1
GPS RECEIVER CALIBRATION – WHY IS IT NECESSARY?
Dr. Nadya Goldovsky and Dr. Ilya Kuselman
National Physical Laboratory of Israel,
Danciger “A’ Bldg., Givat Ram, Jerusalem 91904
Tel.: 02-6536534, fax: 02-6520797, e-mail: nadya.go@moital.gov.il
Abstract
Measurement uncertainty of the majority of commercial GPS receivers varies from 10-11
to 10-13 by the frequency scale, and from 100 ns to 50 ns by the time scale, being
dependent on the receiver design. The main sources of uncertainty in GPS
measurements are the GPS receiver position error, the orbital error, the satellite and
receiver clock errors, the ionospheric and the tropospheric delays, the receiver internal
delay, the satellite antenna and cable delay, the receiver noise, and the multipath error.
The frequency uncertainty for a GPS receiver is larger than that for Cs-standard by 2-3
orders within a short-time interval (1 – 1000 s), and by one order within a long-term
interval of about one week. A GPS receiver’s time scale bias from the Universal
Coordinated Time (UTC) can be in order of microseconds. Not every GPS receiver is
suitable for use as a traceable primary frequency and/or time standard. Therefore, GPS
receiver calibration against the primary time and frequency standard (the Cs-atomic
clock traceable to UTC) is of great importance and implies the calibration of both output
frequencies and time scale. The frequencies calibration is performed through
comparison of one of the outputs (1 pps, 10 MHz, and/or 5 MHz) with the
corresponding reference frequency of the caesium atomic standard. The user’s GPS
receiver time scale calibration is fulfilled through comparison between 1 pps signals of
the user’s GPS receiver and those of the Cs-atomic standard.
Keywords: Global Positioning System (GPS); GPS receiver calibration; Time and
frequency measurement
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Introduction
Global Positioning System (GPS) is well known as a tool for both positioning and for
high accuracy time and frequency transfer. Hundreds of companies sell GPS products,
and many of manufacturers advertise their units as being time and frequency standards.
The characteristics of a GPS receiver depend on the applications for which it was
designed. There are two main types of GPS receivers: commercial GPS receivers
intended for navigation (for example, in commercial and military aircraft, marine and
automobile navigation) [1], and GPS receivers used in time and frequency metrology
[2].
Commercial GPS receivers intended for navigation provide X,Y,Z coordinates of their
location. Receivers used in cars are generally intended for driver navigation or for
sending information on the location of a car to an emergency response center in case of
accident. Receivers intended for commercial airliners have usually a data port for
integration into the air navigation systems. The required uncertainty of such receivers is
of the order of 1 – 100 m [1].
GPS timing receivers provide a 1 pulse per second (1 pps) electrical output. Most
receivers use the coarse acquisition (C/A) code broadcast on the frequency of 1.57542
GHz (L1) as their time and frequency reference. The 1 pps output can provide time
synchronization at locations anywhere on earth, or provide the timing reference for
either a telecommunications network or for an Internet timeserver.
Another type of GPS receivers known as GPS disciplined oscillators [3], provide
standard frequencies of 5 MHz and/or 10 MHz, and sometimes produce frequencies of
1.544 MHz or 2.048 MHz used in telecommunications. Digital telecommunication
networks that carry voice, data, and facsimile information require a reference frequency
source with an uncertainty of 10-11 or less [2,4] for ensuring quality-of-service to the
clients.
Two other types of GPS receivers used for more precise measurements are commonview GPS receivers and carrier-phase GPS receivers [2]. A common-view GPS receiver
is actually integrated system that combines a standard GPS timing receiver with
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measurement hardware and software. These hardware and software allow the system to
make measurements from individual satellites and to store the measurement results that
can be processed later.
Carrier-phase GPS receivers are designed for geodetic and surveying applications.
Usually more expensive than the traditional time and frequency receivers, they track
and measure the precision (P) code broadcast on two carrier frequencies L1 and L2 (the
last one is at 1.2276 GHz). Their potential positioning performance is exceptional, the
positioning uncertainty being within centimeters or even millimeters ranges [2].
Common-view and carrier-phase measurements require more effort, including postprocessing of the measurement data. For this reasons, they are usually used in
international time and frequency comparisons between National Metrology Institutes
(NMI) [2].
Although GPS broadcasts are continuously monitored by National Institute of Standards
and Technology (NIST), USA, not all GPS receivers are suitable for use as traceable
primary frequency standards. The importance of the GPS receiver calibration, as well as
the calibration method used in the National Physical Laboratory of Israel (INPL) are
discussed in the present paper.
