Table Of Contentoko) “Satie PAS 1.5§ 27 OL
NASA Conference Publication 3102
a Flight
Mechanics/Estimation
Theory Symposium
1990
NASA Conference Publication 3102
Flight
Mechanics/Estimation
Theory Symposium
FOREWORD
The papers presented here have been derived primarily from
speakers' summaries of talks presented at the Flight
Mechanics/Estimation Theory Symposium heid May 22-24, 1990 at
Goddard Space Flight Center. For completeness, abstracts are
included of those talks for which summaries were unavailable at
press time. Papaers included in this document are presented as
received from the authors with little or no editing.
Page
SESSION 1
Comparison of Two On-Orbit Attitude Sensor
Alignment Methods
K. Krack, M. Lambertson (CSC),
F. Markley (NASA/GSFC) ...ccccsscccceesesesesesees 3
Attitude Sensor Alignment Calibration for the
Solar Maximum Mission
D. Pitone (CSC), M. Shuster (APL) ....-ceeeeeeeees 21
Inflight Estimation of Gyro Noise
O. Filla, T. Willard, D. Chu (CSC),
J. Deutschmann (NASA/GSFC) eeneeeneneeneeneeneneeneneeneeeee 41
Fixed-Head Star Tracker Magnitude Calibration on
the Solar Maximum Mission
D. Pitone, B. Twambly, A. Eudell,
i SY MED 6.06:00.0666006000000000000000008066 59
COBE Attitude as Seen From the FDF
J. Sedlak, D. Chu, E. Scheidker (CSC) .....eeeeees 79
Accuracy of the ERBS Definitive Attitude
Determination System in the Presence of
Propagation Noise
D. Chu, E. Harvie (CSC) ...seseeees ccccccccccccoes 97
SESSION 2
An Accuracy Assessment of Magellan Very Long
Baseline Interferometry
D. Engelhardt, G. Kronschnabl,
J. Border (JPL) .cccccccccccsccsssesess TEETTLILTL 115
Joint JSC/GSFC Two-TDRS Navigation Certification
Results for STS-29, STS-30, and STS-32
T. Schmidt, E. Brown, V. Murdock (Rockwell),
J. Cappellari, E. Smith, M. Schmitt,
J. O'Malley (CSC), F. Lowes (NASA/JSC),
Be Ge GED 4ceccecdccccsocccocococecocceces 133
Ionospheric Refraction Effects on Orbit
Determination Using the Orbit Determination
Error Analysis System
Cc. Yee, D. Kelbel, T. Lee, J. Dunham (CSC),
G. Mistretta (NASA/GSFC) ...cecceccscccsssecseeses 151
A Comparison of Operationally Determined
Atmospheric Densities From Satellite Orbit
Solutions and the Exospheric Temperature From
the Jacchia-Roberts Model
D. Ward, E. Smith, M. Phenneger (CSC) ......s++e6- 171
Procedures for Minimizing the Effects of High
Solar Activity on Satellite Tracking and
Ephemeris Generation
G. Bredvik (Kaman) ee eeneneeneneneneneeneneneeneteeeeeneenenees*t « 189
Space Station Freedom Altitude Strategy
B. McDonald, S. Teplitz (MDSSC) ....nceeeessseeces 197
SESSION 3
The Accuracy of Dynamic Attitude Propagation
E. Harvie, D. Chu (CSC),
M. Woodard (NASA/GSFC) eseneneeneeneeneeneneneneeneeneneeneeset ff © 213
Comparison and Testing of Extended Kalman Filters
for Attitude Estimation of the Earth Radiation
Budget Satellite
J. Deutschmann (NASA/GSFC), M. Rokni (CSC),
I. Bar-Itzhack (Technion-Israel Inst. Tech.) ..... 233
Attitude Determination and Calibration using a
Recursive Maximum Likelihood-Based Adaptive
Kalman Filter
D. Kelly, A. Fermelia (Hughes),
G. Lee (N.C. State University) ......cceecessecces 255
An Experimental Study of Nonlinear Dynamic System
Identification
G. Stry, D. Mook (SUNY/Buffalo) ....... weTTTTTT T y 275
Downdating a Time-Varying Square Root Information
Filter
b. Muellerschoen (JPL) eseeeeneneeneneneneneneneneneteneneeneneneests 291
The NAVSTAR GPS Master Control Station's Kalman
Filter Experience
M. Scardera (USAF) se eeeneneeneeeneneneneneneeneeneneeneneneeeesese# * 299
SESSION 4
