Download Detection of Artificial Satellites in Images Acquired in Track Rate Mode

Detection of Artificial Satellites in Images Acquired in Track Rate Mode.
Martin P. Lévesque
Defence R&D Canada- Valcartier, 2459 Boul. Pie-XI North, Québec, QC, G3J 1X5 Canada,
[email protected]
Presented to: Advanced Maui Optical and Space Surveillance Technologies Conference, Maui, September 13-16, 2011
ABSTRACT
For surveillance of space purposes, satellites must be re-observed periodically to measure their positions and update their orbital
parameters. This represents an incredible volume of data for which an automatic processing capability is desired. Previous developments
[1,2,3] produced automatic detection algorithms for images acquired in Step Stare mode (SSM) with sidereal tracking. However, it was
proven that the track rate mode (TRM) is more sensitive. Hence, the algorithmic framework was redesigned and applied to this mode.
When an imaging sensor tracks a satellite (or a satellite cluster), the stars appear as streaks while the satellites are point-like objects. A
series of algorithms was developed for the detection of satellites and star streaks. The centroids of the star streaks are detected first. They
are necessary for the astrometric calibration of the image. Thereafter, the satellites are detected using two possible scenarios; they are
detected with the maximum of sensitivity against the dark sky background, or they are detected with the contrast criteria if they are
overlapping star streaks. This algorithm framework automatically extracts all required information from the image and adapts the
processing parameters and strategy consequently, so no a priori knowledge is require for their execution.
INTRODUCTION:
The maintenance of the Space Surveillance Network (SSN) catalogue of space resident objects (RSO) requires an incredible amount of
fresh observations. Thousands of objects need to be observed almost every month. This is done by several observatories which must
acquire hundreds of observations every night. This represents a huge amount of image data that must be analyzed and reduced to
observation update reports. This can be done completely automatically with the appropriate processing facilities.
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The goal of the recent sensor development is the creation of autonomous observatories which could do the entire job automatically [4].
Ultimately, they should be operated by a single person, who checks the system status, error reports and consistency of observation reports.
Presently, this goal is achieved. When TLEs (Two lines element set) become too old, new observation requests are transmitted to the
sensor operating center and the scheduler program generates the observation tasks. This program determines when a RSO will be
observable by a specific observatory, generates sequences of command lines that will control the dome, telescope mount and camera
shutter. These command sequences are uploaded into the observatory controlling computer. Once the observatory has performed its task,
the images are downloaded and processed with the automatic detection algorithms presented in this paper. The detections are reported to
SSN and the TLE database is updated. Presently, all these process can be done completely automatically.
The RSO observation can be done in several different modes. Automatic image processing algorithms [1,2,3] were developed for the step
stare mode (SSM), i.e., the sidereal tracking mode. But this acquisition mode is not used anymore because the track rate mode (TRM) is
more sensitive and is now almost the only widely-used acquisition mode. Therefore, the processing scheme had to be rearranged [6] for
these images where stars make streaks and where satellites appear like points. In this new image processing framework, the image
background is still removed first [5]. After, the star streaks are filtered and detected. Once the stars are adequately filtered, they are
removed from the background-free image and the remaining point objects become apparent and easily detectable. This paper presents an
overview of this processing.
IMAGE and PROCESSING MODEL:
The model for the original image is:
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I0 = B + S + O + n
B: Background (or flat field)
S: Star streaks
O: RSO
n: noise
Once the background is estimated ‘«B»’ and removed, the background free image ‘I-B’ is:
I-B =
I0 – «B»
=
S + O + RB + n.
where the background residue ‘RB’ is negligible (RB = B - «B»).
I0
original image
- «B»
- background estimate
= I-B
= background free image
Then, knowing the star streak length and orientation (sl, sθ), a matched filter ‘M’ [1,2] provides a very clean estimation of the streaks ‘«S»’
which is noise free and where the possible overlapping point objects (tracked RSO) are clipped. This matched filter function also provides
the image ‘C’ which is the result of the convolution of the streak «S» by the streak model ‘s(sl, sθ)’, a line segment with the streak length
and orientation.
[«S», C] = M (I-B, s(sl, sθ) ).
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After removing the streak estimation «S», the resulting streak-free image ‘I-S’ is dominated by the remaining RSOs:
I-S = I-B - «S» = O + RB + RS + n.
I-B
background free image
«S»
filtered streaks
Inserted pattern with controlled A real satellite
SNR for sensitivity testing.
overlapping a star streak.
