A weighted least squares processor is examined. Research conducted in support of the NASA satellite aided Search and Rescue program is presented. An estimated NIMBUS 6 ephemeris, accurate to 1.5-2.5 km and 0.5-2.5 m/s relative to a reference orbit, is obtained during the three day signal transmission period. This suggests updating the knowledge of the relay satellite ephemeris by one reference beacon is needed during the Search and Rescue demonstration

Koch, D. W.

Lefler, J. G.

English

NASA Technical Reports Server

General Disclaimer 
One or more of the Following Statements may affect this Document 
 
 This document has been reproduced from the best copy furnished by the 
organizational source. It is being released in the interest of making available as 
much information as possible. 
 
 This document may contain data, which exceeds the sheet parameters. It was 
furnished in this condition by the organizational source and is the best copy 
available. 
 
 This document may contain tone-on-tone or color graphs, charts and/or pictures, 
which have been reproduced in black and white. 
 
 This document is paginated as submitted by the original source. 
 
 Portions of this document are not fully legible due to the historical nature of some 
of the material. However, it is the best reproduction available from the original 
submission. 
 
 
 
 
 
 
 
Produced by the NASA Center for Aerospace Information (CASI) 
https://ntrs.nasa.gov/search.jsp?R=19790007861 2020-03-22T01:31:03+00:00Z
INASA.
Technical Memorandum 79678
NIMBUS 6 DOPPLER PROCESSING
USING THE FAIRBANKS
CALIBRATION PLATFORM
D. W. Koch and J. G. Lefler
(NASA-TM-79678) NIMBUS 6 DOPPLER PROCESSING
	 N79-16032
USING THE FAIRBANKS CALIBRATION PLATFORM
(NASA)
	 18 P HC A02/MF A01
	 CSCL 22B
Unclas
G3/15 13575
OCTOBER 1978
National Aeronautics and^
Space Administration	 v
Goddard Space Flight Center
[:pL,11Greenbelt, Maryland 20771
s
NIMBUS 6 DOPPLER PROCESSING USING THE
FAIRBANKS CALIBRATION PLATFORM
David W. Koch
Joan G. Lefler
ABSTRACT
The weighted least squares processing of Doppler shifted signals transmitted from Fairbanks
to the NIMBUS 6 satellite is examined. The paper represents research conducted in support of the
NASA satellite aided Search and Rescue program. An estimated NIMBUS 6 ephemeris, accurate to
1.5 — 2.5 km and 0,5 — 2,5 m/s relative to a reference orbit, is obtained during the three day signal
transmission period. This suggests updating the knowledge of the relay satellite ephemeris by one
reference beacon is needed during the Search and Rescue demonstration. Per pass frequency offsets
are recoverable on the order of 600 — 610 Hz f0.4liz. Residual statistics indicate an excellent data
fit with a near zero mean and at observed noise generally less than 2.0 I-Iz.
pi2,la=lNG PAGE BLANK NOT FILMED
iii
1CONTENTS
Page
1. INTRODUCTION ......................................................
	 1
2. DATA PROCESSING APPROACH ........... .......... .. . ......... . . . .... ' 2
3. RESULTS ............................................................ 	 3
4. CONCLUSIONS .......................... 	 ...........................	 8
S.
	
REFERENCES ........................................................
	 9
APPENDIX ............................................................... 	 10
TABLES
Table	 Page
1	 Estimates of Frequency Offsets and their Accuracy for NIMBUS 6 Passes over
Fairbanks, Alaska Calibration Platform June 1 - 3, 1977 ......................	 7
2	 Mean Value W and Standard Deviation (o) of Doppler Sldit Residuals for
NIMBUS 6 Passes over Fairbanks, Alaska Calibration Platform June I - 3, 1977 ..... 8
A-1 Corrections to Current NIMBUS 6 Velocity Vector vs
Iteration Number Du .g Doppler Processing . .. . ........................... 10
ILLUSTRATIONS
Figure	 Page
I	 Corrections to Current NIMBUS 6 Position Vector vs Iteration Number
DuringDoppler Processing ............................................. 	 4
2	 Accuracy of NIMBUS 6 Ephemeris Estimate ................................
	
