The Return Data Delay technique which requires knowledge of spacecraft range is commonly used for correlating a spacecraft clock against a ground time standard when millisecond accuracy is required. An analysis is presented that allows using the user spacecraft clock calibration system (USCCS) to correlate a spacecraft clock to better than one microsecond accuracy. The basic USCCS algorithm has been simplified and it is shown to result in about one microsecond accuracy without requiring orbital information. By considering the relative motion of the user satellite, the TDRS and the earth station about the center of the earth, a correction of almost two orders of magnitude can be made. Such accuracy is required for scientific investigations that require correlating coincident radiation or particle detection with a remote laboratory

Sank, Victor J.

English

NASA Technical Reports Server

N94-2i345
USING THE USCCS FOR SUB MICROSECOND SPACECRAFT CLOCK CALIBRATION
Victor J. Sank, Ph.D.
Fredrick Herold & Associates, Inc.
7303A Hanover Parkway
Greenbelt, Maryland 20770
(301) 982-4001
Summary
The Return Data Delay technique which requires knowledge of
spacecraft range is commonly used for correlating a spacecraft
clock against a ground time standard when millisecond accuracy is
required. An analysis is presented that allows using the user
spacecraft clock calibration system (USCCS) to correlate a
spacecraft clock to better than one microsecond accuracy. The
basic USCCS algorithm has been simplified and it is shown to
results in about one microsecond accuracy without requiring
orbital information. By considering the relative motion of the
user satellite, the TDRS and the earth station about the center
of the earth, a correction of almost two orders of magnitude can
be made. Such accuracy is required for scientific investigations
that require correlating coincident radiation or particle
detection with a remote laboratory.
Backqround
An accurate absolute time reference is required on
scientific spacecraft for operational purposes and for
correlating scientific data. Typical accuracy required for many
satellites has been of the order of one millisecond; examples are
ERBS, SMM, SME, UARS, EUVE, LANDSAT and HST. This accuracy is
obtained by reading the spacecraft clock (or oscillator count
values) simultaneous with a particular bit edge in the telemetry.
As the telemetry is received on the ground an absolute time
reference is recorded periodically for selected bits in the
telemetry. The absolute ground receipt time of the bit edge that
was simultaneous with the onboard clock reading can thus be
determined. Orbital knowledge and equipment time delays then
allow the calculation of the time the particular bit was created
on board and, hence, the time the spacecraft clock was read based
on the ground clock. The reading on the spacecraft clock is sent
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to the ground in a later portion of the telemetry and serves as a
clock calibration by Comparing it with the earth based standard.
The main limitation in this method, which is referred tO as
the return data delay (RDD) or return channel telemetry delay
(RCTD), is accurate knowledge of the spacecraft range (and thus
the space propagator delay) from the ground receiving station.
The calculations are done after a 9ass with the tracking, data
and relay satellite system (TDRSS) and uses predicted orbital
positions. The results are extremely sensitive to the quality of
the orbital data but can be accurate to about 3 _s with respect
to the ground time reference (atomic clock at the NASA Ground
Terminal (NGT)). The RDD method is an open loop method.
The CGRO project decided that because they required a i0 _s
clock setting accuracy, they would take advantage of the pulses
used in the TDRSS spacecraft ranging system and implement a
closed loop time correlation technique. This became the user
spacecraft clock calibration system (USCCS). GPS accuracy is
approximately l_s and today would be a competing technique.
Usinq Ranqe Pulses for Time Correlation
The standard ranging technique used in the TDRSS is a closed
loop method in which a pulse is sent from the TDRSS ground
station at White Sands New Mexico (WSGT) to a user via a TDRS and
then returned from the user to the WSGT via the same TDRS. The
signal propagation time which is used to determine the range to
the user is combined with the known TDRS orbit to determine the
user satellite orbit. The time accuracy between pulses is
specified to be ± 35 nanoseconds. For orbit determination,
doppler shift is also used.
The changes required to use the range pulses for timing
were:
I. to extract the range pulse from the spacecraft
transponder and use it to trigger a reading of the
spacecraft clock.
276
• to make an absolute time reading of the ground station
range pulse transmission time, and the range pulse
receipt time. For range purposes the delta between
these times were measured accurately but the absolute
times were not.
The range pulses, referred to as pseudo random (PN) code
epoch pulses, are the part of the PN spectrum spreading code used
in the TDRSS where there are 18 ones in a row. The code has a
length of 256 x 1023 chips (PN bits) generated at a rate of
approximately 3MHz. This results in a PN epoch pulse
approximately every 0.085 milliseconds (25500 Km at the speed of
light).
USCCS
