely to be observed by the camera.

Such stars are filtered out of the catalogue. The error in above magnitude estimation is an

important source of uncertainty of the star magnitude during the recognition process. For SSATT

the optional step is used to determine the instrumental magnitudes.

Fig. 1.3 Step 7: Polynomial description of B-V (x) dependent Mi-Mv (y)

1.1.2 Calculation of triangles

There are various ways to select a triangle belonging to a star. Quine and Liebe are algorithms

without a need for a priori attitude knowledge and formed the basis for Douma. DUDE is a furtherextension of Douma:

Quine triangle: selects the brightest two stars within a certain radius from the base star [10].

Liebe triangle: stores all conceivable triangles that could be used for identification of the brightest

stars in the sky in the database. When an image is taken, each base star in the picture and its two

closest neighbors form a triangle that is looked up in the database [1].

y = -0.1432x2

- 0.476x - 0.066

R2

= 0.8563

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

-0.5 0 0.5 1 1.5 2

Series1

Poly. (Series1)


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Douma triangle:Douma [11] extracts the same Liebe triangles of closest neighbors from a sensor

image, but has stored only the 'most likely' one for each base star. The objective is to save

considerable data and calculation time while limiting the loss in reliability.

Douma follows the philosophy from Quine that a single stored triangle per star should be

sufficient, in case plenty of stars are expected in each picture. From the estimated instrumental star

magnitude for each star the probability is calculated that it is bright enough to be observed by thecamera. The Liebe triangle with the highest probability is selected for the database.

DUDE triangle: This extended Douma algorithm closes the gap between Liebe and Douma andadds a number of refinements and additional features:

DUDE uses probability offsets to accept or reject a triangle. Triangles that have too low a

probability are rejected. Furthermore, a triangle that is maybe not the most likely one, but has a

probability greater than the acceptance offset is added to the database: a single star can now have a

(controlled) number of triangles for identification.

DUDE takes into account the effect of the relative positions of the neighboring stars and the

limited size of the Field Of View (FOV). These dependencies have an impact on the triangleprobabilities not considered by Douma or Liebe. (Not included in V1.0 delivery).

DUDE includes magnitude buffer for improved rate performance: only the brightest stars in the

catalogue are used.

Example of the different triangle selection algorithmsThe next example illustrates the differences in the triangles selected by each algorithm.

Fig. 1.4 Distinctive example for different triangle algorithms: stars in the rectangular FOV of a camera.

Star 2 is out of the image. Star 0 is discussed as base star. Size indicates relative brightness.

Star Magnitude

(TH=5.5, =0.12)

(Liebe)

Probability

for observability

(Douma)0 5.35 0.6

1 6.1: too weak 0.0

2 5.0: observed for certain 1.0

3 5.45 0.8


5 5.46 0.8


Table 1.1: List of stars used in example, ordered in increasing distance to star 0

0

1

2

3

4

5

6


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Quine: Quine will search for the brightest 2 stars between the donut around base star 0. Theselected triangle will therefore be:

Quine = 06

4

Liebe: All possible triangles that can be made with stars 0 and 1,2,3 and 4 will be stored,

considering that star 1 cannot be detected, and star 2 and 4 will be seen for sure ('certain' stars).Stop condition for the list of possible first neighbors is the first certain neighbor in the list (star

with a magnitude brighter than the threshold minus 3): star 2. The same condition is used to endthe list of possible secondneighbors: star 3 and star 4. In this example Liebe will yield a total of 2.

For each of these, 18 conceivable possible geometrical descriptions are stored, taking into account

different combinations of measurement errors. Thus:

Liebe,1-18 = 03

2; Liebe,19-36 = 0

4

2.

Typically ~180[7]

triangles per star are stored.

Douma: Douma selects the most likely Liebe candidate. In the above example, the Douma

probability of the 2 possible Liebe triangles is calculated as follows:

12.0]4[].3[]2[]1[]0[]4

20,[

48.0]3[]2[]1[]0[]3

20,[

PPPPPP

PPPPP

It can easily be seen that all other possible triangles have probability 0 and do not have to be

considered. The 'most likely' triangle stored in the database according to Douma is:

Douma = 03

2

N.B. in[11]

it is proposed to find above Douma triangles by following the trail (going fromneighbor to neighbor in direction of increasing distance) and pick the first two stars with chance

higher than 50%. However, this is not correct. The correct way is to calculate the probability of

any possible triangle, and pik the highest. In searching through all combinations the way to save

time is to use a good stopping condition: e.g. it does not make sense to look for triangles beyond

star 4 in above image. Good stopping conditions have been derived and are described in the

SSATT code delivered with this manual (CamTool.Button1Click.MLTriangle).

DUDE: Both the Liebe and Douma triangles as described above are determined independently of

the FOV of the camera. In reality, very large triangles, even though made up out of very bright

('likely') stars, have a smaller chance of being in the FOV -given their base star in FOV- than very

small triangles. Triangle 04

3could occur more often than triangle 0

3

2, even though 0

3

2was

previously determined 'most likely'. There is a complex relation between the triangle size, the

Douma probability and the actual probability that all stars in the triangle are both in FOV and

detected.

The refinement introduces a dependency of the relative angular distances between the stars.

Triangle 04

3was given likeliness 0 using above calculation, but is in fact quite well imaginable

and may even be the most frequent triangle occurring - and would then be selected by DUDE. The

dependency in this case is, that if 4 is in FOV, 2 may very well not be in FOV, and 3 is likely to be

in FOV, together with a rather high probability to be observed by the camera. In general, likeliness


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of triangles with a distant neighbors and an angle between them close to 180 degrees is severely

reduced (Fig. 1.6).

Fig. 1.5 Graph Correlation vs B

Fig. 1.6 Triangles in Orion according to Quine (left) and Liebe/Douma/DUDE (right). Lighter stars have

been successfully identified.

The effect was quantified and implemented by the S/W developed. It turns out that ~10% of thetriangles differ from that of Douma.

1.1.3 Uniformization of the triangle set

When the triangles have been determined, they need to be stored in a database, in such a way that

they can easily be retrieved.

A logarithmic feature search in case of 4096 entries (=212

) would have to compare 12 values before

a target is found, and it can only treat one feature at the time. Using a tiled star catalogue and

rejecting the irrelevant part of the sky could counter these disadvantages, but requires a priori

knowledge of the attitude.

The DUDE method for data storage is to use a pointer array. The range of the feature, say A, is

divided in a number of parts, each part corresponding to a position in a pointer array that holds apointer into a candidate array of pointer lines, of which the entries point into the datalines of allcandidates in yet another file (Fig. 1.5).


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Fig. 1.7: 1D Pointer based data storage

Fig. 1.8: Candidates are drawn from array elements corresponding to feature measurement error

range.

A candidate is searched for within the expected error range from the measured value, as in Fig. 1.6.

It can be shown that the smallest number of candidates that will have to be investigated is achievedwhen the size of the pointer array parts is equal to the size of the search range. This pointer array is

called maximally fine array of ~1500 elements, which is rather much. However, the distribution of

the A values and of the triangle features in general is not homogenous (Fig. 1.7). The pointer array

element ranges can be sized by an estimator function such that the distribution is uniformized and

thus data entropy is maximized. A uniform distribution guarantees minimal memory andprocessing effort for selection of the right candidate. The described process is called

uniformization of the database.

Increasing A 0: 0

3: 2

2: 0

1: 1

0: No triangle

3: 12,14,98

2: 1

1: 4,5

1: lon = 80.0; lat = 123

4: lon = 9; lat = 238

3: lon = -12; lat = 37

2: lon = 65.7; lat = 340

Pointer array Candidate array Data File

Increasing A 0: 0

3: 2

2: 0

1: 1 Measured value for

A

A-3 search range

A+3 search range

Distribution distance to 1st neighbor

0

50

100

150

200

250

300

0 1.206 2.412 3.618 4.824 6.03

Distance [deg]

NumberofStars


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Fig. 1.9: Triangle feature distribution: A & B including analytical approximation

We define uniformity by the average number of candidates per array element as a fraction of the

statistically expected array element size when selecting an arbitrary triangle from the complete set.

