Seite - 47 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations
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The linearised observations can be written as
∆ω˙=DACC∆α , (6.2.13)
where∆ω˙= ω˙− ω˙0 and ω˙0 are the angular accelerations derived from q0 through
polynomial differentiation.DACC is a double differentiation matrix based on a poly-
nomial of degree d as described in section 2.7.DACC has a roughly block-diagonal
structure, with each block of size 3×3 due to there being three angles per epoch. For
a polynomial of degree d=2,DACC would be
DACC= 












 D0,0 D0,1 D0,2 0 · · · 0
D1,0 D1,1 D1,2 0
0 D1,0 D1,1 D1,2 ... ...
...
... ... D1,0 D1,1 D1,2 0
0 D1,0 D1,1 D1,2
0 · · · 0 D2,0 D2,1 D2,2 













3N×3N ,
(6.2.14)
with
Di,j=wi,jI3×3 (6.2.15)
andwi,j the j-th weight factor of the differentiation polynomial computed to be
evaluated at the support i. For the accelerometer observations, it is desirable to co-
estimate calibration parameters such as biases or scales. These Pcal parameters are
collected in the 3N×Pcal matrixAcal. The design matrix for the angular accelerations is
then
AACC= [
DACC Acal ]
3N×3N+Pcal . (6.2.16)
The initial weights for the angular acceleration observations are set to the values given
by (Klinger, 2018), 5 ·10−6rad/s2/√Hz for the x- and z-axis, and 2 ·10−7rad/s2/√Hz
for the y-axis.
6.2.4 Combination
The two observation groups are combined in an iterative least squares adjustment,
with variance component estimation used to determine their relative weights. The
initial Taylor point for the orientationq0 at each epoch is set to the nominal orientation
of the satellite. The combined observation equation system for both SCA and ACC
observations
is[
∆q[1:3]
∆ω˙ ]
= [
ASCA 0
DACC Acal ][
∆α
∆xcal ]
. (6.2.17)
6.2 Sensor Fusion 47
Contributions to GRACE Gravity Field Recovery
Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations
- Titel
- Contributions to GRACE Gravity Field Recovery
- Untertitel
- Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations
- Autor
- Matthias Ellmerr
- Verlag
- Verlag der Technischen Universität Graz
- Ort
- Graz
- Datum
- 2018
- Sprache
- englisch
- Lizenz
- CC BY 4.0
- ISBN
- 978-3-85125-646-8
- Abmessungen
- 21.0 x 29.7 cm
- Seiten
- 185
- Schlagwörter
- Geodäsie, Gravitation, Geodesy, Physics, Physik
- Kategorien
- Naturwissenschaften Physik
- Technik