5
A-]	 Accuracy of NIMBUS 6 Radial Position Estimate ............................ 11
A-2 Accuracy of NIMBUS 6 Along Track Position Estimate ....................... 12
A-3	 Accuracy of NIMBUS 6 Cross Track Position Estimate ........................ 13
t	 PRECEDIir'; ?„ ,1; BLANK NOT 1'!L ;p
4
v
r,
r:
sf,	 ,
NIMBUS 6 DOPPLER PROCESSING USING THE
FAIRBANKS CALIBRATION PLATFORM
INTRODUCTION
This paper examines the processing of some actual are-way Doppler shifted signals transmitted
by the Fairbanks, Alaska calibration platform to the NIMBUS 6 meteorological satellite for three
days during June 1977. Processing consisted of the weighted least squares estimation of the NIMBUS
6 epoch state and frequency offsets for individual satellite passes over the platform. The accuracy of
results is measured by a 6 day comparison of the estimated NIMBUS 6 ephemeris with a reference
orbit of known accuracy and examination of residual statistics.
Several considerations motivated tile paper:
(1) to provide an example of the orbit determination accuracies obtainable for NASA appli-
cations satellites using only uplink signals transmitted from fixed platforms. The use of
reference beacons co-located with local user terminals (LUT) to update the relay satellite
knowledpa during Search and Rescue operations is under consideration (Ref. 1).
(2) to observe the long term behavior of individual radial, along track, and cross track orbital
position errors during both tracking and free propagation. Such behavior is of particular
importance for the Search and Rescue demonstration onboard the Television Infra-Red
Observation Satellite (TIROS-N) for which each orbital position component must satisfy
a different accuracy level.
(3) to extract from real data a measure of frequency offset. During Search and Rescue oper-
ations the emergency b+aeon emits distress signals accurate to only several kl-Iz. Conse-
quently the offset must be extracted from the data to remove its degrading influence
upon beacon location estimates.
The processing was performed using a weighted least squares parameter estimation program
(Ref. 2-4). The program is coded in FORTRAN-H with double precision arithmetic and resides on
permanent disk on an IBM 360/95 digital computer at Goddard Space Flight Center (GSFC). A
typical data reduction required 400 K bytes of core storage and three minutes each of Central
Processing Unit (CPU) and Input/Output (I/O) time.
2. DATA PROCESSING APPROACH
A nominal NIMBUS 6 ephemeris from June 1 — 4, 1977 was generated from a typical epoch
state selected from predicted vectors available at GSFC. The ephemeris was numerically integrated
with variable stepsize using a power series solution through 16th order to the equations of motion.
Tile Earth's gravitational field was modeled by the spherical harmonic coefficients from the
Goddard Barth Model-7 (GEM-7) (Ref. 5) truncated at degree and order 8. Constants for the
Earth's mass, radius, and flattening corresponding to GEM-7 were included.
The calibration platform at Fairbanks, Alaska nominally transmitted signals on a carrier fre-
quency of 401.2 MHz :L5 kHz to the NIMBUS 6 meteorological satellite throughout June 1977 in
conjunction with the Tropical Wind Energy Conversion and Reference Level Experiment (TWERLE)
(Ref. 6). The platform is one of five worldwide employed to correct the NIMBUS 6 orbital along
track error during daily operations. The transmitted signal experiences a frequency shift upon re-
ception by NIMBUS 6 because of the satellite's motion relative to the platform. These Doppler
shifted signals constituted the data type processed. Twelve passes of data scattered over the first
three days of June 1977 were selected. These passes contained 140 data points collectively with an
individual pass including between 8 and 15 points separated by one minute. Near horizon data
points were ignored.
A weighted least squares adjustment process was used to reduce these data. Software con-
straints necessitated the conversion of the data from Doppler shift to metric range rate by multi-
plication with the negative of the signal wavelength. The signals were transmitted at 401,2 MHz on
a wavelength of 0.75 meters. The eighteen adjusted parameters included the 6-dimensional NIMBUS
6 epoch state and one frequency offset for each of the twelve passes. The a priori state chosen to
initiate the iterative adjustment process was assumed poorly known. hidividual components were
2
weighted with uncorrel p .ted uncertainties of 10 km and 100 nu/s. For each pass a zero value for the
initial frequency offset with all 	 of 1.3 ktiz was postulated.
The adjusted NIMBUS 6 epoch state was subsequently propagated forward for six clays using
modelling identical to that of the data processing. This propagated ephemeris was then differenced
over tills same interval from the most accurate available estimate of the true NIMBUS 6 ephemeris.
This e^tinnate was independently derived front
	 interferometer tracking data and has an
advertised accuracy of 500 meters RMS. Thus the errors in the estimate during both signal trans-
mission and free propagation call
	 examined.
3. RESULTS
The primary parameters extracted from the Doppler shift data were the six components of the
NIMBUS 6 epoch state. Figure i illustrates the successive corrections to the current position epoch
state at each iteration during the processing. Corrections to individual components (AX, AY, WO
and total position (Ar) are displayed. Corresponding corrections to the velocity
 vector are found in
Table 1 within the Appendix.
The initial epoch state was adjusted by 7 km in total position after the first iteration. There-
after the total corrections decrease rapidly to less than 30 meters after three iterations, Corrections
to individual position components vary widely. After the third iteration the adjustment process
stabilizes with only minor (i.e., less than 10 meters) corrections. Convergence occurs within five
iterations to all 	 epoch state accurate to 412 meters and 38 cnn /s RSS. Each velocity
component is estimated to an equal degree of accuracy.
Subsequent to adjustment, the estimated epoch state was propagated forward for six days
tinder assumptions identical to those of the data processing. To obtain a measure of the long term
accuracy of this propagated ephemeris, it was subtracted over this same time interval from the most
accurate available estimate of the true NIMBUS 6 ephemeris. Figure 2 depicts the differences be-
tween the two ephemerides and is an accurate measure of the error in the estimated NIMBUS 6
3
t
4
x
4\Dr
•
\
DX''	 \
2 ^^O,r
^^ 6Y
+400
+300
+200
E +100 ^ .
z0
0
w
o:0
V
-1001-
CONVERGENCE
ITERATION
NUMBER
4	 5
-200
	