The importance of GPS receiver calibration
While GPSs differ significantly, there are two common key factors that contribute to a
GPS receiver performance, namely, the quality of the receiver’s internal oscillator and
the quality of the software algorithm that processes data obtained from satellites [3].
The majority of GPS receivers have frequency short-term stability of about 10-10 – 10-11
[2]. Models with the best short-term stability discipline an oven-controlled quartz
oscillator or a rubidium oscillator to the GPS signal. However, even GPS receivers of
this type have a short-term stability that is lower than the Cs-standard stability. Such
standard is maintained, for example, at INPL [5-8].
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Many receivers do not discipline an oscillator at all. Instead, they divide the output of a
small temperature-controlled crystal oscillator down to 1pps, and then synchronize 1
pps with GPS signal. As a result, the short-term stability of these models is poor (the
frequency uncertainty is about 10-9 – 10-10 over the averaging time about 1 –1000 s
[2,3]).
Most GPS receivers automatically select satellites used for the timing solution.
However, software algorithms used to select satellites are different, and each receiver
has its own thresholds at which it chooses to keep or to omit a satellite. Some
algorithms limit the timing solution to just one, or to a few satellites. Others can use as
many as 12 satellites in a solution. For this reason, two GPS receivers can yield
different results even when connected to the same antenna at the same location.
Since each GPS satellite is visible at a given location for a limited time, all GPS
receivers must add and remove satellites from the group used to obtain time and
frequency information. Often, adding and/or removing a satellite from the timing
solution causes an instantaneous frequency change.
Various receivers handle GPS broadcast errors differently. Some receivers have built-in
software designed to remove “bad” data, other have no such software. But all GPS
receivers might bias their time scale or even fail under certain conditions, namely,
strong ionospheric disturbances (for example, ionospheric scintillations).
Different types of GPS receivers are applied in different types of GPS measurements.
These measurements in the field of time and frequency metrology can be divided into
four general categories: one-way, common-view, carrier-phase, and two-way satellite
time and frequency transfer (TWSTFT) [3]. The majority of user GPS measurements
are one-way measurements. The one-way GPS technique uses the signals, obtained
from a GPS receiver, as the reference for a calibration. The purpose of the measurement
is either to synchronize an on-time pulse, or to calibrate a frequency source. The GPS
signal is used in real time, and no post processing of the measurement results is
required.
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The main error sources in one-way GPS measurements are expressed by the basic
equation for pseudorange [9]:
p = ρ+dρ+c(dt-dT)+dIon+dTrop+ερ+ρmult ,
(1)
where p is the measured pseudorange; ρ is the calculated geometric range between
satellite and receiver ( i.e. [(XS-XR)2+(YS-YR)2+(ZS-ZR)2]1/2 ); XS,YS,ZS and XR,YR,ZR
are the coordinates of the satellite and the receiver, respectively; dρ is the orbital error;
dt and dT are the satellite and the receiver clock errors, respectively; d Ion is the
ionospheric delay; dTrop is the tropospheric delay; ερ is the receiver code noise; ρmult is
the multipath error [10].
Common-view, carrier-phase, and TWSTFT measurements are more precise
measurements and require post-processing of the measurement data. The collected data
are analyzed and processed using precise satellite orbit information and detailed models
of the ionosphere and troposphere. These types of GPS measurements are usually used
for international time and frequency comparisons between NMI.
In common-view time transfer the time difference between two clocks is determined by
simultaneous observation of the same satellite at the same time in two different
laboratories. The measurement results are then exchanged and the difference between
two time scales is obtained. This technique gives improved performance over the oneway technique. It eliminates satellite clock errors, and reduces orbital errors,
ionospheric and tropospheric errors [3]. By forming the double and triple difference [3]
using two and more satellite observations, the receiver clock errors also can be
eliminated. The accuracy of common-view time transfer is typically in the 1 to 10 ns
range. The GPS common-view technique has been used for many years by the Bureau
International des Poids et Mesures (BIPM) as one of its main techniques for
international time comparisons.
The TWSTFT technique eliminates nearly all of the propagation delay errors because
the signal path symmetry for both stations [3]. Recently BIPM has started using twoway technique as a primary time transfer technique. The uncertainty of TWSTFT over a
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24 hours period is better than 1 ns and has been be as low as 100 picoseconds in some
systems [3].
