Computer program plan for simulating real time observation schedules and combined effects of dynamic model errors in three-dimensional satellite motio

Bailie, A. E.

Jazwinski, A. H.

Levine, N.

Schmidt, S. F.

English

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https://ntrs.nasa.gov/search.jsp?R=19680024358 2020-03-12T06:24:34+00:00Z
.	
V.
Final Report
SUBOPTIMAL FILTERING
Part 4;
TEST-BED COMPUTER PROGRAM
Andrew H. Jazwinski
Stanley F. Schmidt
,Ann E. Bailie
Norman Levine
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Washington Office
Analytical Mechanics Associates, Inc.
9,101 Annapolis RCoad, ,
Lanham, Maryland 20801
FOREWORD
This final report is in four parts:
Part 1: ADAPTIVE FILTERING
Part 2; COMPENSATION FOR MODELING ERRORS IN ORBIT
DETERMINATION PROBLEMS
Part 3. LIMITED MEMORY OPTIMAL FILTERING
Part 4: TEST-BED COMPUTER PROGRAM
The first three parts describe several suboptimal filter concepts developed
under this Contract, A number of these filters have been simulated in the
J
rectilinear orbit problem.. These simulations are described therein. In
order to provide a more realistic environment for testing those suboptimal
filters, a more general, test-bed computer program is under development,
This program enables the simulation of real observation schedules and
combined effects of dynamical model errors in three-dimensional satellite
motion. This program is briefly described in Part 4.
The authors wish to express their appreciation for- the active interest
and support of this work by Mr. R. K. Squires of Goddard Space Flight
Center. The contributions of Dr. H. Wolf and Mr. S. Pines are also gratefully
ao,knowledged.
(i)
TEST-BED COMPUTER PROGRAM
Ann E. Bailie
Analytical Mechanics Associates, Inc.
PROGRAM DESCRIPTION IN-BRIEF
This computer program consists of two decks. 6D-Part 1 generates
an observation tape which is processed by the filters in 6D-Part 2.
6D-Part 1 ; Generates Observations
This program accepts a real observation tape and generates simulated
observations on the basis of the times and observation types corresponding
to the real data, The simulated orbit (three-dimensional) contains real-world
error effects which are superimposed on two-body motion via the theory des-
cribed in Reference [1]. The output of this program is an observation tape
which is input to 6D-Part 2
' Read from the real observation tape are times in hours from 1960, 0,
the observation types (range, range rate, t. and m direction cosines), and the
station numbers. Input ;required includes initial, range (R) and range rate (R)
vectors (in km and km/sec, resp. ), and initial time in years, days, hours,
minutes and seconds. R and R, are converted to earth radii and earth radii per
hour, and all computations are performed in these units.
The program reads the real observation tape and updates R and R to
the time of the (next) observation. The updating is performed either by two-
body theory [input NC(72) = 11, or by rotating conic theory of Ref [1]
[input NC(72) = 6 ].
Following the update, if NC (71) = 1, six independent Gaussian noise
samples are added to each of the six state (position and velocity) compon^;nts .
1
The noise distributions are zero-mean with variances V,ARX(I), I = l., 6.
This section is skipped if NC(71) 0,
The appropriate observations are then computed for that time,
Observation types are labeled. by NTYPE. Zero-mean, independent, Gaussian
noise samples with variances RVAR(NTYPE) are generated and added to the
observations.
An observation tape is generated.
The first record on the tape contains the initial conditions, thu number
of stations, the noise variance in each observation type, and several para-
meters for each station which are functions of the stations' latitude, longitude
and altitude. We assume that the stations are on a spherioal, rotating earth.
Each successive record contains:
Time in hours from 1960, 0 of the observation;
Greenwich siderial time;
Station number;
Observation type number: range = 3, range rate = 4, t = 7, m = 8;
The noisy observation;
True R and k .
6D-Part 2: Filters
This program accepts the observation tape generated by 6D-Part 1,
and stores the records on that tape in a table numbered from 1 to NTTMX,
NTTMX s 1500. Time is now referenced to an initial time of zero.
Depending on input, the program will process the observations via
any or all of the following (currently available) filters:
2
Filter No, 1: Kalman filter
Filter No. 2: Limited Memory filter (see Part 3 of this report)
Filter No. 3: Exact filter (optimal for the system noise case)
Filter No, 4., Adaptive filter (uses estimator (27) of Part 1
of this report).
The dynamics in all the filters are two-body dynamics, which do not
take into account the model error effects included in the true orbit,
Printed after each observation are the filter number and estimation
err Ax	 xors (x i	 their predicted variances P W and ( x i
	
i )/P for each
 ii
filter.
0Aw
References
[13 Samuel Pines, "On the Modeling of Real World Error Sources for Near-
Earth Orbits, 1 ► Analytical Mechanics Associates , Inc. report, Paper
presented at NASA-GSF C Seventh Semi-Annual Astrodynamics Conference,
April 16-17, 1968,


Suboptimal filtering. Part 4 - Test-bed computer program Final report

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