AZ
NOTE:
1. AX, AY, 6Z ARE CORRECTIONS TO
POSITION COMPONENTS.
2. Lr IS TOTAL POSITION CORRECTION.
Figure I. Corrections to Current NIMBUS G Position Vector vs Iteration Number
During Doppler Processing
4
11
	
-300
	 111111
	
-400	
1
1
e
1
-.I
ORIGINAL PAon v
OF POOR Qljm ?"
`	
`
^
I
o
4I
NI
I 4 Z
^_^ I x
N
^^ I
r
U
¢
w
Oix
°I Z w
w
Z
k
w
`
I	 p 0 Xg
"
y
m
_ 1	 y U OwmcoLL
fr^ O w c?ZmccFN RQ V QO
a
W
^N+
,/ ¢	 LL a x w 2 ^O
^1 I ^, Z
w_
I
z o l ( a
p°i ( I	 _ N N
al
o	 I
^°^
_ x W
w
k
wol
¢ o.
r' I
N
I _ .. ^. _
I	 I	 I	 I	 I ^c..— f _	 I I o
n	 m	 to	 V	 M	 N .- O Z w
(s/w) HOHH3 AilOO-13A'IVIOI
^„	 I	 I	 I	 I	 I	 I I I
``n	 m	 ,n	 a	 r,	 N ^ o
( LUM) HOHH3 NOUISOd "IH101
5
F
t
C
F,.
YF
'.s
s..
ephemeris. The corresponding radial, along track, and cross track position errors are found in the
Appendix. The 3 kin level represents the TIROS-N orbital position accuracy requirement
for the Search and Rescue demonstration. During the signal transmission period from June 1 — 3,
both position and velocity errors are periodic. The former oscillates between 1.5 and 2.5 km and
thri latter between 0.5 and 2.5 m/s. Their complementary behavior typifies the conservation of
angular momentum of the NIMBUS 6 orbit. Outside the transmission period both errors exhibit
continued oscillation superimposed upon it strong secular growth. Note the required TIROS-N ac-
e
curacy requirement is easily achieved but only during periods of signal transmission. Thus during
tine Search and Rescue demonstration continuous updating by at least one reference beacon is
necessary.
The transmitter at the Fairbanks, Alaska calibration platform has a nominal frequency of
401.2 MHz ±5 kHz. In reality, the true transmit frequency deviates continuously from this nominal.
Deviations occur even over very short time periods such as the 15 minutes required for a typical
satellite pass over a transmitter. They are caused by crystal oscillator instability and normal degra-
dation of hardware components. The deviation between the true and nominal frequency is termed
frequency offset. During Search and Rescue operations, an emergency beacon will transmit signals
accurate to only several kHz. Thus the offset must be adjusted to remove its degrading effect upon
the more important beacon location estimates.
Table 1 lists estimates of the frequency offsets with their accuracies for each of the 12 passes
of NIMBUS 6 over the Fairbanks platform during June 1 — 3, 1977. A remarkable uniformity in
,magnitudes of estimates is evident. All offsets are approximately recoverable between 600 to
610 Hz accurate to 0.4I-Iz. estimates are independent of the number of data points processed.
The accuracy of the estimated NIMBUS 6 ephemeris was determined previously by comparison
with a reference orbit (Fig. 2). Another technique commonly employed to assess the accuracy of
estimates is examination of data residuals. A parameter estimation program uses geometry to gen-
erate data. These internally generated data, i.e. the "computed" measurements, are then
compared point by point to the data being processed,
6
l
ORIGINAL PAGE IS
OF POOR QUALITY
Table 1
Estimates of Frequency Offsets and their Accuracy for
NIMBUS 6 Posses over Fairbanks, Alaska Calibration Platform June I — 3, 1977
Pass
No,
No. Length
of Pass
(min)
,
^a	 of
Data Points
Estimates
—
Frequency
Offset
(Hz)
Accuracy
(Hz)
1 9 9 607 0.4
2 10 8 611 0.5
3 12 12 608 0.4
4 13 13 601 0.4
5 11 12 608	 — 0.4
6 10 9 611 0.4
7 12 11 605 0.4