In formula (1.1):

starsofnumberelementsarrayincandidatesrival

elementsarrayincandidatesrivalUniformity

__)____(

)____(

2

2

1 2 4 5 5 4 2 1

Number of candidates in a non-uniformized pointer array pointer array

3 3 3 3 3 3 3 3

A uniformized pointer array

Fig. 1.10: uniformization of data in array by adjusting array element ranges

The pointer array can also be 2 or 3 dimensional, with e.g. feature B in the second dimension etc.

A rough trade-off yielded minimum storage for a 2D array, although a 3D array could also be

favored as it will save some validation effort[13]

.

Fig. 1.11: Uniformized triangle distribution of A.

Figure 1.10 shows the contents of the 2D pointer array, in terms of number of appointed candidate

triangles per array element, between various features. Correlation is shown before and after

uniformization. The most uniform distribution of features is vs. B.

Distribution distance to 2nd neighbor

0

50

100

150

200

250

300

0 1.206 2.412 3.618 4.824 6.03

Distance [deg]

N

umberofStars

Distribution of distance to 1st neighbor after uniformization

0

10

20

30

40

50

60

70

80

0 6.03

Uniformized distance scale

NumberofStars


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Fig 1.12a: Correlation A vs B. Fig 1.12b: correlation C vs. A

Fig 1.12c: Correlation vs. C Fig 1.12d: Correlation vs. BFig 1.12: Correlation of features (Vertical vs. Horizontal), left without uniformization, right after

uniformization.

1.2 Image processing, Star identification and Attitude determination algorithms

In this paragraph, some further algorithms are discussed. They are the on-board algorithms that

process a list of star co-ordinates in the camera frame, output of the camera's image centroiding,

into an attitude estimate. Also the apparent multiple star or star group model is discussed.

1.2.1 Centroiding and image simulation

The SSATT simulates the outcome of a centroiding algorithm of a camera, based on statisticalmagnitude and position disturbance models.

A more refined method is to simulate an image at a pixel level, including noise, defocus etc. and

adding a centroiding algorithm that delivers its output to SSATT. The overall characteristics of

such a model as implemented by Oude-Lansink2[18]

:

2B-V vs magnitude polynomial used to determine instrument magnitudes (step 7 in 2.1). The total number of created photoelectrons

depends on this magnitude and on the integration time.


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Lens properties: focal length, F/no, a rough model for chromatic aberrations, vignetting,transmissivity (included in the overall instrument response);

Exponential energy distribution: the standard deviation depends on the amount of defocusingand the volume is defined by the total amount of photoelectrons produced by the starsincoming energy. In the TPD-like model, most of the energy is spread over 4 pixels.

CCD elements included in the model: array dimensions, number of pixels, size of pixels,integration time;

CCD noise sources: dark current, photo-response non-uniformity (PRNU), fixed pattern noise(FPN), floor noise, photon shot noise, bad pixels;

Detection module: stars below a certain threshold are not detected. A linear combination of theaverage pixel energy over the complete array and the standard deviation of the noise is

considered. If there is more noise, the threshold is higher;

Centroiding done by computation of the center of gravity in a fixed area of e.g. 3x3 pixelsaround the star image.

From these models and [15] the 1 error in star position on the screen has been chosen to be 12arcsec for the tests in this paper.

stars in FOV

0 2 6 8 10

1

2

3

5

6

7

8

9

10

Fig 1.13: Energy distribution over pixel array including noise

1.2.2 Apparent multiples model

For a typical camera with deliberately defocussed star images with angular size of ~0.1 of arc, 5-

10% of the stars is apparently clustered in indistinguishable groups. Of these groups, ~95% are star

couples. As a camera cannot distinguish between them, also the database should take them into

account as single stars, with averaged position and combined magnitude. In case two overlapping

stars are both brighter than the detection threshold of the camera, they jointly determine the

location that a centroiding algorithm will yield, by a first moment like for a center of gravity, but

in this case one of light intensity. In case one star of a couple is weaker than the camera threshold,

0

2

4

6

8

10

0

2

4

6

8

10

0

0.5

1

1.5

2

x 104

0

2

4

6

8

10

0

2

4

6

8

10

0

0.5

1

1.5

2

x 104


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its overlap does contribute to the brightness of the brighter one, but hardly affects its position (no

adjoining pixels will be taken into account during centroiding), see the below schematic image.

Grouping is performed from the catalogue data to build up the on-board triangle database.

Independently, it is also done to reconstruct the appearance on a SSATT simulated CCD image.

Apparent doubles are taken into account as realistically as possible, considering the generalistic

approach of SSATT.

In case of groups of more than two stars, the first two stars are treated as a couple first, then thenext is added to form a new couple etc. etc. Weak stars below a certain user defined offset are nottaken into account at all and can thus break up of a chain of close stars in several multiple groups.

In reality, groups of more than two visible stars are rare. In perhaps a handful of these cases the

multiple model can be expected to create groups with position and/or magnitude that are less

realistic than the pairs, but still quite indicative.

1.2.3 Identification & validation

A triangle is taken from the centroiding information by a 'spiral' algorithm, in terms of base star

and neighboring star positions. The descriptive features of the triangle are calculated. The pointer

array is now used to find the triangle candidates whose features fit within the estimated error

range. Then, the candidate triangles pass through the prevalidation: a user defined filter that is acomparison to a third or further feature. Validation is performed afterwards. The different methods

implemented in SSATT are mentioned in Chapter 6.

1.2.4 Attitude determination

The performance of the algorithms is assessed by achieved attitude accuracy following from the

QUEST (Quaternion Estimator) method[4,6]

.

Noise

level

Resultingposition and

brightness

Members

of starrou


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Chapter 2: Test Tool Start-Up window

The first window that appears is the Test Tool Start-Up window.

Fig. 2.1: Test tool start-up window

The purpose of this window is to transfer the input star catalogue (see Input Catalogue) to a format

that can be easily accessed during the user activities in the SpatCat Settings and the TakePicture

windows. The program prepares files that will be used for image and SpatCat generation and will

minimize the time for investigations of different camera settings, SpatCat properties and

validations.

2.1 Start-up window buttons and I/O screens

The file created on the click of [Transfer Star Catalogue]button is called Neighbors.bin. On a

Pentium 200 it takes 1.5 hour to create an ~12 Mb large file. The filesize is dependent on the

maximum magnitude threshold (user input) and the maximum number of neighbors (system

setting).

The more neighbors are being taken into account for each star, the larger will be the FOV that canbe handled: the image simulation uses a list of neighbors ordered in increasing distance from any

star. Such a list can help to quickly determine which stars are visible in any field of view. The

current setting for the number of neighbors is 450, enough for a 25x25 degree FOV. However, a

larger number of neighbors results in a large file (8 MB) and rather time consuming SPATCAT

production (15 s).

You can request to have this system setting changed.


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The files produced are valid for a FOV and threshold smaller than the maximum input [Magnitude

Threshold] in the Start-Up window. It is therefore advised that you input maximum values in this

window that encompass all the settings that you envisage to test later on.

There are three parameters for creating the Neighbors.bin file:

Multiple star offset [MaxMultipleStarOffset]: the multiple star offset determines the maximum

distance between two stars in order to treat them as an apparent multiple-star. This distance is

actually a camera parameter. It is the maximum defocus effect or star projection size of a camera

that you think to use, expressed in degrees.