Gamma Ray Observatory (GRO) OBC Attitude Error
Analysis
R. Harman (NASA/GSFC) se eeneneneneerereteeee se ec eeeneneeeestse?* 321
Two Axis Pointing System (TAPS) Attitude
Acquisition, Determination, and Control
J. Azzolini, D. McGlew (NASA/GSFC) .....ssssee8. ee 341
vi
A Method of Determining Attitude From
Magnetometer Data Only
G. Natanson, S. McLaughiin, R. Nicklas (CSC) ..... 359
On-board Attitude Determination and Control
Algorithms for SAMPEX
T. Flatley, J. Forden, D. Henretty,
E. Lightsey, F. Markley(NASA/GSFC) ......ss+eee08: 379
Attitude-Dependent Launch Window Analysis for the
Hubble Space Telescope Mission
J. Lenio (Rockwell) se eeneeneneneneneneneneeneneeeneneneeneertrrrtete 399
Contribution of Zonal Harmonics to Gravitational
Moment
Ce Roithmayr (NASA/ JSC) ese eeweeeteneenetneeneneeeneeeree8e @ 417
A Technique for Optimal Temperature Estimation
for Modeling Sunrise/Sunset Thermal Snap
Disturbance Torque
D. Zimbelman, C. Dennehy, R. Welch (Fairchild),
G. Born (Univ. Colorado) ....csceeececceces cccccece 431
The Generalized Tsiolkovsky Equation
Vv. Dvornychenko ee nereieneeneeneeneneeeneneneneneneneneneneneneneneneeeetse?*® 44¢
Calculation of Double-Lunar Swingby Trajectories:
II. Numerical Solutions in the Restricted
Problem of Three Bodies
BS. STALCS (CHC) cccccccccccccescecccccccssccccceces 459
Optimal Aeroassisted Orbital Transfer With
Plane Change Using Collocation and Nonlinear
Programming
Y. Shi, R. Nelson, D. Young (MDSSC) ............-. 471
Aerobraking for Capture into Martian Orbit
W. Suit, M. Lee, P. Tartbini,
B. Tomlinson (NASA/Langley) .....eeeeesessseeceees 491
Upper Stage In-Flight Retargeting to Enhance
Geosynchronous Satellite Operations
O. Lee (General DymamicS) ....cccccceccsseeseseces 511
Constant Propellant Use Rendezvous Scenario
Across a Launch Window for Refueling Missions
M. Hametz, R. Whittier (CSC) ...cscscccccccssceces 521
Optimal Trajectories Based on Linear Equations
T. Carter (Eastern Connecticut) ......ececeseeccces 539
vii
FLIGHT MECHANICS/ESTIMATION THEORY SYMPOSIUM
MAY 22-24, 1990
SESSION 1
COMPARISON OF TWO ON-ORBIT ATTITUDE SENSOR ALIGNMENT METHODS
Kenneth Krack and Michael Lambertson
Computer Sciences Corporation bs
10110 Aerospace Road
Lanham-Seabrook, MD 20706
and
F. Landis Markley
National Aeronautics and Space Administration (NASA)
Goddard Space Flight Center
Greenbelt, MD 20771
Abstract
This paper compares two methods of on-orbit alignment of vector attitude
sensors. The first method uses the angular difference between simultaneous
measurements from two or more sensors. These angles are compared to the
angular differences between the respective reference positions of the sensed
objects. The alignments of the sensors are adjusted to minimize the
difference between the two sets of angles. In the second method, the sensor
alignment is part of a state vector that includes the attitude. The align-
ments are adjusted along with the attitude to minimize 211 observation residu-
als. It is shown that the latter method can result in much less alignment
uncertainty when gyroscopes are used for attitude propagation during the
alignment estimation. The additional information for this increased accuracy
comes from knowledge of relative attitude obtained from the spacecraft gyro-
scopes. This paper presents the theoretical calculations of this difference
in accuracy. Also presented are numerical estimates of the alignment
uncertainties of the fixed-head star trackers on the Extreme Ultraviolet
Explorer spacecraft using both methods.