Defence R&D Canada
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note:(RS = S - «S»)
I-S = O + RB + RS + n.
= RSOs + processing residues + noise
STAR DETECTION:
The positions of the detected RSOs are done relative to the position of the known close stars (astrometric calibration). Hence, enough stars
have to be detected and the position of their centroids measured. With enough stars, software like ‘PinPoint’ [7] can calculate
the conversion of pixel coordinates into real sidereal coordinates.
DETECTION OF STREAK LENGTH AND ORIENTATION (sl, sθ):
There are enough star streaks in the image to be able to automatically extract their parameters. Streaks are all alike and they are similar to
a ‘rectangle’ function. Consequently, the profile of the Fourier transform is dominated by the sin(x)/x function. The absolute value of the
FFT gets rid of the eiθ phase factor (in the Fourier plane) and preserves only the profile common to all streaks. With a directional signal
summation (done with a Radon transform), the highest contrasted profile is obtained when the modulation are well align with the
integration direction. Hence, the maximum of the Radon transform indicates the orientation ‘sθ’ of this pattern.
ABS ( FFT ( image ))
Image in TRM
The profile of the Radon transform in the streak orientation
‘sθ’ shows the sin(x)/x function profile, which is the typical
Fourier transform of the rectangle (streak) function. The
FFT
measurement of the zeros (or minima and maxima) allows the
calculation of the length of the streaks ‘sl’.
Integrated
Image 1
Image 2
h
i l
145 degrees
Extracted
profile at 145
degrees
Radon ( ABS ( FFT ( image)))
Maximum intensity of the extracted
angle-dependent profiles
Central
Radon
profile
145
degrees
With (sl, sθ) known, the streak can be model and matched
filter (I-B, s(sl, sθ) ) can be computed.
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Angles (degrees)
MATCHED FILTER AND STAR STREAK MEASUREMENT
With the known streak parameters, the iterative matched filter [1,2] is able to provide a clean view of the streaks, with reduced noise and
clipped overlapping RSOs. This is illustrated in the following figure.
Bright streak
Faint streak
Original streaks
Streak model: s(sl, sθ)
Streak convolved by the streak model;
C = I-B s(sl, sθ)
Filtered streaks
«S» = min(I-B, 2C)
(Refs. 1,2)
Profiles:
Red line: streak profile
Blue line: convolution peak profile
Bright star
Mean value
Faint star
Threshold
set at 1σn
centroid
The streak length (previously estimated with the modulation of the Fourier transform) can be validated with the length measured at halt
height of very bright streak. The maximum of the convolution peak provides the mean value of the streak intensity. This is an easy way
to measure intensity of very faint streaks because this convolution peak is still clearly measurable for objects with intensity comparable
to the noise level. The position of the maximum of the convolution peak also corresponds to the position of the streak centroid.
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Extracting individual streak and measuring star position and intensity:
All streaks are separated into individual object with a binary mask, which is obtained by clipping the image above a low value
threshold. The streak centroid (center of intensity), intensity and length is measured for every object. Binary masks can be done
from filtered streak ‘«S»’ (with limited faint star extraction capability) or from convolved streak ‘C’ (it merges close bright streaks).
Intensity
Intensity
Mean length in pixels
PSF width
Profile coordinates in pixels
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Mask B: for faint stars
Pixel
Perpendicular profile
Re-filters image
The extraction solution consists in using a two-pass algorithm. The bright
stars are extracted first with the sharp ‘mask A’. Very often, there are not
enough bright streaks for the establishing of a valid astrometric solution.
Therefore, the first detected stars are erased from the image, the image is refiltered and a new binary mask ‘B’ is created for the extraction of fainter
stars. The detection limit is SNR > 1. Usually, this provides enough stars
for positioning reference.
Bright stars extracted and
detected with mask A:
Two-steps star detection
Mask B: made with
convolved streaks C > 1σn
Faint stars extracted and
detected with mask B:
Mask A: made with filtered
streaks «S» > 2σn
First detected stars erased Mask A:
Filtered streaks
Unmerging merged streaks:
A current issue is that, very often, several streaks overlap each other and are extracted as a single object. The processing facility is able
to deal with these objects. A merging case is detected when the size of the extraction box is oversize (length of the window diagonal) or
when the centroid (the maximum of the convolution peak) is far away from the box center (centroid error). When this occurs, the first
detected star is erased and the algorithm search for another one. The process continues until what remains is only noise or processing
artefacts that do not have the appropriate profiles.
expected length
first maximum
object length
geometric center
model
model
centered here
and subtracted
second maximum
Two close streaks
merged by their
extraction mask...