Apparent multiple stars will be grouped as a single star with equivalent magnitude, to simulate the

output of the centroiding algorithm. The SpatCat will be produced with the same assumptions.

[Maximum FOV]: [Deg] determines the maximum guaranteed FOV for an image that can be

created using the Neighbors.bin file; however, if a centering factor > 2 is used in the TakePicture

window [see Chapter 6], FOVs upto 1.5 times this value can be successfully tested.

If you find to many FOV warnings appear during your test, you should use a smaller FOV or you

can contact Delta-Utec to request a setting change in the utility file (at the cost of increasedruntime and program memory).

[Magnitude Threshold]: determines the faintest stars that will be transferred to Neighbors.bin file.

N.B. It is recommended to make a back-up of the Neighbors.bin files, so it is not accidentally

overwritten by a new run.

If the Neighbors.bin file already exists one can directly proceed to the next window by a click of

the [Continue to Settings] button.

2.2 Start-up window: detailed information

Input catalogue

The SSATT needs data on the stars, magnitudes, spectral information and of course, sky position.

The source of this data can be any star catalogue. Different catalogues have different formats.

However, the file that the SSATT actually uses as input is of a standard SSATT format. This file is

called InputCatalogue.txt. Such an input file has been delivered to you with together with the

SSATT software. It is based on the Bright Star Catalogue (BSC). It contains 9096 stars and is

complete upto visual magnitude 6.5.You can simply produce your own input file based on any other star catalogue. However, the

maximum number of stars is now set by code to the same value of 9096. You can request to have

this setting changed.

If you want to produce your own input file, you will have to process the star catalogue of yourchoice in a spreadsheet like Excel, to make it fit the standard format for SSATT. The file

InputCatalogue.txt has the following column description:


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Star number: For backtrack reference. New ID numbers will be assigned that are used

throughout the program

Equatorial Longitude: Degrees, 0-360.

Equatorial Latitude: Degrees, sorted from 90 to 90.

Galactic longitude: Not used (For backtrack reference)

Galactic latitude: Not used

Visual Magnitude

B-V color (UBV) Optional but preferred. All spectral class>M need B-V value.Spectral type Format [ ]-optional, *-any character(s):

[d/g/sg] StarClass(O/B/A/F/G/K/M) [*] Subclass(0-9) [*]

The B-V values are needed to make a good estimate of the instrumental magnitude that is

determined by the properties of the camera that is tested. If you do not give an input, an estimate

will be made of B-V based on the stars spectral class.Remove lines without magnitude or co-ordinate data. All the blanks left should be filled in with

9999.If you prefer to use the galactic longitudes i.s.o. equatorial, switch and resort their columns.

2.3 SSATT I/O

An overview of SSATT input and output is given below.

Input SSAT

Data Star Catalogue

Statistical Models

Camera FOV Width/Height

Magnitude Threshold

Integration time

Projected Star Diameter

Centroiding Cut off magnitude threshold

Star position accuracy

Models Apparent Binaries

Rate effectMagnitude conversion & error

Algorithm

settings

Douma/Liebe triangle rejection/acceptance

offset or Quine

Dbase sorting parameters

Dbase size

Dbase uniformization

Validation options

Edge processing options

Imaging Direction/rotation

Rate

# False stars


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Output of SSATT

Primary performance Position accuracy

Reliability

Successrate

CPU time

Memory requirement

Statistics star recognition: Stars in FOVValidation fraction

Ambiguity fraction

Failure fraction

Secondary performance Influence apparent binaries

Error messages

Database statistics Uniformity

Correlation

Other

Codes in the following:

[Ref] For reference

[i] Input[OB] On-Board file

Input files necessary for executable:

InputCatalogue.txt See above [i,Ref] NormDis.txt Normal distribution (see SSATT code & comment) [i] InvNormDis.txt Inverse normal distribution (see SSATT) [i]

Files produced by Start-Up window:

Mainbase.txt Reduced catalogue for SSATT [Ref,i] Neighbors.bin List of each star's neighbors [i] CloseNeighbors.bin Candidates for apparent multiples [i]

CloseNeighbors.txt Idem [Ref] MultipleGroups.txt Maximally sized multiple groups [Ref]

Files produced by Settings for SPATCAT window:

PicDB.txt All stars that could possibly be seen by the camera [Ref] SCpointarray.txt 2D Array in which each location represents a combination of 2

triangle properties and is filled with a pointer to a line in

SCstararray [Ref, OB]

SCstararray.bin Each line contains pointers to SCValidation of each stars thatfulfils the triangle property combination as meant above [OB]

SCValidation.bin Each line contains the OB information on each star: direction &

validation info [Ref, OB] Correlat.txt Looks like StarPointArray, but contains number of SC2Array lineentries in place of each pointer, thus giving a correlation between

occurrence of the two triangle properties [Ref, i]

Histofile.txt Histograms of triangle properties [Ref, i]

Files produced by Take-Picture window (optional):

*.sum file Summary file of run [Ref] *.mc file Results of processing of all individual images [Ref]


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Chapter 3: Settings for SpatCat window

In this window the SpatCat (Star PATtern CATalogue) and a validation file are created based on

the selected camera and algorithm settings.

For this, the visual magnitudes are converted to instrumental magnitudes using a quadratic

estimation based on visual magnitude and B-V and or spectral class. The quality of the SpatCatand its properties can be examined in the statistics window [Database Statistics] [Chapter 4]. A

click on [Disturb Sky] button will add disturbances to the star magnitudes and positions,

depending on camera and S/C rate settings. The TakePicture window will also appear. In this

window one can take sky pictures, change further settings, do a Monte Carlo simulation, identify

the stars and store the investigation data [Chapter 6].

Fig. 3.1: Settings for Camera and SpatCat window

3.1 Settings for Camera and Spatcat window buttons and i/o screens

Buttons:

[Extra]: opens the advanced settings window [Chapter 5] [Make SpatCat]: creates a new SpatCat, validation file and PicDB.txt based on the selected

settings

[Database Statistics]: opens the statistics window [Chapter 4] [Disturb sky]: adds disturbances on the star position and magnitude and opens the take picture

and identify stars window [Chapter 6]. Every time this button is clicked, the sky will be

disturbed again, so alternating this button and the ID button in the TakePicture window, fora given direction, will produce new results every time.


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Camera group:

[FOV width]: camera Field Of View width in degrees [FOV height]: camera Field Of View height in degrees [FOV]: For information only: camera diagonal Field Of View in degrees (N.B. should be

smaller than MaxFOVSize Start-Up window).

[Cam TH]: magnitude of faintest star that the selected camera can detect.

CCD read-out group:

[Magnitude TH]: magnitude of faintest star taken into the SpatCat algorithm and passing thecentroiding algorithm.

[Sigma Magn]: magnitude accuracy of the visual to instrumental magnitude conversion (1sigma)

[Sigma Pos]: position accuracy of the centroiding algorithm (1 sigma) in arcsec for star atMagnitude TH

SC property 1&2 group:The Douma algorithm prescribes that each star will be stored in a database by the triangle of the

base star and its two neighbor stars that are most likely to be observed as being the nearest two,

taking into account the stars magnitude and the camera magnitude threshold.

Douma does not prescribe how to store and retrieve the data. For quick retrieval and small memory

size, the Delta-Utec implementation of the Douma algorithm sorts all the triangles into a 2D-array,

each direction of which is equivalent with the value range of one of the features of a star triangle.

This feature can be selected from a series of options. The complete range for a feature (e.g. 0-360

degrees for the angle gamma between the two neighbors) is segmented in a number of elements

that can be input as well.

The actual value for the feature itself is not stored: every observed combination of feature values in

the image is mapped to a certain array element of the SpatCat.

