Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation

557 Pages·2003·15.523 MB·English

by  Theodore D. Moyer(auth.), Joseph H. Yuen(eds.)

Formulation for
Observed and Computed
Values of Deep Space
Network Data Types
for Navigation
Formulation for
Observed and Computed
Values of Deep Space
Network Data Types
for Navigation
Theodore D. Moyer
@ E E L l E N C E
A JOHN WILEY & SONS, INC., PUBLICATION
(‘opriplit ( 2003 by .Ioliii Wile) & Soils. Inc. 411 rights reserved
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Contents
[Mote: Each section has a detailed table of contents.]
Fore~~or..d..... ....................................................................... .................................. v11
Preface ................................................................... ...................................................... ix
Acknowledgments ................................................................. ..................................... x
1 Introduction ...................................... .................................................. 1
2 Time Scales and Time Differences ................................................................... 5
3 Planetary Ephemeris, Small-Body Ephemeris, and Satellite Ephemerides .......................... 33
4 Spacecraft Ephemeris and Partials File ...................................................... ..... 55
5 Geocentric Space-Fixed Position, Velocity, and Acceleration Vectors of
Tracking Station ................................................................................... ...... 103
6 Space-Fixed Position, Velocity, and Acceleration Vectors of a Landed Spacecraft
Relative to Center of Mass of Planet, Planetary System, or the Moon ................................ 183
7 Algorithms for Computing ET-TAI ...................................................................................... 205
8 Light-Time Solution .............................................................................................
9 Angles ...................................................................
10 Media and Antenna Corrections .......................................... ........................... 307
I1 Calculation of Precision Light Times and Quasar Delays .................................................. 353
12 Partial Derivatives of Precision Light Times and Quasar Delays ....................................... 393
13 Observables ...................................................................................................... 4 I9
14 References ........................................................................................................................... 539
15 Acronyms ....................................................................................................... 541
Index ................... ..................... ....... 55 1
V
Foreword
The Deep Space Communications and Navigation Systems Center of
Excellence (DESCANSO) was recently established for the National Aeronau-
tics and Space Administration (NASA) at the California Institute of Technol-
ogy’s Jet Propulsion Laboratory (JPL). DESCANSO is chartered to harness
and promote excellence and innovation to meet the communications and navi-
gation needs of future deep-space exploration.
DESCANSO’s vision is to achieve continuous communications and precise
navigation-any time, anywhere. In support of that vision, DESCANSO aims
to seek out and advocate new concepts, systems, and technologies; foster key
scientific and technical talents; and sponsor seminars, workshops, and sympo-
sia to facilitate interaction and idea exchange.
The Deep Space Communications and Navigation Series, authored by sci-
entists and engineers with many years of experience in their respective fields,
lays a foundation for innovation by communicating state-of-the-art knowledge
in key technologies. The series also captures fundamental principles and prac-
tices developed during decades of deep-space exploration at JPL. In addition, it
celebrates successes and imparts lessons learned. Finally, the series will serve
to guide a new generation of scientists and engineers.
Joseph H. Yuen
DESCANSO Leader
vii
Preface
This report documents the formulation of program Regres of the Orbit Determination Program
(ODP) of the Jet Propulsion Laboratory (JPL). Program Regres calculates the computed values of
observed quantities (e.g.,d oppler and range observables) obtained at the tracking stations of the
Deep Space Network (DSN). It also calculates media corrections for the computed values of the
observables and partial derivatives of the computed values of the observables with respect to the
solve-for parameter vector q. The Orbit Data Editor (ODE) obtains the actual quantities that are
observed by the DSN. These quantities are used to calculate the “observed” values of the DSN
data types using the formulation given in this report. These “observables” are given to program
Regres on the OD file. The definitions of the observed values of the DSN data types calculated in
the ODE and the computed values of the DSN data types calculated in program Regres are the
same. The estimation programs of the ODP set fit the computed values of the observables to the
observed values of the observables in a least squares sense by differentially correcting the values
of the solve-for parameters. This process uses the observed-minus-computed residuals and the par-
tial derivatives of the computed values of the observables with respect to the solve-for parameter
vector q calculated in program Regres. The resulting estimated values of the solve-for parameters
determine the trajectory of the spacecraft.
The last external report that documented the Regres formulation was Moyer (1971) (see Sec-
tion 14, References). That report gave the complete formulation of the ODP. This report gives the
formulation for program Regres only. I started working on the Regres formulation when I arrived
at JPL in 1963. Prior to publication of this document, the Regres formulation was contained in
parts of Moyer (1971), and in many JPL-internal memoranda. The purpose of writing this docu-
ment was to place the entire Regres formulation in a widely available external document. I! will be
used in the Next-Generation Navigation Software, which is currently under development at JPL.
Also, the formulation is available and can be used by any organization that is developing an ODP.
It applies for navigating a spacecraft anywhere in the Solar System.
Theodore D. Moyer
October 2000
ix
Acknowledgments
I am indebted to many people who contributed to the Regres formulation and helped me
understand their contributions. These include, in particular, the following individuals: John D.
Anderson, James S. Border, Frank B. Estabrook, William M. Folkner, Gene L. Goltz, Ronald W.
Hellings, Robert A. Jacobson, Andrew Kwok, Gabor E. Lanyi, Jay H. Lieske, E. Myles Standish,