1. INTRODUCTION
This paper compares two methods of determining the in-flight alignment estima-
tion of vector-type attitude sensors. The two methods of alignment estimation
will be referred to as attitude-independent and attitude-dependent and are
outlined below. The estimated accuracy of the two approaches will be dis-
cussed.
Vector-type attitude sensors are those sensors whose output are vector mea-
surements of the lines-of-sight to some reference object. Examples of this
type of sensor are Sun sensors and star trackers. A minimum of two vector
observations are needed for attitude determination. The analysis presented in
this paper will be restricted to observations from two fixed-head star track-
ers (FHSTs) for simplicity.
Section 2 discusses the theoretical differences in the accuracy of these two
approaches. Section 3 presents a numerical example of both methods using the
Extreme Ultraviolet Explorer (BUVE) spacecraft as a typical mission case.
AITTINTUDED- EPENALIGDNMENET NESTITMATI ON
The attitude-independent method of sensor alignment estimation discussed here
is based on an algorithm first presented in a paper by Shuster, Chitre, and
Niebur (Reference 1) and later refined by Bierman and Shuster (Reference 2).
This method of sensor alignment estimation uses the angle between two vector
observations as its basic observation. This scalar observation is compared to
the angle between the corresponding reference objects, and the sensor align-
ment is adjusted to minimize the difference. The wethod requires simultaneous
measurements in each sensor. Wo a priori knowledge of the attitude is used
nor does the algorithm solve for the attitude. The algorithm seeks to mini-
mize the overall deviation of the sensor alignments from their prelaunch
values.
ATTITUDE-DALEIGNPMEENTN DESTEIMNATTIO N
In an attitude-dependent alignment estimation method, the spacecraft attitude
is part of a state vector that includes the sensor alignments. The attitude
is either solved-for along with the alignment or is treated as a known quan-
tity. The primary observation quantity is the unit vector measurement from
the sensors as opposed to the scalar measurement of the attitude-independent
Oe,
method. Residuals are computed between estimated observations based on the
state vector and the actual observaiions. The state vector is adjusted to
minimize the residuals. Two procedures are in common use to obtain this
minimization: the sequential filter and the batch filter. The sequential
filter updates its estimation of the state vector at discrete times using a
previously estimated state that has been propagated from the time of the last
sensor observation. The batch filter considers a collection of sensor obser-
vations in toto and seeks to minimize all residuals simultaneously. Both
procedures require knowledge of the motion of the spacecraft between observa-
tions. This knowledge is usually obtained from gyroscope measurements but
could be inferred from a dynamics model of the spacecraft. The analysis in
this paper will restrict itself to the batch filter and will assume dynamics
information is available.
2. THEORETICAL EVALUATION
As stated in the introduction, this analysis will assume a spacecraft with two
FHSTs. The state vector (References 3 through 5) to be estimated is
a(t)
x(t) = *,
*,
- -
where S6(t) is a vector of attitude error angles around the spacecraft body
axes and a (for 1 = 1 and 2) is a vector of sensor misalignment angles around
the i‘” FHST axes (References 4 and 5).
A batch least-squares estimate of the state at an epoch time t. ignoring the
effects of dynamics noise and consider parameters, has the covariance
(Reference 3)
Pit )« e|x (t )x Ct) «ew
°o o °o fn
where ve is the normal matrix,
weW oF UF
fn o