The SpatCat generation will be based on the selection of two out of the following triangle features

/properties (see Fig 1.1):

Distance A: the angular distance from the base star to its nearest neighbor. See figure. Distance B: the angular distance from the base star to its second nearest neighbor. See figure. Distance C: the angular distance between the base stars nearest- and second nearest neighbor.

See figure.

Gamma: the angle between the base stars nearest- and second nearest neighbor. See figure. MagnitudeCS: the magnitudes of all three stars, combined into a single short integer: the

Magnitude CheckSum. The purpose of this number is to store efficiently the magnitude data

of all three stars of each triangle. When selected, the magnitude range of the uniformized

magnitude histogram will be divided a small number of groups. The number of groups is

determined from the input #Array Els, according to the formula:

NumberOfMagnitudeGroups = Trunc(3(NumberOfArrayElements))

Or:


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Input Number

Array Elements

Actual Number

Magnitude Groups

Actual Number of

Array Elements

in SpatCat

8-26 2 8

27-63 3 27

64-124 4 64

125-215 5 125216-342 6 216

343-511 7 343

512-728 8 512

Et cetera. A uniformized distribution is created for the star magnitudes divided over the ActualNumber Of Magnitude Groups. Based on the value of its base stars magnitude, each star triangleentry is allocated to a certain group.

The Magnitude CheckSum is now determined by regarding the Number of Magnitude Groups asthe base number for calculation and adding the magnitude group numbers of resp. the base star,

neighbor A and neighbor B as a powered sum. If there would be 10 groups, The base star wouldbe in group 3, A in 2 and B in 1, the CheckSum would be 321, which is 3*10*10 + 2*10 + 1. In

the same way, for only 5 groups with the 3 stars distributed among the same groups, the

CheckSum would become: 3*5*5 + 2*5 + 1 = 86.The advantage is that a lot of validation data can be stored as a single integer. To have only a few

groups may be sufficient, because the magnitude cannot be determined very accurately anyway (3

sigma ~ 0.5 m). Because of the large range for each of the magnitude groups, the search range for

the Magnitude CheckSum is always 1: only one Magnitude CS value is checked when searching

for a certain triangle, so no adjacent magnitude groups are searched for candidates of a certainobserved triangle.

Magnitude: the magnitude of the base star. MaxMagnitude: the magnitude of the brightest star in the triangle.

Number of array elements screen:[# Array Els.]: for both property 1 and 2, the number of array elements (respectively rows and

columns) in the SpatCat, can be chosen.

SC 1&2 Uniformization group:The properties can be uniformized in order to increase the efficiency of the created SpatCat.

Uniform (Uniformity=1) means that there is an equal amount of rival candidates in every array

element [see 1.1.3]. Consequently the array element size gets smaller when the density of rival

candidates increases. A uniform distribution gives a well predictable number of rival candidates

for each observed triangle, so recognition of each triangle will take the same time, on the average

less validation effort is needed and, because the arrays are sized for the maximum number of rivals

in the SpatCat, the O/B memory size can be smaller.

The next four options are available:

None: the SpatCat matrix element width (property 2 array element size) and the height(property 1 array element size) are (a different) constant for both properties.

Analytical: analytical expressions have been derived for this purpose for the uniformization ofdistance A and distance B. N.B. C is not implemented.

These expressions are based on the assumption of a random distribution of the stars over the

sky.


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N(A


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property 1; property 2

X

Fig. 3.1: 2D SPATCAT pointer matrix

Triangle group:Four triangle definitions can be selected:

Douma DUDE Liebe triangle

Quine triangle

In Chapter 1 and in Development and Validation of a Fast and Reliable Star Sensor Algorithm

with Reduced Data Base[21]

, the different star pattern recognition algorithms have been explained.In SSATT the triangles of the Liebe and Quine algorithm as described above are implemented for

comparison. However, the storage and validation methods are always based on DUDE.

Based on the triangle selection the Offset group will automatically adapt.

Offset group:

[ProbForReject]: most likely triangles with a probability smaller than the rejection offset willbe rejected for the database.

[TriangleAccept]: triangles that are not most likely, but with a probability higher than the

triangle acceptance offset will be stored in the SpatCat. DUDE setting. Standard >0.5 forDouma, equal to ProbForReject for Liebe.

[MagShift]: Stars brighter than MagShift are handled for the database as stars with amagnitude of MagShift.

[MaxMag]: Liebe only. Stars less bright than MaxMag are not considered. [QR]: Quine only: Quine radii: inner radius (left), outer radius (right), degrees.

0.5-0.6

1.2-1.25


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S/C rate settings:[S/C Rate]: the programs rate simulation is effectuated by introduction of a change in camerathreshold and noise in position and magnitude determination accuracy obtained by the centroiding.

The functions used are indicative only for the sort of dependency that can be expected, as in real

life they will be very dependent on the details of your camera system and centroiding. The

functions and limitations are described in the advanced settings Chapter 5.

The threshold dependency assumes that the the star light is distributed evenly over the star spotdiameter (Extra input) on the CCD image. It assumes that if a pixel occurs of the same lightintensity as the equivalent for the camera threshold, it will invoke recognition by the centroiding

algorithm. The equivalent camera threshold is assuming that the (input) Camera Threshold is

determined from a static image with an integration time as defined in the Extra input.

When the rate setting is changed, no new SpatCat needs to be produced. One can proceed directly

with Disturb Sky.

Information windowsThere are 4 information windows:

Starttime making of SpatCat

Endtime making of SpatCat Number of stars (#) used for SpatCat Maximum number (Max) of triangles belonging to a single star occurring in SpatCat


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Message screen:

Warning 1: The visual to instrumental magnitude conversion failed.At least for one star, the starclass description is either of an unknown format or unknown.

The visual magnitude is used.

Warning 2: Array-size failure - Choose SpatCat more distinctive.MaxRivals: the maximum number of entries for a single SpatCat location (see CorrelationGraph) is larger than the system maximum. Recognition performance will be degraded.

Choose a more distinctive SpatCat, as your current choice of SpatCat would lead to many

ambiguously recognized slowing down and degrading the identification process. This can be

by choosing more or different property elements, a less sensitive camera threshold or better

uniformization.

Warning 3: Too many property 1(2) array elements for measurement accuracy.It makes no sense to force a distribution of the triangles over this number of elements, as it

suggests a better quality of centroiding data than your measurement accuracy allows. TheSpatCat will be automatically adjusted. Recognition quality is not affected, but you are using

more memory space than necessary. Reduce the number of property elements.

Warning 4: SpatCat not filled optimally, because of property 1(2).There is empty space in your SpatCat following the uniformization. There is no influence on

recognition quality. You can try to use another uniformization method.

Error 5: Fatal Array Failure - Sigma Too Small, property 1(2).The uniformization algorithm uses the sigma pos and sigma magn you input to estimatethe property distribution. If this sigma is too small, arrays will be filled out of boundary. You

cannot continue without adjusting the sigma that probably caused the failure. If the indicated

property is related to magnitude, adjust sigma magn, otherwise adjust sigma pos.

Warning 6: Internal Setting For MaxB Estimate Too SmallThe apparent multiples are only determined around a given star within a radius MaxB, aconservative estimate for the maximum distance B that will occur. If this warning occurs,

unusually large triangles have been found that may not be quite accurate. However they will

only be inaccurate if they were to contain an apparent multiple as a neighbor outside MaxB.


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Chapter 4: Database statistics window

In the database statistics window one can look at the statistical data of the SpatCat that was

produced.

One can toggle [Toggle] between two screens:

The correlation between property 1 and property 2 is plotted in a graph [Fig 4.1]. The graph isbuild up from 4 colors: white, yellow, red and purple.The white color represents SpatCat

matrix elements with 1 star candidate only. Yellow between 2 and 3 rival candidates, red

between 4 and 6 and purple for all matrix elements containing more than 6 rival candidates.

The numbers that separate the colors can be changed by the user for better interpretation of the

image. Toggle twice to reactivate.