8 14 13 605 0.4
9 11 12 601 0.4
10 13 14 604 0.4
11 14 15 596 0.4
12 9 10 595 0.4
i.e. the `observed" measurements. The differences between the two are labelled "residuals" and
their magnitudes reflect the quality of the data fit. The smaller the residuals implies the better the
fit. Table 2 lists the mean value (p) and standard deviation (a) of the Doppler shift residuals for the
12 NIMBUS 6 passes over the Fairbanks platform. The near zero mean value indicates an excellent
least squares fit to the data. The magnitude of this statistic is relatively independent of the number
of data points. The standard deviation is a measure of the noise on the actual data. Table 2 reveals
their magnitudes are generally less than 2 Hz, a value consistent with TWEIRLE frequency resolution
of ±1 liz.
:R,
7
Table 2
Mean Value (µ) and Standard Deviation (a) of Doppler Shift Residuals for
NIMBUS 6 Passes over Fairbanks, Alaska Calibration Platform June 1 — 3, 1977
Pass
No.
Length
of Pas Points
No, of µ*
(10"q Hz)
o**
(Hz)
1 9 9 0.68 1.60
2 10 8 0.77 1.84
3 12 12 0.51 0.77
4 13 13 0.47 1.35
5 11 12 0.52 0.72
6 10 9 0.70 1.29
7 12 11 0.57 1.03
8 14 13 0.48 2100
9 11 12 0.54 1.33
10 13 14 0.48 1.20
11 14 15 0.46 1.27
12 9 ^10 0.67 0.97
*esthuate of quality of fit
**estimate of data noise
4. CONCLUSIONS
This paper has presented results of weighted least squares processing of actual NIMBUS 6 Dop-
pler shift data resulting from transmission by the Fairbanks, Alaska calibration platform oil
1 — 3, 1977. The paper was prompted primarily by considerations arising from satellite aided Search
and Rescue operations. Results indicate that a NIMBUS 6 ephemeris accurate to 1.5 — 2.5 km in po-
sition and 0.5 — 2.5 m/s in velocity is possible during periods of signal transmission. Outside this
period both errors grow without bound. This implies that updating by one reference beacon is
needed to meet orbital accuracy requirements during the Search and Rescue demonstration onboard
TIROS-N. The frequency of all 	 transmitter will usually only be known to several kHz.
8
Hence position location software must estimate frequency offsets In addition to the emergency
transmitter location. This paper has .mnown that offsets are recoverable on the order of 600 — 610 Hz
to an accuracy of 0.4 Hz. Finally, statistics of the measurement residuals indicate an excellent least
squares fit to the Doppler data and an observed noise consistent with expected values.
5. REFERENCES
1. D. W. Koch, "Orbital Updates by Reference Beacon Doppler Data for Satellite Aided Search
and Rescue," NASA TM 78081, December 1977.
2. J. J. Lynn, J. G. Hartwell and R. S. Nankervis, "Network Analysis Program, NAP-3, Mathc-
matical Analysis Documentation." DBA Systems, Inc., June 1, 1970.
3. R. Garza-Robles, S. Guion, 7'. Lewis and D. Lynn, "Network Analysis Program, NAP-3,
Program Analysis Documentation." DBA Systems, Inc., June 1, 1970.
4. Old Dominion Systems, Inc., "User's Guide to Data Preparation, Navigation Analysis Program
(NAP 3.1)," April 1974.
S. C. A. Wagner, et al., "Improvement in the Geopotential Derived from Satellite and Surface
Data (GEM 7 and 8)," GSFC Report X-921-76-20, January 1976,
6. The NIMBUS 6 User's Guide, GSFC, February 1975.
9
E
a
,c
10
f
E
APPENDIX
Table A-1
Corrections to Current NIMBUS 6 Velocity Vector vs
Iteration Number During Doppler Processing
Iteration
Number	 (cm/s) (cm /S) AL(cm/s) DV(cm/s)
1 —356 —423 —355 657
2 +4 —1 +18 18
3 —1 —2 —1 2
4,5 0 0 0 0
E w
 