The traceability requirements for time and frequency measurement
According to [11], the metrological traceability is “the property of a measurement result
relating the result to a stated metrological reference through an unbroken chain of
calibrations of a measuring system or comparisons each contributing to the stated
measurement uncertainty”. The traceability chain for measurements in field of time and
frequency is shown in Fig.1 [4]. The traceability chain is beginning from a measurement
instrument, for example, a time interval counter. Link A is the link between the
measurement instrument and the user’s GPS receiver. Measurement uncertainty sources
in link A are: user’s GPS receiver uncertainty, multipath error [10], satellite clock error,
uncertainty of the time delay in atmosphere, errors in satellites orbit calculation,
uncertainty of calibration procedures, and human errors.
The uncertainty of the user’s GPS receiver is caused by receiver’s noise, the internal
oscillator’s instability, software error, uncertainty of time delay in antenna, in antenna’s
cable, and finally GPS receiver internal delay. GPS receiver calibration is carried out in
order to determine: 1) frequency deviation from its nominal value and uncertainty of
this deviation; 2) the GPS receiver second bias from the SI second; 3) the GPS receiver
time scale deviation from the Universal Coordinated Time. The deviation of the GPS
receiver time scale from UTC can be relatively large (several microseconds) and is
dependent on the time delays in the GPS receiver, in GPS’s antenna and in antenna’s
cable; on the error of atmospheric delay calculation, and other software errors.
Therefore, the calibration of GPS receiver against the time and frequency standard (the
Cs-atomic clock traceable to UTC and SI second) is of great importance.
It should be noted that UTC is a “paper” theoretic time scale calculated by BIPM in
Paris. The time signals received by user’s GPS are referenced to real time scale called
GPS time.
The GPS system includes a constellation of 24 satellites [2]. The GPS satellites are
controlled and operated by the United States Department of Defense. Each satellite
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carries either rubidium or caesium oscillators, or a combination of both. The on-board
oscillators provide the reference GPS time for transmission. The relation between GPS
time and UTC involves a variable number of seconds as a consequence of the leap
seconds and is as follows:
[UTC – GPS time] = -13 s + C0
(2)
where C0 is the correction given in the BIPM monthly Circular-T at 0h UTC. The C0
values vary in the range of ± 20 ns, and their expanded uncertainty is in the range of
±10 ns [12].
Link B connects the user’s GPS receiver to the broadcast signal monitored by NMI.
Measurement uncertainty in this link is caused by the signal path from the GPS satellite
to GPS receiver’s antenna. This uncertainty consists of tropospheric delay error,
ionospheric delay error, orbital errors, and multipath errors. There are several agencies
that provide calculation of satellite orbit, ionospheric delay, and tropospheric delay, for
example, the Center for Orbit Determination in Europe and the International GPS
Service. Among the error sources mentioned above, the major uncertainty is caused by
tropospheric and ionospheric delay, which can reach to several hundreds of ns for low
elevation angle satellites.
Link C is the control, or monitoring, link between an NMI (for example, INPL) and the
broadcast service. Link C connects the NMI to GPS satellite system. This link is
established through the NMI’s measurements of the GPS signals.
Link D is the chain between the UTC scale and the local Coordinated Time Scale
UTC(NMI) maintained by the NMI. UTC is calculated by averaging of data collected
from more than 200 atomic clocks located in about 50 national laboratories spread
worldwide and regularly reported to BIPM. The uncertainty of link D can be evaluated
using BIPM’s Circular T.
The SI second is defined as the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between the two hyperfine levels of the ground state of
the caesium 133 atom. Frequency (expressed in hertz) is derived from a second and
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equals to the number of events over a 1-second interval. Thus, GPS receiver cannot be
used as primary frequency and time standard, it can be used as secondary frequency and
time standard only.
As for every traceability chain, the measurement uncertainty in the chain shown in
Fig. 1 is increasing in the direction opposite to traceability, i.e. from link D to link A.
User’s GPS receiver frequency calibration at INPL
Results of measurements and calibrations in field of time and frequency in Israel are
traceable to the National Standard of Time and Frequency and the UTC(INPL) scale
maintained by INPL, according to the law on the National Israel Time Scale since 1992.
Once traceability to INPL is established, it is accepted as well in other countries that
signed the mutual recognition arrangement [13].
In order to show traceability of a GPS receiver to UTC(INPL), an unbroken chain must
be established between the measurements made by GPS receiver at the user’s site and
the UTC(INPL) time scale.
The block diagram of the GPS receiver calibration system used at INPL is shown in Fig.