The basic concept of the USCCS time correlation method is
extremely simple. When a PN epoch pulse is transmitted from the
ground the time is recorded, t I. It arrives at a spacecraft at
some time t 2 which is unknown. The spacecraft transponder
immediately retransmits the pulse to the ground where its arrival
time, t3, is recorded. Upon receipt of the pulse at the
spacecraft, the spacecraft's clock is read and the reading, t2_ ,
is transmitted to the ground along with other telemetry. On the
ground, t 2 is calculated from t I and t 3 and compared to t2,c for
calibration. The pulse arrival time at the spacecraft t 2 is
approximately half-way between t I and t 3.
tl+ t3 (i)
t2 - 2
When the signal propagation is viewed by an observer on the earth
it may seem that this in not an approximation• Proper analysis,
however, requires that the system be viewed from an inertial
reference frame.
277
For a low earth orbiting (LEO) spacecraft at about a 400 Km
altitude, and a geosynchronous relay satellite, the round trip
distance traveled by an epoch pulse never varies by as much as
25500 Km, thus, there is no ambiguity between a transmitted epoch
and its corresponding return epoch. No orbital information is
needed, other than t I and t3, when correlating epochs to
approximately determine t 2.
Accuracy of the USCCS
The correction to half-way between t I and t 3 does not depend
on the LEO spacecraft velocity or the RF signal doppler shift.
The correction does depend on the LEO position and the fixed
quantities: earth rotational speed; geosynchronous relay
satellite rotational speed; relative position of earth station;
and, of course, the speed of light. The solution for t 2 with the
various motions is now examined and numerical values are given
for an example of orbits in the earth equatorial plane. It will
be shown that the required correction of up to about 1 _s is
asymmetric with the relative position of the LEO and relay
satellite and, thus, not related to the doppler which is almost
symmetric. The doppler can be used if orbital data is not
otherwise available to determine the longitudinal component of
the relative ground station, TDRS, and user position, which can
then be used to determine the required correction to Equation i.
Doppler
Consider the example of an object (user spacecraft) moving
away from a fixed observer at a constant velocity, Figure 2. The
frequency transmitted from the observer, fl, and received by the
observer, f3, are different (doppler), BUT the transmitted epoch
pulse is at the user at a point in time t2, which is exactly
half-way between when it leaves the observer, t I, and returns to
the observer, t 3. Note that the relative velocity, v, between
278
observer and user spacecraft can be determined from the
observer's measurement of forward and return PN periods, T_ and
T3, respectively. For the USCCS, an observer at the WSGT on a
slowly rotating earth and a spacecraft in orbit, the above
concept is approximately true. For the constant velocity case
this equation is exactly true no matter how fast the user
spacecraft is moving.
A simulations viewing earth, TDRS, and user spacecraft
actual motion from a reference frame moving with the center of
the earth shows the correction term to Equation 1 to be less than
1 _s and, again, independent of the user spacecraft motion,
Figure 3. This analysis thus tells us that Equation 1 is
accurate to 1 Vs.
Special relativistic considerations are not included since
they are of the order v2/c 2 and which is about one nanosecond
(v2/c 2 x round trip time of 0.5 second).
Simulation
We observe the three bodies from above the north pole of the
earth with the earth center being the center of our reference
frame, and the TDRS and user orbit in the same plane, Figure 3.
Due to the earth's curved path (orbit) around the sun this also
is not a true inertial reference frame, but the remaining errors
are below our desired accuracy.
From Figure 3, we see that the forward path and return path
are not the same. Since the forward and return paths are
different, the signal that left the ground at t I and returned at
t 3 is not at the spacecraft exactly half-way in between. Since
the signal is at the user for only an instant of time at t2, it
may be intuitive that the difference in forward and return time
is independent of the user spacecraft velocity. This is similar
to the constant velocity example given earlier.
The difference in forward and return travel time is due to
both the earth and TDRS motion. Clearly the TDRS motion during
the 0.25 second that the signal travels from the TDRS to user and
279
back to TDRS causes a difference in forward and return travel
time. In addition, a more subtle effect is the difference
between the GT-to-TDRS and TDRS-to-GT travel time. As a signal
moves through space from the GT to TDRS-E, the TDRS is moving
away. Thus, the distance traveled by the signal is greater than
the instantaneous GT-to-TDRS distance. Similarly, as a signal
travels from TDRS-E to the GT, the GT moves toward the signal so
the distance traveled by the signal is less than the
instantaneous distance, since the TDRS and GT are always in
fixed relative positions, the forward travel time of one pulse is
the same as the forward travel time of the following pulse.
Similarly, the return travel time from TDRS to GT for successive
pulses is the same. For TDRS-E the forward time is .395 _s