u
 
z w
 
a:
 
w
 
+
30
0 
+
20
0 
u
. 
+
10
0 
a.
. 
o
 
z o
 !::: en o 0.. -'
 
<
{ o 
o
 
<
{ 
-
10
0 
a:
 
CD
 
en
 
::
J co
 
:;;:
 
z 
-
20
0 
-
30
0 
-
4
0
0
" 
! 
SI
G
N
AL
 T
R
AN
SM
IS
SI
O
N 
-
-
-
-
r.
 
,
 
,
-
-
-
-
r.
 
-
-
-
I-
+
-A
--
- " 
r.
 
'"
 
-
tr
--
-\
J-
11
\j-
'
-
"
 
"
 ....
 
-
-
-
R
EQ
UI
RE
D 
TI
R
O
S-
N 
AC
CU
RA
CY
 
LE
V
E
L 
_
.
.
J _
_
_
_
_
_
_
_
 _
 
v
 
c
~
 
"
=
j;:
:; 
.
.
.
.
 
~C
5 
c 
.
.
.
.
.
 
c
Z 
;:;:
I> 
OH
 
12
H 
OH
 
12
H 
OH
 
12
H 
OH
 
12
H 
OH
 
12
H 
GH
 
12
H 
OH
 
lO
t"
"' 
c:
;'t
:I 
>
:>
 
t"
"'
Q
 
~
~
 
JU
NE
 1
, 1
97
7 
JU
N
E
2 
JU
N
E
4 
JU
N
E
6 
CA
LE
ND
AR
 D
AT
E 
~o
o 
Fi
gu
re
 A
-I
. 
A
cc
vr
ac
y 
o
f N
IM
BU
S 
6 
R
ad
ia
l P
os
iti
on
 E
st
im
at
e 
<
 
'6 
xN
co
= W
O Z
O2	 ^N
VN
W
C
=	 O
O	 w
O
Cr
.1V
C
N	 LLI [-^h to
a O
^ O Q
LLI OO Z Ca] In
W p
J G
x	 U ZN
O
h
=	 U
O	 U
Q
N
=	 4
N^r	 C
CA
LL
N
= W
O Z
n
n
O
O .-
uJ	 LLI
I
0
_N
co	 V	 N	 O	 N	 v
.I.	 +	 }
( W N) ]ON3a3dd10 NOUISOd NOV81 ONO -lV 9 snaNIN
12
f
.. ti
xN
N
= W
O Z
xNr n
nm
s '-
O W
Cl)	 Z
I
7
S
0
0
xN
O
= W
O Z
7
S
N
S
O
N W
cc
d
WO ? q
IZ
J ^
Q ^
C14	
U
+	 +	 O	 N
( WTI) 3ON3a3dd10 NOIlISOd >mvmi SS02lo 9 snGININ
13


Nimbus 6 Doppler processing using the Fairbanks calibration platform

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server