2. The calibration system comprises: Cs-Standard traceable to UTC via GPS commonview link; the unit under test (UUT), for example, user’s GPS receiver; a time interval
counter; a pulse distribution amplifier; a 1 pps generator (optionally, when UUT does
not have its own 1 pps output); a personal computer (PC1) for GPS time transfer data
processing; a INPL GPS receiver applied for common-view measurements; a satellite
antenna; a microprocessor with time interval counter; a monitor; a printer; an
ionospheric calibration receiver (ICR) with a satellite antenna; a commutation switch
box; a personal computer (PC2) for calibration data processing; a high frequency (5
MHz) signal distribution amplifier [14, 15].
The GPS receiver calibration implies the calibration of output frequencies and the
calibration of time scale. The frequencies calibration is performed through comparison
of one of the outputs (1 pps, 10 MHz and/or 5 MHz) with the corresponding reference
frequency of the INPL caesium atomic standard. The time interval counter measures the
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time differences between calibrated and reference signals. UTC(INPL) calculation is
developed in [5-8]. The frequency calibration procedure and the procedure for
comparisons between UTC(INPL) and UTC are described in detail in [14, 15].
Frequency standards and oscillators stability is described by the fractional frequency
deviation and Allan variance [16-18]. The fractional frequency deviation is:
y=(fUUT–fREF)/fREF,
(3)
where fUUT is the calibrated frequency of the UUT; fREF is the reference frequency of
the Cs-Standard.
Allan variance σy2(τ) is:
N-1
N-1
σy2(τ)=(1/2) · (N–1)-1·∑(yk+1-yk)2=(1/2) · (N-1)-1τ-2 ∑(xk–2xk+1+xk+2)2,
k=1
(4)
k=1
where N is the number of measurements; x is the difference between signals of the
UUT and the reference clock; τ is the averaging time (the time between two successive
x measurements). The square root from the variance σy2(τ) is the Allan deviation σy(τ).
The y of the calibrated GPS receiver over all the measurement time is defined as the
slope of the linear regression fit for the time comparison results between UUT (a GPS
receiver) and the reference Cs-Standard. The number of measurements N of time
differences x between the UUT and the reference Cs-Standard is about 20 000 – 32 000.
To determine the metrological characteristics of the calibrated GPS receiver relatively
to UTC, the reference frequency yREF and its uncertainty UREF should be taken into
account. Thus, the corrected value of the UUT frequency yUUT-UTC and its uncertainty
UUUT-UTC are calculated by the following equations:
y[UUT-UTC] = y[UUT-INPL] + yREF ,
(5)
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where y[UUT-INPL] is the fractional frequency deviation of the UUT relatively to INPL
reference frequency; yREF = y[INPL-UTC] is the fractional frequency deviation of the INPL
reference frequency relatively to UTC frequency, computed from the last BIPM
Circular T. The expanded uncertainty of the calibrated GPS receiver frequency is:
UUUT-UTC = k ( u2UUT-INPL + u2REF )1/2 ,
(6)
where k is the coverage factor (k=2 for 95% confidence level in case the number of
degrees of freedom N-1 is larger than 20 000); uUUT-INPL is the standard uncertainty of
the calibrated GPS receiver frequency relatively to the INPL reference; uREF is the
standard uncertainty of the INPL reference frequency yREF relatively to UTC, computed
from BIPM Circular T for the minimal τ. The expanded uncertainty of the INPL
reference frequency is:
UREF = k σy(τ) / √ N
(7)
The expanded uncertainty of the INPL caesium atomic standard is about 10-14 over one
week averaging, while the uncertainty of user’s GPS receivers relatively to INPL
frequency reference uUUT-INPL is about 10-13 – 10-11.
User’s GPS receiver time scale calibration at INPL
The calibration of user’s GPS receiver time scale is performed at INPL according to the
block diagram shown in Fig. 2. The measurements are performed simultaneously in two
parallel channels. In the first channel, the user’s GPS receiver time scale is compared
with the UTC(INPL). For this purpose, the 1-second signals (1 pulse per second) of the
user’s GPS receiver and the INPL Cs-Standard are compared by the time interval
counter. The obtained difference between UTC(INPL) and UUT time scales is D1 =
UTC(INPL) – UUT time. Connecting cables delay is subtracted from the difference in
the D1 value calculation.
In the second channel, the international comparisons between the local and GPS time
scales are performed by the INPL GPS receiver operating in the common-view mode.
The obtained difference between UTC(INPL) and GPS time scales is D2 = UTC(INPL)
– GPS time. These comparisons are performed continuously, and their results are
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reported to BIPM once a week. The time delays in the INPL GPS receiver, its antenna,
antenna’s cables, and connecting cables are known with the uncertainty of ± 1 ns.