Fig 4.1: Database statistics window: correlation graph

The occurrence histograms of the SpatCat properties.

Several histograms show the distribution of the occurrence in value intervals of triangle features

and uniformized SpatCat properties for the current camera and SpatCat settings. The horizontal

axis are intervals of the feature value from 0 to the feature range. The vertical axis is the number of

stars (occurrences) that have a triangle with a feature value that fits in the interval of the horizontal

axis. These graphs are auto-scaled in horizontal direction for optimum comparability. The scale in

vertical direction can be set to any integer value or to the maximum (by typing Max).The selected properties become visible when the mouse covers one of the Property select groups.


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The histogram result panel shows (column 1 graph 1, column 2 graph 2):

Uniformity: the uniformity of the SpatCat property, see formula 1.1 = Mean/Exp. Cand Exp. Cand.: the expected number of rival candidates per array element Mean: the average number of rival candidates over all array elements Max # stars: the maximum number of rivals in an array element # Groups: the total number of array elements for the property Hor. range: the horizontal graph range for the selected property. (Hor. Range/# groups)

gives the range of one array element.

Average: the average feature value

Fig 4.2: Database statistics window: histograms


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Chapter 5: Advanced Settings window

The advanced settings window was designed to give the user additional flexibility to change

models used in the SSATT coding.

Figure 5.1: Advanced Settings window

5.1 Advanced Settings window buttons and i/o screens

Magnitude Conversion Function Group:The instrumental magnitude is approximated by a function of spectral response of the camera,

visual magnitude of the star, the stars (B-V) and its spectral class.If B-V is known, the instrumental magnitude will be estimated as being quadratically dependent on

(B-V). The estimation is based on the specific camera settings specified in a,b,c. If the stars (B-V)is larger than the input value B-V, the stars instrumental magnitude will no longer be estimated by

the quadratic function described by a, b, c, but will be estimated by the stars visual magnitude plus

the input value mc-mv. This has been found to be a better approximation, see figure 1.3.

If (B-V) data of a star is missing, it will be estimated by (B-V)0that is based on the stars spectral

class

[11]

.

Your change will have effect only if you click Make SpatCat.

B-V Estimation Function From Star Class group:When in a database no data is available on a stars (B -V), SSATT estimates the (B-V)0 by a 2

nd

order polynominal function:

cSCbSCaVB Estimated ..)(2


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With a,b,c the input values for the star types Main, Dwarf, Giant, Super Giant. SC is an increasing

number based on the stars subclasses (A0, A2 - A9, etc.). Starting at 0 with O0 and increasing with

decreasing temperature (OBAFGKM, (O Be A Fine Girl Kiss Me)). E.g. B1=11, A5=25 etc.

The reddening effect of the interstellar gas is (for these (B-V)0 estimations) thus not taken into

account.

If both B-V and spectral class are missing warning 1 appears and the magnitude remainsunchanged.

Your change will have effect only if you click Make SpatCat.

Success group:These two variables are used in the definition of the success as given by the program in the *.sum

report (see Chapter 6). If the attitude determined by the QUEST algorithm is better than defined by

the following statement, the identification is considered successful:

AttitudeReconError


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Also if warning Normally warnings (except No star in FOV) are excluded. If thisoption is selected, and an image fits the other requirements, it

will be taken into account (e.g. when many images have

incomplete FOV, but enough stars for attitude determination.

No multiples Include images in which there are no multiples Binaries Include images in which there are one or more binary star groups,

but no groups containing more than 2 stars. This option isavailable because the binary groups are modeled better than the

rare larger multiples.

All other multiples Include images with one (or more) groups containing more than2 stars.

The selection gives the user the flexibility to do statistical analyses focussed on or less dependent

of e.g. the modelling of the multiples [Chapter 1].

After changing this value you can immediately click ID again, if you wish.

Multiple Centroiding Model group:

As the star images are defocussed, 5-10% of the stars is apparently clustered in indistinguishablegroups. Of these groups, ~95% are star couples. The camera cant distinguish between them andalso the database should take them into account as single stars, with averaged position and

combined magnitude [Chapter 1].

FaintOffset: Stars brighter than the magnitude threshold plus the faint offset are considered for

grouping.

StarSize: SSATT does not work with true pixels, as it has no centroiding algorithm included yet.

The starlight intensity surface (see 1.13a) is therefore modeled as a perfect cylinder with adiameter starsize in degrees. A good value, depending on the lens defocus, is about 1.5 equivalent

pixel size. This model is used to determine overlap between stars, as well as to determine the

spreading of the light intensity in the presence of a camera rate.

RecogDist: The model assumes that if the distance between two stars is larger than theRecogDist*StarSize, the camera is able to distinguish a group from a single star. This can be used

for validation purpose or exclusion of unreliable star IDs for the QUEST algorithm.

In the SC and Attitude Algorithm subgroup one can select whether one wants to include multiples

that have been identified for the attitude determination algorithm or avoid them:

Include multiplesAs apparent multiple stars will have a larger uncertainty, not selecting them will increase the

attitude estimation. However in case the image doesnt contain many single stars (e.g. small FOV)one could still prefer to include the multiples when determining the attitude. IfCritic#ValStars or

more single stars have been identified the attitude algorithm will not use the multiples for its

attitude determination. If less then Critic#ValStars singles have been identified in the image, theidentified multiples will be taken into account by QUEST.

Avoid multiplesIf this option is selected, there will be no multiples in the SpatCat. However, the image will still

contain all multiples that the centroiding algorithm cannot recognize (see RecogDist). Only the

groups large enough to be discovered by the centroiding can be avoided for further image

processing.


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Rate Error Estimation Functions:The position and magnitude sigma rate dependency functions are interpolations of the tables

referred to by Douma [11].

Defined are:

R: rate [deg/s]m: the stars visual magnitude

T_I: IntTime: the image integration time in seconds.

D: StarSize: star diameter on image [degrees]

AT: algorithm magnitude threshold

a,b,c,d,f,g: parameters

OBRate: on board rate knowledge as a fraction of the true rate of the spacecraft,

used for the image processing.

The model used for calculating the effect of the spacecraft rate is:

magn_noise = (a.R2

+ b.R + c) * ed*m

magnitude = (2

magn_noise + 2

magnconversion)

position = positionstatic/ef*m_AT

* ef*m

* e(g*R)

Atfor rate = ATno rate + 2.5 log (D/R/T_I) [if D/R


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Chapter 6: Take picture and identify stars window

Fig. 6.1: Take picture and identify stars window

In this window the image processing is performed and the attitude is determined. It features several

statistical reporting possibilities.

6.1 Take picture and identify stars window buttons and i/o screens

The direction to which the camera is pointing can be manually input by:

Celestial longitude [deg] Celestial latitude JD2000 ECE [deg] Rotation w.r.t. North Pole [deg] (clockwise looking ON celestial sphere)

In case that the Choose Random Direction checkbox is checked, the computer picks a random

direction and rotation for the camera. The number of simulations is on default at 1 and can be set at

any value. A hint pops up showing the minimum number of random simulations needed to do one

full sky test. For multiple simulations without display, the average results will be displayed (6.2).

Display options:

Display image processing: displays the search strategy for every stars first two neighbors. Anexample of the image processing is given in figure 6.2. The picture is build up by coloredspirals around the base star, searching for its neighbors. White and yellow are used to indicate

base stars and neighbors respectively. By decreasing grid density the spiral will be more

refined and slow down as well, giving a better idea of whats happening.


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Figure 6.2: Image processing screen

Display triangles: displays the triangles found by the image processing, see figure 6.1.

The stars are displayed as yellow spots in the image, they are scaled based on magnitude.