Richard F. Sunseri, James G Williams, and Sien C. Wu of the Jet Propulsion Laboratory; X X
Newhall, Ojars J. Sovers, and J. Brooks Thomas, recently retired from JPL; Jeff A. Estefan,
formerly of JPL; John R. Smith, retired from JPL; and John C. Ries of the University of Texas at
Austin. I am grateful to Peter J. Breckheimer, John E. Ekelund, James B. Collier, Tseng-Chan
(Mike) Wang, and Dah-Ning Yuan for converting the Regres formulation to program Regres.
Also, many thanks to Roger Carlson and Judi Dedmon in the JPL Technical Information section
for editing and producing this document.
x
Formulation for Observed and Computed Values o f Deep Space
Network Data Types for Navigation. Theodore D. Moyer
Copyright 0 2003 John Wiley & Sons, Inc.
ISBN: 0-471-44535-5
SECTION 1
INTRODUCTION
For determining the trajectory of a spacecraft, computed values of
observed quantities are fit to the observables by varying the values of the model
parameters. The estimated values of these so-called solve-for parameters
determine the trajectory of the spacecraft. This report documents the current
formulation for the observed and computed values of the observables and the
corresponding partial derivatives of the computed observables with respect to
the solve-for parameters. This formulation is used in program Regres of the
Orbit Determination Program (ODP) of the Jet Propulsion Laboratory. h s
third-generation program has been used to determine spacecraft trajectories for
lunar and planetary missions since 1968. Recently, it has also been used to
determine the orbits of Earth satellites.
The last external report which documented the Regres formulation was
Moyer (1971). The scope of that report was the formulation of the entire ODP.
This report documents the complete formulation of program Regres of the ODP
and the relativistic terms of the formulation of program PV, whch generates the
spacecraft trajectory and the corresponding partial derivatives with respect to
the estimable parameters. Thus, this document contains all of the relativistic
terms that affect the computed values of observed quantities. The complete
formulation of program PV will eventually be documented by Richard F.
Sunseri, the programmer/analyst for that program. The user’s guide for the
ODP is given in DPTRAJ-ODP User’s Reference Manual (2000).
All of the observables can be placed into the following broad categories:
doppler, range, spacecraft and quasar very long baseline interferometry (VLBI),
and angular observables. They are described in detail in Section 13. The model
parameters whose values can be estimated can be placed into the following
categories:
(a) Dynamic parameters that determine the spacecraft trajectory,
1
2 SECTION 1
Station location parameters that determine the Earth-fixed locations
of the tracking stations,
Earth orientation parameters that determine the space-fixed
orientation of the Earth,
Reference parameters that determine the relative positions of the
celestial bodies of the Solar System,
Quadratic coefficients of corrections to atomic time at the spacecraft
and tracking stations,
Quadratic coefficients of the correction to the spacecraft transmitter
frequency (when it is the transmitter),
Range biases,
Parameters of the Earth's troposphere and ionosphere,
The relativity parameters /3 and
The right ascensions and declinations of quasars.
Those parameters, such as range biases, that affect the computed values of
the observables but not the position vectors of the participants (the spacecraft
and the traclung stations) are referred to as observational parameters.
There are two variations of the formulations used in programs PV and
Regres of the ODP. One of these is the original formulation which is referred to
the Solar-System barycentric relativistic frame of reference. It applies for a
spacecraft anywhere in the Solar System. The alternate formulation is referred to
the local geocentric relativistic frame of reference. It applies for a spacecraft near
the Earth, such as an Earth orbiter. Note that lunar missions must be analyzed in
the Solar-System barycentric frame of reference.
'The errors in the computed values of range and doppler observables due
to neglected terms in the formulation for computing them are less than 0.2 m
INTRODUCTION 3
(one-way) and m/s per astronomical unit (AU) of range to the spacecraft.
These figures assume two-way data (the receiving station on Earth is the
transmitting station). Also, they do not account for errors in input items, such as
the planetary and spacecraft ephemerides, precession and nutation models, and
traclung station locations.
Section 2 discusses time scales and the calculation of time differences. This
material is presented first because time is discussed in all of the other sections of
report. The planetary and satellite ephemerides the quantities
th~s and
interpolated from them are described in Section 3. Section 4 presents the
equations used in program PV for the acceleration of the spacecraft due to
gravity only (Newtonian and relativistic terms) in the Solar-System barycentric
and local geocentric frames of reference. Section 5 gives the extensive
formulation for the geocentric space-fixed position, velocity, and acceleration
vectors of a fixed tracking station on Earth. The formulation for the space-fixed
position, velocity, and acceleration vectors of a landed spacecraft on one of the
celestial bodies of the Solar System is given in Section 6. Section 7 gives the four
algorithms used for calculating the difference between coordinate time of
general relativity and atomic time at the transmission or reception time at a
traclung station on Earth or an Earth satellite. Section 8 gives the light-time
equation and the algorithm for the spacecraft light-time solution. It also gives the
corresponding quantities for the quasar light-time solution used in calculating the
computed values of quasar VLBI observables. The formulation used to compute
the auxiliary angles is given in Section 9. The calculation of antenna, tropospheric,
and charged-particle corrections is described in Section 10. Section 11 describes
how precision range (round-trip or one-way light times) and quasar delays are
calculated from quantities computed in Sections 7 to 10. The partial derivatives of
the computed precision ranges and quasar delays with respect to the solve-for
parameters are given in Section 12. Section 13 gives the formulations for the
observed and computed values of the various types of doppler, range, VLBI, and
angular observables, and the equations for calculating media corrections for the
computed values of the observables and partial derivatives of the computed
values of the observables with respect to the solve-for parameters. The Orbit
Data Editor (ODE) obtains the observed quantities from the tracking stations and