... and their equivalent
convolution peaks
(truncated by the
extraction mask)
Here is the modeled of the
convolution peak. Its intensity is
scaled to match the intensity of the
detected object, and center on its
position.
After subtraction of the peak
model, it remains only the peak of
the second object.
•
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Example of unmerged streaks: the first detections are
marked with a yellow crosshair. Red crosshairs
indicate following streaks that were detected with the
unmerging process.
RSO detection:
The RSO detection depends of two factors: 1) the image PSF and 2) the image background, which can be the dark sky or an overlapping
start streak. For a very sharp PSF (less than one pixel), the basic detection threshold, in the streak-free image ‘I-S’ is set to 9σn;
Basic detection:
I-S > 9σn
This high threshold value prevents the declaration of false alarm cause by noise (more or less Gaussian) produced by the CCD sensor and
the ADC. Hence, only detections with almost 100% of probability of being a real target are declared. For larger PSF width ‘wPSF’, the
local average «I-S »wPSF, estimated over the PSF area (wPSF x wPSF pixels) provides a better SNR. The detection declaration is done with:
PSF adapted detection:
«I-S »wPSF
> 9σn / wPSF.
If there is an overlapping star streak, the contrast ratio between the tracked RSO and the star streak is now the dominant factor. The
modified detection condition is now:
Detection in presence of overlapping streak:
«I-S »wPSF
> 2 «S’» + 9σn / wPSF,
where «S’» the best estimate of the RSO brightness of the overlapping streak. Experiments showed that a single contrast ratio ‘«S’»’
generates several false alarms, but the ratio ‘2«S’»’ has proven to be adequate. This test is done in three steps.
- Test 1: A pixel-to-pixel comparison is done by using the (smooth with the local average) streak-free image «I-S » with the image of
filtered streaks «S» provided by the matched filter. Note that in absence of streak, this detection condition is only limited by the noise
level. But, in the presence of streaks, the contrast ratio is dominant. Unfortunately, even with the contrast criteria, too many false
alarms are raised in the streak areas. These alarms must be checked again with the following more restrictive conditions.
- Test 2: An object-to-object comparison is done. Due to the quantization of the signal, streak pixels have strong intensity fluctuations.
This produces high value pixels on the streak edges, where the signal should be faint (PSF profile). Therefore, the previous detection
condition has a tendency of generating false alarms on the streak contour. But these alarms are usually fainter that the streak-mean
value. Hence, for a declared alarm, a verification is performed to see if the alarm overlapped a streak (inside a streak binary mask A)
and its intensity is compared with the value of the corresponding streak. This eliminates all false alarms produced by normal signal
fluctuations over the faint contour.
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- Test 3: For the remaining alarms, a last test verifies if this alarm is just beside a streak and in the PSF range. It often occurs that false
alarms are just beside a streak, without being included into its mask. Then the object-to-close-object intensity comparison is done.
This eliminates all remaining close-to-a-streak false alarms. At the end, only alarms with significant contrast are reported as valid
detections.
raw streak
Examples: filtered streak
eliminate by test 1
eliminate by test 2
eliminate by test 3
Results:
Detected satellites
Detected star streaks
DETECTION REPORT
DETECTED STARS:
PSF width:
2.3
Streak length: 24.0
rank bright- object length of
ness
index
window
diagonal
1 37979
60
98
2
9850
263
72
3
8593
305
55
4
8328
70
52
5
6996
432
35
…
position
centroid PSF merged
line column position
stars?
error
165
116
31.1
2.46
y
117
441
12.5
2.40
y
200
476
12.2
2.96
y
638
139
4.5
2.49
.
26
639
0.5
2.98
.
DETECTED SATELLITES:
PSF width:
index SNR
49
60
95.3
438.1
2 detected
2.3
Position sat/streak
line sample ratio
291
180
12.5
320
246
11.2
satellites.
Rejected detections
index
1
2
…
SNR
55.6
6.5
Position sat/streak cause of
line sample ratio
rejection
4
2
6.8
:truncated by image border
218
2
1.7
:faint ratio
These images illustrate the result of all the processing described previously. This image was acquired in the galactic plane. For an accurate
astrometric calibration of the image, the galactic plane should be avoided because it is difficult getting a unique solution for the recognition
of the star pattern (too many stars). But this is an excellent test image. The PSF and streak length and orientation are calculated with the
image content. The detection thresholds are set consequently and two RSOs are detected and reported. The crosshairs indicate the
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centroids of the detected star streaks. The color code indicates how they are detected. Yellow means the bright streak is detected in the
first step with the binary mask A. Red means the streak is detected with the unmerging process. Yellow is for the faint streaks detected in
the second step with the binary mask B, recalculated after the first-detected bright-streak are erased.