Centering scrollbar:The centering factor [1-20] is a factor that determines the location of the first star in the field of

view that is selected for the image production and processing. The subsequent stars are organizedby increasing distance to the first star. The image production time increases with an increasing

factor, but there is no influence on the identification time. A factor of 1 will find the first star in

field of view at the edge, a factor of 20 closely in the center of the image. For a FOV close to the

maximum value it is recommended to set the factor to at least 3. This ascertains that the opposite

picture edges are filled with stars.

The first star in the field of view is displayed as a blue spot in the image.

Number of False Stars scrollbar:One can introduce randomly placed false stars with a magnitude chosen randomly between 0 and

the magnitude threshold according to the following function:

Magnitude False Star:= MagnThreshold*(1-RANDOM10)

The false stars will be processed as stars to be recognized. They are displayed as purple spots in

the image.

Grid densityFor identifying the triangles, the image screen will be divided by a grid. A triangle will be found

for any star by spiraling out through the grid starting from that star, looking for neighbors. The grid

density determines on the average how many stars each grid square will contain. A large griddensity will save memory space, but will cause many stars to be investigated as candidates for

being one of the stars nearest neighbors. A very small density will minimize the stars to beinvestigated for being a neighbor star, but will have a big penalty for memory and (largely empty)

grid construction time. Realistic grid densities are in the range between 0.04 and 4.

Search range scrollbars

For both property 1 & 2 there is a SR scrollbar defining the error range (in [e.g. sigma pos orsigma magn]) within which, for each property, the database (pointer array) is searched for when


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looking for candidate stars. In chapter 1 and figure 1.6 this search method is explained in more

detail.

Edge Processing group:Stars at the edge of the image have a smaller chance of being identified correctly as there is a

reasonable chance that one of its direct neighbors is not in the image.

Therefore the tool has three options for the processing of the edge of the image:

No edge: all stars in the image are processed. Process edge: all stars are processed, a star will only be used for identification if its second

nearest neighbor is closer than the edge or closer than the edge offset.

Edge Offset: the stars within the edge offset from the image edge are not being processed. Theedge offset is depicted in the image.

Memory group:An order of magnitude estimation is given on the resources needed for the selected algorithm andits validation.

RAM: the memory that needs to be available for identification and validation

FastRef: the memory can be determined making different assumptions (see code), if FastRef isselected, the memory is determined while optimizing the array layout for calculation speed, if not,

the on-board array layout is assumed to be optimized for memory.

N.B.: FastRef has no influence on the identification process, but only on the memory estimate.

Prevalidation group:A validation is needed to select the right star from the rival candidates. A simple validation can be

performed on a combination of the following features: Distance A, Distance B, Distance C,

Gamma, Magnitude, MaxMagnitude, MagnitudeCS, AllMagnitudes. Each candidates observedfeatures are checked for being within 3.1 sigma from the catalogued value.

It is of little use to select a property 1 or 2 feature for validation as the rival candidates are selected

via these features. When AllMagnitudes is selected, Magnitude, MaxMagnitude and MagnitudeCS

are automatically deselected as this would mean a redundant validation.

Validation group:There are five validation routines that can be switched on or off by the user. Method 1 & 4 require

extra storage, but very little computational effort.

1. Double: Initial validation through doublesThis validation is added to minimize number crunching. When a candidate is found for a base star(in a directmanner from its own triangle), the candidate's neighbors can be regarded as indirect

candidates for the on-screen neighbors of the base star. If there are two or more identical

candidates for a single star, of either direct and/or indirect origin, by this routine this star will be

validated.

2. DistInit: Initial validation through distance consistencyTwo stars in the screen are selected, and the distance between them is compared to the distance

between the candidates' coordinates from the database, until two candidates are found of which the

distance matches within the expected error range. The couple is validated.

3. DistCont: Continued validation through distance consistency


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If at least one star is validated, other star's candidates can be compared directly to this star's for a

consistency check of the angular distance between them, as in method 2, but less alternatives have

to be processed.

4. Snowball: Snowball validation.This recursive validation is added to minimize number crunching. If a star is validated being one of

its direct candidates, its neighbors can directly be identified (and thus validated) as being the storedneighbors of that direct candidate. This process can continue as a snowball growing when rolling

downhill, so computation time is saved and a larger number of stars can be identified than with e.g.

DitsIni/DistCont only.

5. Indirect:When validation through distance consistency is selected, it validates direct candidates. With this

option also indirect candidates will be validated, meaningful if no direct candidates are present.

[Identify image button]This button starts the processing of the selected number of pictures.

Stars In Image screen: all stars that are in the image are listed in this screen together with theirSSATT number and position in the image (center = 0,0). In case a star is correctly recognized it is

checkmarked. The final two digit code has the following meaning:

Digit 1: size of star group0: not an apparent multiple.

1: part of an apparent multiple, but the other stars are very weak.

2: star group of 2.

3: star group of 3

etc.

Digit 2: recognizable bit

0: multiple cannot be distinguished from single star

1: multiple is large enough to be distinguished from single star

Simulation results group:

Acc: The accuracy of the reconstructed attitude w.r.t. boresight direction. Only longitude andlattitude are considered. The rotational accuracy is generally an order of magnitude less

accurate. (Needs several cameras).

Time: time for identification. This value is not very accurate for a single identification (NoQUEST). Look at the average of a Monte Carlo series for a good indication. The time indicates

the time that your computer needs. This value is influenced by your systems processing speed,other programs being run in parallel (like Windows 95) and by your file access speed. The

CPU time is affected somewhat negatively w.r.t. flight S/W by processing that needs to be

performed because of the general purpose application of SSATT.

Successfully recognized: reports the number of successfully recognized stars-to-be-recognizedin the image. In case of multiple random simulations the average fraction is given.

Successfully recognized stars to be recognized are displayed as green spots in the stars to be

recognized.

NVa: Reports the numbers of stars that have been recognized by the recognition algorithm andare not ambiguous, but have not been validated. They are pink. In case of multiple random

simulations the average fraction is given.


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Ambiguously recognized: reports the number of stars-to-be-recognized in the image that werenot uniquely identified, i.e. that still have rival candidates after validation. In case of multiple

random simulations the average fraction is given. Ambiguously recognized stars to be

recognized are displayed as orange spots in the stars to be recognized.

NRe: Not recognized: reports the number of stars-to-be-recognized in the image that have notbeen not recognized, because the processed triangle properties didnt match the SpatCat

triangle properties. In case of multiple random simulations the average fraction is given. Falsely recognized: reports the number of stars to be recognized in the image that have been

uniquely, but falsely recognized. In case of multiple random simulations the average fraction is

given. Such false recognitions will lead to decreased attitude determination performance.

Falsely recognized stars-to-be-recognized are displayed as red spots in the stars-to-be-

recognized.

Error and warning screen:

Warning 10: No Star Found in FOV.Use a larger FOV, more sensitive camera or lower S/C rate.

Warning 11: Array Error. Lower Grid Density

Current grid density causes too many stars to end up within a single image gridsquare, causing array overflow. Performance will decrease.

Warning 12: Array Error. Raise Grid Density.

Current grid density combined with the number of stars in the FOV commands too

small an image processing grid that would cause array overflow. It is

automatically set to the smallest possible value. There is no influence on

performance.

Warning 13: FOV incomplete. Raise Centering

There are too little stars in the FOV. This is caused by the method SSATT builds

up its pictures. The center star is selected and the FOV is filled with its 450 closest

neighbors. In case of a large FOV and the center star not being centered, it could

occur that the image is incomplete at the edge. By raising the centering this can be

solved. If the warning still occurs, the user should contact Delta-Utec to seewhether more neighbors can be incorporated for building up the image.

Warning 14: Array Error. Too many recognitions.

More than 150 stars have been identified and validated. The system settings are

such that the QUEST algorithm cannot take more input. QUEST automatically

limits itself to 150 inputs. Performance is (slightly) degraded.

