agis: micro-meteoroids
TRANSCRIPT
AGIS: Micro-meteoroids
David Hobbs
Lund Observatory
Attitude UpdateThe attitude specifies the celestial orientation of the instrument axes in the SRS as a function of time.
We model the attitude using unit quaternions, q(t), fitted by cubic splines:
where the B-splines are piecewise polynomial fits to the onboard attitude.
The coefficients, bij, are solved for using weighted least squares fitting and a robust Cholesky factorization.
)()()( 1
2
1
kk
k
kj
jiji ttttBbtq
impact causes
sudden change
of rate
fitted cubic spline (red curve)
residuals (10) show
chacteristic pattern
Developments for Attitude Update
• Handling of micro-meteoroid impacts which cause a change in the
angular velocity of Gaia. Insert multiple knots at the impact time.
• Weight equalization of observations between 2 FoVs are achieved
using an evenly distributed subset of observations or by down-
weighting the observations in the dominant field.
Micro-meteoroid Impacts
Impacts may come with a variety of magnitudes and
durations.
A simple attitude and observation simulator has
been developed. This allows us to:
• test n-order splines for any period
• generate scaled micro-meteoroid impacts at any
time
Insertion of a triple knot at the impact time allows
the rate to become discontinuous
Iteration 1
Iteration 2Iteration 1
Iteration 0
Observation and attitude residuals with insertion of a triple knot exactly at the impact time 0.06015 days (0.0 sec)
Iteration 1
Same plot of observation and attitude residuals with 100as noise, triple knot with 0.0 sec.
Iteration 1
Iteration 2
Iteration 0
How are impacts modeled in our Simulator?
Observations are calculated by scanning for transit times in
the FoV and then combining this data with the NSL attitude
to calculate the field angles.
The impact can be modeled by perturbing the attitude with,
for example:
= 500 sec
r = 0.005 arc-sec/sec
= *r*(1 - e(-(t – timpact)/)
QP = (0.0, 0.0, sin(0.5*), cos(0.5*))
Q.QP
Rough calculation shows there are f=0.1*2*N** = 55
observations per second on average. Current simulation has
~8 stars per sec ~7 time smaller. N=25000 deg-2, =0.66 deg,
=1/60 deg/s.
Uli Bastian
There will be no discontinuity in the
rates, but instead a smooth change
over 4.4 seconds.
Astrometric scan speed starts at
physical impact time minus 2.2s and
ends at physical impact time plus
2.2s.
The graphs show the physical angle
and rate in black, and the effective
ones seen in the Gaia centroid data in
red.
Modeling the impact
Without smoothing the impacts time (t0) is modelled as:
With smoothing over a period T (i.e. for ±T/2):
Note: for small T we have:
max
0
0
/)(
where
f
f
)1(
0)(
0
rA
tti
tti
eAt
tt
2if1
22if1
2
2if0
)(1
)(
0
22
00
2
0
0
2
2
0
0
Ttte
T/τ
eeA
Ttt
Tteτ
Ttt
T
A
Ttt
dssT
t
)/τt(tτT/τT/
/τT
tt
Tt
Tt
2
222
241
T
T/τ
ee τT/τT/
Simulated Observations ( 2.2s and 0.0s)
0.005 arcsecs/sec
over 500s
Smoothing effect over
2.2 seconds
Top two graphs show how the
micro-meteoroid is simulated
including the centroid read
out smoothing
Bottom graph
shows the actual
perturbation
introduced in
the observations
for an impact at
0.06015 days
2.2s
Max peak is accurately determined
Max peak is ~0.43s late
Max peak is ~0.43s late
Max peak is accurately determined
With larger periods the errors are biased
negative!
The magnitude of the error is not constant with knot period
Linear scaling with smoothing length
0.4 for ±2.2s
0.8 for ±4.4s
Biases are largely
corrected if we don’t
model the corrective
thruster firing until after
the smoothing period
The negative bias is caused by how we model the impact
Error fitting with noise (no smoothing) is 0.049s
Iteration 1 Iteration 2
Iteration 1Iteration 0
Carefully chosen error fitting with noise and smoothing is 0.0082s, i.e. very accurate
Iteration 1 Iteration 2
Iteration 1Iteration 0
Conclusions
Micro-meteoroid impact detection in ongoing.
Local data simulator was used to test the algorithm more effectively.
Introduction of realistic CCD readout smoothing makes detection more difficult.
Smoothing causes an additional sine wave error with a period equal to knot separation.
The sine wave error can be largely corrected, but its amplitude varies with knot period.
Final results are reasonably good and will improve slightly.
Are triple knots really necessary, maybe 3 knots spread over the impact would be better!
Performance with impact detection needs to be studied.
Robustness of code will improved (i.e. handling multiple impacts, varying magnitudes, etc.)
Current code implemented in new test case, will eventually be moved to AGIS code after
refactoring.