longer than the return time. For TDRS-W the values are reversed.
We now consider the portion of the signal path between the
TDRS and the user. The computer simulation shows the signal
travel time from TDRS to the user to be a maximum of 0.466 _s
longer than the traqel time from the user to the TDRS. This
occurs when the angle between the TDRS and the user spacecraft is
approximately 90 ° , the LOS point. At AOS the values are reversed
because the user is approaching the TDRS and the TDRS-to-user
time is less than the user-to-TDRS portion. For a user in a
polar orbit, the effect is less.
The net effect of combining the GT-TDRS and TDRS-user
portions is such that for TDRS-E at LOS the forward travel time
is 0.86 _s longer than the return travel time. At AOS it is
about 0.072 _s less, Figure 4. For TDRS-W the conditions are
reversed.
As in the constant velocity example of Figure 2, the forward
and return PN periods T l and T 3 can be used to determine the
longitudinal component of the user's velocity, v. In the real
case the complete motion, as shown in Figure 3, must be taken
into account, but the results will be approximately equal to that
given by the equation for v in Figure 2.
The maximum doppler effect will cause the PN period at the
spacecraft to vary by about 2 _s from the period transmitted from
280
the GT. Thus, the return PN period at the GT will be a maximum
of 4 _s different from the transmitted. Even though the PN
periods as measured at the GT reflect the longitudinal component
of the velocity of the user spacecraft, Figure 5, their magnitude
does not directly relate to the correction needed in the USCCS to
determine t 2. The values of T l and T 3 serve only to tell us where
the user is in his orbit relative to TDRS. The geometry of
Figure 3, the TDRS motion and earth rotation, must then be used
to calculate the sub-microsecond correction needed to obtain the
correct value of t 2. That is, T I and T 3 at a given time are used
to find v. Knowing v we can find the relative orbital angle
between TDRS and the user, Figure 5. Once the angle is known,
the difference between the forward and return travel time, t F -
tR, can be found from Figure 4 and used to find the correction
required for Equation i.
t2 t1+t3 tr-t R= + (2)
2 2
Correction Term
Using Figures 3, 4 and 5, we can model the correction term
tv - tR as follows. The user velocity as seen from TDRS (not
orbital velocity) varies approximately sinusoidally as
v - vusin
2 8c '
-i00 ° <= Or <= i00 ° (3)
where:
8 r is the relative angle between the TDRS and user
measured from earth center,
8 c is
r u
cos -1 __
r r
, the relative angle at which the user
is moving directly toward or away from TDRS,
v. is the user's orbital speed.
281
In terms of T I and T3, v is approximately
v r3-rl
- C
TI+T3
(4)
Equation 3 is used to solve for _r
20c __v
8r -- __ sin -I
v u
(5)
where v is known in terms of T l and T 3 from Equation 4.
From Figure 4, the correction term t F - t R can be represented by
tF - tR = .4665 sin e x + .3945 _s (6)
Using Equation 2 with this correction yields about two orders of
magnitude correction over Equation i. T l and T 3 are sufficiently
slowly varying that T1(tl) and T3(t3) will suffice.
Conclusion
Exploring the physics of the USCCS for the CGRO because of a
problem that was found to be simply a misplacement of data in the
telemetry, lead to the previous analysis. After examining the
full signal path from an inertial point of view it became clear
that the basic formula, t 2 = (tl+t3)/2 , is accurate to 1 #s
without any further correction (except of course, equipment
delays). The analysis did show that greater accuracy,
approaching that of the TDRSS ranging system, is possible but
requires knowledge of the relative position of the user
spacecraft and ground station relative to the TDRS. Other
limitations in the system as currently implemented are that the
time tags are only resolved to 0.i #s; and, although sub
microsecond accuracy with respect to the ground station time
standard is possible, it is only kept within about 1 _s of UTC.
282
At - -dc ='5sec°nds
TpN = .085 seconds
&_.L. = 5.8 epoch periods
TpN
<_ TDRS
RTN
FWD LINK ,_,
(TDRS-SC) ,_
LINK
(SC-TDRS)
SC TLM
PN RANGE CODE
SC CMD
PN RANGE CODE
RTN LINK
(TDRS-GT)
SC TLM
PN RANGE CODE
TYPICAL DISTANCE
FWD LINK
(GT-TDRS)
SC CMD
PN RANGE CODE
GT-TDRS
TDRS-USER
TDRS-USER
TDRS-WSGT
d=
40,000 Km
36,000 Km
36,000 Km } variable
40,000 Km
152,000 Km
 i!iiiiliiiiiiiiiiii!iiiiiiiiii!i!iii!i iiiiiiiiiiiiiiiiiiiiiiiii!  ,ii, i!i....
Figure I. System Overview
283
v = constant
T, = FWD PN period at GT
T= __ PN period at SC
T = RTN PN period atGT
X, = FWD PN wavelength at GT
= PN wavelength at SC
L, = RTN PN wavelength at GT
c = speed of light
t 2 = tl + t3
2
t 2
SC
t=
_=C
T
X2=Xl-va"2
C-V
_L3 = T2C + T2v
T3 = v+C T2
c
T3 = v+c T1
C-V
T 3 - T 1
v- c
T_+T3
Fixed Observer
! Itt, t, t, t= t'=
el !T,= t',-t, = h-t,
T,= t_-t, = t_'-t',
t l! !T, = t= t= = t,-t,
T 1 < T 2 < T3
Figure 2. Signal Path For Object At Constant Velocity
284
TDRS-E
t3 t 2 t_ t 1
Return
Forward Forward
LOS AOS
User
Spacecraft
Orbit
Figure 3. RF Signal Path
285
o o o _ o o _ _ o o0 0 0 0 0 0
o__
LL
286
0_.x.:.:+:-:_ :_,-::::_x: _:-:,:+:.:-:-x -.'_.'::.',:::_:: ;::_:::::::::::::::::::::::::::::::.%::_ :::
0 ,0 0 0
_._I_-
287



Using the USCCS for sub microsecond spacecraft clock calibration

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