6.2 ReportingTwo types of report can be produced, the summary file of a Monte-Carlo simulation and an

extended file of the full Monte-Carlo simulation. This paragraphs shows the content of these

reports:

6.2.1 Summary fileThe summary file start with a list of the selections made by the user for the Monte-Carlo

simulation (see for definitions also 3.1). The contents of the summary file is printed in Courier,

additional comments for explanatory purposes is given in italic Roman.


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Definitions of terms used:

Success (~probability): the number of successful attitude determinations as a fraction of the total

number of images taken during a Monte Carlo whole-sky simulation.

Successful Identification: the number of correctly identified stars as a fraction of the total number

of stars that were imaged during a Monte Carlo whole-sky simulation.

Reliability: the number of successful attitude determinations as a fraction of the number of images

that have yielded an attitude estimate.

**************************************************************************

Summary of 100 RANDOM sky simulations started at 10/14/98 3:27:53 PM

CAMERA SETTINGS

Camera FOV : width x height Diagonal : in deg

Sigma Magn : 1 sigma magnitude

Sigma Pos : sigma position in arcsec

Algor. TH : threshold used for algorithm

Camera TH : camera threshold

ALGORITHM : name

AccTH : acceptance threshold (probability)

MaxMag : maximum magnitude for Liebe

QRIO : Quine radii: inner & outer, degrees

OFFSETS

StarDiameter : degRejection :

MagShift : magnitude shift

SPATCAT SETTINGS

Property 1 Property 2

Property Selected property p1 Selected property p2Elements Selected # elements p1 Selected # elements p2Uniformity Selected uniformity p1 Selected uniformity p2SPATCAT DATA

1 Sigma Resulting 1 sigma p1 Resulting 1 sigma p2Range Resulting range p1 Resulting range p2

Max#Rivals : resulting maximum number of possible star solutions for the selected SpatCat

#SCEntries : number of stored triangles in SpatCat

MEMORY : estimated RAM memory

Optimized for : memory (fastref off), CPU time (fast ref on)


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IMAGE PRODUCTION SETTINGS

#FalseStars : number of false stars per image

LstDistTim : last time thedisturb sky button was pressed and disturbances on the starposition and magnitude were applied

Rate : S/C rate [deg/s]

IntegraTim : integration time

IMAGE PROCESSING SETTINGS

O/B RateEst : the on-board knowledge of the spacecraft rate as a fraction of the actual rate

GrdDensity : average number of stars per grid element

SearchRange : for respectively property 1 & 2 in sigma.

EdgeProcess : information on the processing of the edge of the image

EdgeOffset : the distance to the edge of the picture in degrees, on which the edge processing

is applied

PREVALIDATION: DistA DistB DistC Gamma Magn MMagn MagnCS AMagn

Marked (x) are the prevalidation methods selected for this MC run:

Distance A

Distance B

Distance C

Gamma

Magnitude of base star

Max magnitude in triangle

Magnitude CheckSum (has MCS# from Advanced Settings instead of X)All magnitudes

VALIDATION: Doubl DstIn DstCo Snow Indir

Marked (x) are the validation methods selected for this MC run:

Doubles

Distance initiationDistance continued

Snowball

Also indirect candidates used for distance validation

ADVANCED SETTINGS

Success Law : image Success definition from AdvSet windowFactor Power

Distributio : filename of stochastic distribution model

Multiples : avoided or included

RecogD : Recognition Distance from AdvSet window (fraction of StarDiameter)

CrValSt : Critical Number of Validated Stars (AdvSet window)

FunctionIDs : These numbers can be used to identify the parameter sets for B-V, magnitudeconversion and rate error

B-V

MagC

Rate

IncludeStat : NoMul Bins Rest Warn

Marked (x) are the selected images to be included in the MC statistics: No Multiples, Binaries,Other Multiples, Also if Warning


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SIMULATION RESULTS

Longitud : average camera boresight longitude of runs (ABSOLUTE IF ONE RUN ONLY)

Latitud : average camera boresight latitude of runs

Rotation : average camera rotation of runs

Acc : average accuracy of runs

SucR : average success rate

NVa : average percentage of not validated starsAmb : average percentage of ambigious identified stars

NoR : average percentage of stars not recognized

FaR : average percentage of stars falsely recognized

CPU : average CPU time

#Stars : average number of stars in image

Rel : average reliability = fraction successful attitudes/total attitudes

Suc : average success = fraction successful attitudes/total images

Runs : number of runs for this MC simulation

Exc : number of runs excluded for the statistics

Bin : average number of apparent binaries (per image)

Mul : average number of groups larger than 2 (per image)

WORST CASE INDICATION

MaxNum: lon, lat, rot #StarsFOV see above Acc: see above Suc: see above

Reports the results of the image with the maximum number of stars in FOV

MinNum: lon, lat, rot #StarsFOV see above Acc: see above Suc: see above

Reports the results of the image with the maximum number of stars in FOVMaxErr: lon, lat, rot #StarsFOV see above Acc: see above Suc: see above

Reports the results of the image with the lowest attitude reconstruction accuracyMaxFaR: lon, lat, rot #StarsFOV see above Acc see above Suc see above FaR see above

Reports the results of the image with the largest number of falsely recognized stars

NoPos : lon, lat, rot: image without attitude determination with largest # stars in FOV

REMARKS

Remarks added by user for this run

WARNINGS AND ERROR MESSAGES

List of warnings

6.2.2 Monte Carlo report

**************************************************************************

Run of 10 RANDOM sky simulations started at 01/07/1999 3:50:35 AM

CS Longit Latit Rotat Acc Suc NVa Amb NoR FaR CPU

0 6.73 -6.76 303.31 1.0 36 1 0 3 0 0.000

0 161.20 71.00 11.78 0.8 36 0 0 9 0 0.050

1 202.22 -32.05 29.20 1.0 32 0 0 9 0 0.000

1 333.15 -11.72 52.56 1.3 33 1 0 9 0 0.000

See Simulation results group in 6.1.


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CS: Message Checksum: determined according to:

MessageCheckSum:=0;

if BinsCount>0 then

MessageCheckSum:=MessageCheckSum+1;

if MultisCount>0 then


if NoPosFlag then


if WarnFlag then


if not IncludeFlag then



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Chapter 7: Notes

This chapter lists a variety of features of the Star Sensor Algorithm Test Tool v1.0.

Note on the input ranges

Information on the input is indicated when the mouse is moved on top of the value.There is no protection against values outside the input range.

The program is protected against array overflow and will inform you when such occurs.

This usually means that your program still works but performance will be degraded and itsadvised to change your settings.

Note on computational speedThe SSATT program is written for multi-purpose use and its set-up is therefore a trade-off

between:

- computation time- file size- memory usage- wide range of parameters for investigationFurthermore, often accurate formulas have been used, where more simple approximations would

do the job. Also the inputfile format (e.g. latitude) can be stored more efficiently (cos(lat)), but has

not been done for users convenience.

Note on array Constants and Limitations of your Computer SystemThe settings for the program are such that they are able to cope with large ranges in input

parameters. The maximum values for array sizes are set in a utility module of your S/W.They were implemented and tested on a Pentium 200 with 32 MB RAM (17 s for SpatCat).

If your computers calculation time for SpatCat production is more than say 30 seconds or if yoursettings are not very demanding, performance can be significantly enhanced by tailoring down

these settings. If your settings (like ultra-high precision of very large FOV) invoke array overflow

you might want to have them changed to higher values.

Additional Settings for CameraValues derived from [11], different from standard settings, can be used alternatively:

Magnitude Conversion:

A -0.3941

B -0.0155

C 0.1502

B-V 1.6

mc-mv -1.7

CamTH 6.5MagTH 5.5

SigMagn 0.12

SigPos 15

FOV 16x12


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Chapter 8: Test results

This chapter reports characteristic results of the tests performed with the DUDE algorithm and

comparisons to the models based on Liebe and Quine.