Comparison of sensitivity for images acquired in TRM and SSM:
In previous works (ref. 1,2,3), algorithms were developed for the detection of satellite streaks in image acquires in SSM (Step Stare Mode),
i.e. the usual sidereal tracking. The method is very sensitive and streaks can be detected with very low detection threshold, lower than the
detection threshold used for the TRM. But, in TRM, the RSO brightness is concentrated on a few pixels only, rather than being spread over
a long streak. The question is: which method is the most sensitive? The following table shows how much energy (or intensity in pixel
count) is required for the satellite to be able to succeed in the detection tests. Definitively, the acquisition in track rate mode is by far very
more sensitive than the SSM, almost by a factor of 5 (2 magnitudes more sensitive).
Acquisition PSF
mode
(pixel)
Streak
length
Detection condition
Total energy (in pixel
count) required to be
detected
I-S > 9σn
9σn
TRM
1
-
TRM
3
-
SSM
3
50 pixels
SSM
3
130 pixels Convolution peak >0.5 σn
«I-S »(3x3)
> 3σn
Convolution peak > σn
45σn
160σn
206σn
Conclusion:
No a priori knowledge is required by the algorithms presented here for detection in TRM mode. All required information is extracted from
the image content. They are the PSF width, noise level and streak length and orientation. Once the streak morphology is known, the star
streaks are filtered, detected and reported for the calculation of the astrometric calibration, and removed for the detection of point objects.
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The star detection method is very sensitive. Almost all star streaks with a SNR>1 are detected. Merged streaks can be unmerged if their
separation is greater than half a streak length or width. This permits obtaining enough stars of reference for the transformation of pixel
coordinates into sidereal coordinates, even in a poor star field.
The tracked-satellites detection method is also very sensitive, but its sensitivity is limited to avoid declaration of false alarm. This method
is self adapting to the noise level, PSF width and to the presence or not of overlapping star streaks.
Satellite detection algorithms have been developed for both SSM and TRM acquisition mode. Both set of algorithms reach the limit of
detection imposed by the noise. In both case, the detection threshold are adjusted to avoid declaration of false alarms. Comparison
of both methods indicates clearly that the TRM acquisition and processing methods are more sensitive by an order of two magnitudes.
This was known by instinct, but now the acquisition and processing experiments are completed and numbers support the hypothesis.
References:
1. Lévesque M.P.,: ‘Automatic Reacquisition of Satellite Positions by Detecting Their Expected Streaks In Astronomical Images’, 2009 AMOS
Technical Conferences, 02 Sept. 2009, proceeding: 10 pages.
2. Lévesque M. P., Buteau S., Image Processing Technique for Automatic Detection of Satellite Streaks. DRDC Valcartier 2005 TR-386. Defence
R&D Canada – Valcartier. http://cradpdf.drdc.gc.ca/PDFS/unc64/p527352.pdf , accessed Apr. 2011.
3. Lévesque M. P., Lelièvre M., Improving satellite-streak detection by the use of false alarm rejection algorithms. DRDC Valcartier TR 2006-587.
Defence R&D Canada – Valcartier.
http://pubs.drdc.gc.ca/PDFS/unc76/p530206.pdf , accessed Apr. 2011.
4. Wallace B., Rody J., Scott R., Pinkney F., Buteau S., Lévesque M. P., “A Canadian Array of Ground-Based Small Optical Sensors for Deep
Space Monitoring”, 2003 AMOS Technical Conference.
5. Lévesque M. P., Lelièvre M., Evaluation of the iterative methods for image background removal in astronomical images. DRDC Valcartier TN
2007-344. Defence R&D Canada – Valcartier. http://pubs.drdc.gc.ca/PDFS/unc69/p52905 4.pdf, accessed Apr. 2011.
6. Lévesque M. P., ‘Image processing algorithms for the automatic detection of artificial satellites acquired in track rate mode (TRM)’. DRDC
Valcartier TR 2010-052. Defence R&D Canada – Valcartier. Limited distribution, in publication.
7. http://pinpoint.dc3.com/, accessed Apr. 2011.
R & D pour la défense Canada
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