Statistical Spacecraft Pointing Performance Calculation - The APP Software Package
D.G.Dungate
Analyticon Limited (UK)
Résumé
Les milieux européens de
l'espace ont depuis longtemps
conscience de l'intérèt d'une
évaluation statistique fiable de
la qualité du pointage des
satellites, tout comme des
difficultés d'une telle
entreprise. Au fil des projets,
on a eu recours à une variété
de méthodes, d'approximations
et de rŠgles ad hoc, d'où un
manque d'uniformité des
méthodes de calcul et un
risque de surdimensionnement
élevé, avec les
conséquences
qui s'ensuivent au plan des
co–ts et des délais. Le manuel
des erreurs de pointage établi
pour l'Agence fournit à cet
égard une méthodologie
cohérente, mais dont la mise
en oeuvre est trop lourde sans
l'aide d'un logiciel. L'outil
APP apporte l'aide requise en
la matière, dans le strict
respect des méthodes et de la
terminologie du manuel.
Contractors:
Analyticon Limited (UK).
Funding:
Basic Technology Research
Programme
Introduction
A spacecraft systems engineer
is frequently faced with the
problem of making statistical
calculations of the overall
pointing performance of a
payload on board a spacecraft.
This will typically include the
combined effect of pointing
errors arising from, for
example, the sensors of the
attitude and orbit control
system (AOCS), the payload
instruments, the spacecraft
structure, spacecraft
integration, thermal distortion,
outgassing, and various other
factors. Historically, a variety
of bespoke and ad-hoc
methods have been used to
perform this task, resulting in
a lack of uniformity in
approach together with a high
risk of over- or under-design
and the associated implications
for schedule and cost.
The solution of the problem,
illustrated in Figure 1, consists
of the following tasks:
each individual source of
pointing error that contributes
to the system level depointing
must be identified;
a statistical description of
each error source must be
formulated, based on available
measured data and its quality;
the overall system level
performance must be
calculated, to a specified
confidence level, from the
individual error statistical
descriptions and the effects of
system geometry.
Figure 1. An overview of the
pointing analysis problem.
To address this issue, a
pointing error handbook was
produced for ESA in 1980 and
this was substantially revised
in 1992. The handbook, often
used by ESA contractors,
provides a consistent and
structured framework for
defining requirements and for
preparing and maintaining
spacecraft pointing and
measurement error budgets.
The techniques used in the
handbook introduce a level of
statistical rigor and remove the
dependence on Gaussian
distributions, the cornerstone
of more traditional methods.
In particular, methods are
introduced to deal with cases
of sparse or poor quality data.
Software support
While the methods of the
handbook represent a
significant improvement over
traditional practice, the
departure from conventional
approaches does render the
problem analytically
intractable in all but the
simplest of cases. Therefore,
to support the use of the new
methods, an Analytic Pointing
Performance (APP) tool has
been developed using
Matlab[1]. APP computes the
entire error budget in full
adherence to the ESA
handbook, and in particular:
the full range of error
statistical distributions
specified in the handbook may
be used;
the effects of system
geometry are included;
measurement data and the
associated accuracy can be
input by the user, and are used
to calculate the description of
the error statistics.
system-level performance
can be evaluated, using the
recommended methods, for the
full range of performance
measures specified in the
handbook.
Control of Accuracy
The software performs
calculations to a user-defined
accuracy using specially
developed internal accuracy
management algorithms. All
possible singular cases arising
in the calculations are fully
handled within the tool.
User Interface
The tool has a graphical user
interface allowing access to all
functions by push buttons and
menus. Data input is via a
formatted text file, which has
a separate section for each
part of the input data
definition. Its flexible structure
facilitates editing and easy
use.
Tabular and graphical output
of statistical information, such
as probability density
functions for component errors
and cumulative distribution
functions for performance
indices are also supported.
Results can also be saved to a
file.
An example of the graphical
user interface is shown in
Figure 2.
Figure 2. An example of the
graphical user interface of
APP, showing some typical
results.
The figure shows,
for a user-selected
specification, a tabulated set
of results at user-selected
confidence levels which can
then be compared with the
requirements. In addition, the
full cumulative distribution
function is graphically
displayed for a wide range of
confidence levels, allowing the
sensitivity of the result to
input uncertainties to be
assessed.
Conclusions
The development of the APP
error analysis tool now makes
feasible the full adoption of a
methodology for handling
pointing errors, originally
developed under contract to
ESA. The tool and its methods
can be used throughout an
entire project life-cycle and
are also suitable for
application to a wide variety
of problems within a range of
scientific and industrial
disciplines.
Note
[1] A software package produced by
Mathworks Inc.
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Preparing for the Future Vol. 8 No. 1
Published March 1998.