The camera setting used in this section are based on different industrial suggestions [15,17]:

Camera

FOV 15x20

Instrumental Threshold 6 magnitude (5.5 MagTH)

Integration Time 0.3 s

Magnitude conversion 0.17 magnitude

Position 12 arcsec

Centroiding model star size 0.09

Pixels 276x385

Table 8.1 Adopted camera parameters

8.1 BackgroundIn the design process of an autonomous star sensor the interaction between H/W and algorithm

performance should be well understood. A trade-off for FOV height and width, instrumentalthreshold, processor choice, memory storage and pixel resolution can be made better when

understanding the performance of the final product.

The attitude accuracy of the star sensor is dependent on the number of stars in FOV (Fig. 8.1),

which on its turn depends on the instrumental threshold.

Fig. 8.1 : Accuracy vs number of stars in FOV

Figure 8.2 depicts for the defined camera the average, the minimum and the maximum number of

stars in FOV.

One can extract the maximum obtainable accuracy with the DUDE algorithm from instrumentalmagnitude threshold, selected FOV and figures 8.1 & 8.2. Figure 8.2 may be used to determine the

minimum required instrumental threshold to guarantee optimal full sky performance.

# Stars in FOV vs. Accuracy (DUDE, Camera 1), 1E4 runs

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100

# Stars in FOV

Accuracy[arcsec


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Fig. 8.2: Number of stars in FOV after magnitude conversion

Figure 8.3 shows the number of catalogued stars with a certain visual magnitude and the number

after conversion of visual to instrumental magnitude ( 1.1.1). The detection probability

(magnitude threshold=5.5, =0.17) is plotted in this graph as well. Overall, the camera is about 0.5magnitude more sensitive than the visual standard. It can also be seen from the exponential growth

in number of stars, that an underestimate of the error in magnitude estimation will lead to anunderestimate of the number of detectable stars.

Fig. 8.3: Number of stars divided by 1000 for instrumental and visual magnitude and the probability to

be detected for the camera.

Figure 8.4: DUDE performance trends

stars in FOV vs Magn Threshold

0

20

40

60

80

100

120

4 4.5 5 5.5 6

Magn Threshold

#starsinFOV

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

3 3.5 4 4.5 5 5.5 6

Magnitude

Probability&Numberofstars/1000

prob

M_instr

M_vis

DUDE Performance Trends (Cam1) vs. # Stars in FOV

0

10

20

30

40

50

60

20 30 40 50 60

# Stars in FOV

Accuracy

[1E-3deg],#Stars

Identifi

ed,

CPUtime[ms]

Accuracy

# Identified Stars

CPU Time


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8.2 Triangle selection algorithm resultsThe selected camera performance of a Monte Carlo whole-sky simulation with DUDE is presented

in figure 8.4. It contains the accuracy, number of successfully identified stars and CPU time.

In the SSATT the Liebe and Quine triangle selection models are tested with the database search

and storage method of DUDE. Table 8.2 gives the results.

mem

[kB]

entries acc arcs reliab succ succ

ID

DUDE 229 9017 1.3 100.00 100.00 82

DUDE high accuracy 542 31480 1.2 100.00 100.00 92.8

DUDE low memory 86 6036 2.3 100.00 98.5 63

Douma 147 6275 1.9 100.00 99.7 54.3

Liebe/DUDE 268 13402 1.2 99.8 99.1 22.6

Quine/DUDE 199 8669 1.4 100.00 99.9 45.8

Table 8.2: Summary of different algorithms for the Lost In Space problem.

A comparison to previously published values of Liebe, Quine and Van Bezooijen [1,10,9] cannot be

given directly as results are dependent on processor choice and quality of the hardware. However

the following is suggested from the available data:

The reliability level as achieved by DUDE is only matched by Van Bezooijen (star pairs).

The DUDE successful identification of stars is unmatched (upto 93% of the stars in eachimage), resulting in highly accurate attitude estimates (Fig. 8.4). A rule of thumb for the

relation between the uncertainty in position of a star in the image and the accuracy is: accuracy

= pos/9. This is a factor 3 improvement with respect to Van Bezooijen in[9], while the

database size is comparable. The Liebe triangles obtain a very good attitude estimate,

especially considering the low successful identification.

The Liebe and Quine triangles perform better than reported in previous publications.Especially Quine reliability seems considerably improved.

The Liebe algorithm using the DUDE database is rather effective in data storage (factor 6 forsame number of stars with respect to [1]).

The tests were performed on an Intel Pentium 200 MHz under W95. The average CPU timewas ~0.013 seconds. A rough conversion for comparison with a 486 66MHz is to apply a

factor 10. Therefore, a possible update frequency of several times per second can be expectedfor a PC104-like [12] on-board computer.

About 6000-10000 stored triangles are necessary for optimal reliability. The effect of themagnitude uncertainty on the obtainable attitude accuracy is small for DUDE.

False starsImages can contain so called false stars due to e.g. hot spots, radiation or planets. False stars can be

detected during the processing of the image. Nevertheless it is expected that some false stars could

appear in the image. The influence of false stars is investigated in pictures containing a range of 0

to 10 false stars. Figure 8.5 and figure 8.6 show the results.


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Figure 8.5: Success probability as a function of number of false stars

Figure 8.6: Fraction of successfully identified stars in FOV as a function of number of false stars

There is a clear influence on the number of successfully identified stars in each image, but the

degradation is not sufficient to significantly reduce the attitude success probability. Furthermore,

increasing the number of false stars from 0 to 10, the reliability goes down from 100.00% to99.8%, while the accuracy degrades from 1.3 to 1.7 arcsec.

ValidationPrevalidation speeds up the post validation by a factor two at the cost of ~20% extra storage

requirement. The total fraction of validation data of total storage is about 33%. The snowball

validation increases the number of successfully identified stars in the FOV with 30%.

RateA spacecraft rate smears out the integrated light of a star over a larger area, and therefore has a

large degrading influence on algorithm performance. A rate of a few degrees per seconds is

devastating for most algorithms. The programs rate simulation includes a change in instrumental

threshold and noise in position and light intensity. From interpolation of measurement values[11]

relations were deduced that are indicative for the sort of dependency that can be expected, as in

real life they will be very dependent on the details of the specific camera system and centroiding.

In order to deal with rate effects, DUDE includes a buffer for magnitude. It takes into account that

fainter stars will not be detected if higher rates are expected. A buffer can be sized for better rate

performance at the cost of decrease in static-case success probability (Fig. 8.7). While a magnitudebuffer of 0.5 still obtains optimal results for very low spacecraft tumbling rates, e.g. a magnitude

buffer of 1.5 performs better for higher rates at an acceptable cost in success.

Influence False Stars on Success Probability

99

99.2

99.4

99.6

99.8

100

0 2 4 6 8 10

Number of False Stars

Success

Probability

False Stars vs. Star Identification

0

10

20

30

40

5060

70

80

90

0 2 4 6 8 10

Number of False Stars

Fractionofsucce

ssfully

identifiedstarsinFOV


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Figure 8.7: Success fraction for different S/C tunmbling rates

A magnitude buffer of 2 is too high: equivalent to an algorithm threshold of only 4, it leaves too

little stars bright enough for inclusion in the database and therefore results in a significantly lower

success.

When rate increases from 0 to 4 deg/s reliability decreases from 100.00% to 99% while the

accuracy degrades from 1 to 6 arcsec.

The triangle selection models of Quine and Liebe were compared to the DUDE model with a

magnitude buffer of 1 (Fig. 8.8). It is noticed that for higher spacecraft tumbling rates the Quine

triangles come

Documents

SSATT Manual1.0