Moreover, the corrections for ionospheric and tropospheric delays are also taken into
account at the D2 value calculation [15].
The obtained values of D1 contain the time delay in the user’s GPS receiver, in its
satellite antenna, in antenna’s cable, as well as the bias caused by user’s software errors.
These factors lead to a deviation of the user’s GPS time scale (UUT time) from the
universal GPS time D3 = GPS time – UUT time. Determination of the D3 value can be
made by subtracting the difference D2 from the difference D1:
D3 = D1 – D2
(8)
For this purpose, D1 and D2 should be obtained for the same real time, in other words,
the measurements in both channels should be performed simultaneously from the same
beginning time point and for the same calibration time. Then the D1 and D2 values
obtained are fitted by two linear regressions. The D3 value is calculated as the mean
difference between these two linear regressions. An example of such fitting is shown in
Fig. 3. Here the mean D3 value is 1.27 microsecond.
The user’s GPS receiver time scale deviation from UTC is calculated by adding [UTC –
GPS time] correction from Circular T to D3 value:
UTC – UUT time = D3 + [UTC – GPS time]
(9)
The uncertainty of the user’s GPS receiver time scale deviation from the GPS time scale
is:
UD3 = k (u2D1 + u2D2 + u2C + u2L)1/2 ,
(10)
where uD1 is the standard uncertainty of linear regression fit for D1; uD2 is the standard
uncertainty of linear regression fit for D2; uC is the standard uncertainty of the
connecting cable delay; uL is the standard uncertainty of the INPL GPS receiver’s delay,
antenna’s delay, and antenna’s cable delay; k=2 is the coverage factor.
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As a rule, the dominant contribution of the expanded uncertainty (10) is caused by a
residual deviation of the user’s GPS receiver scale from a straight line, which is uD1 >
20 ns. For comparison, in the case in Fig. 3, uD2 is about 5 ns, uC and uL are about 1 ns
each. Therefore, UD3 = 41 ns here.
Conclusions
Due to performance differences, two user’s GPS receivers can yield different frequency
results even when connected to the same antenna at the same location. The frequency
uncertainty for user’s GPS receiver is larger than that for Cs-standard by 2-3 orders for
a short-time interval (1 – 1000 s), and by one order for a long-term interval of about two
weeks.
The user’s GPS receiver time scale bias from the Universal Coordinated Time can be in
order of microseconds. It depends on the time delay in GPS receiver, satellite antenna,
antenna’s cable, ionospheric correction error, and software errors.
Commercial GPS receiver calibration service provided by INPL ensure measurement
uncertainty of about 10-14 in the frequency scale, of about 5 ns in the time scale, as well
as traceability to the Universal Coordinated Time.
References
[1] http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html Cited 27.12.04
[2] M.A.Lombardi, L.M.Nelson, A.N.Novick, V.S.Zhang, Time and Frequency
Measurements Using the Global Positioning System, Cal. Lab. (Int. Jour. of
Metrology), July-September 2001, pp. 26-33.
[3] http://www.boulder.nist.gov/timefreq/service/gpscal.htm Cited 27.12.04
[4] M.A.Lombardi, Traceability in Time and Frequency Metrology, Cal. Lab. (Int. Jour.
of Metrology), September-October 1999, pp. 33-40.
[5] A.Lepek, A.Shenhar and D.W. Allan, UTC(INPL) – a virtual time scale, Metrologia,
1995/96, 32, pp. 245-252.
[6] A.Lepek, A.Shenhar, M.Bezalel, The UTC(INPL) time scale, Proceedings of Ninth
International Conference of the ISQA, 1992, pp. 502-506.
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[7] A.Lepek, Atomic scale based on optimum linear prediction, IEEE Frequency
Control Symposium, 1997, pp.382-387.
[8] A.Lepek, Clock prediction and characterization, Metrologia, 1997, 34, pp.379-386.
[9] http://www.geomatics.ucalgary.co/links/GradTheses.html Cited 27.12.04
[10] J.Ray, Mitigation of GPS code and carrier phase multipath effects using a multiantenna system, Ph.D. Thesis, Department of Geomatics Engineering, University of
Calgary, Canada, 2000.
[11] International Vocabulary of Basic and General Terms in Metrology, ISO, Geneva,
2004.
[12] http://www.bipm.fr Cited 27.12.04
[13] Mutual Recognition of National Measurement Standards and of Calibration and
Measurement Certificates Issued by National Metrology Institutes, BIPM, Paris,
1999.
[14] N.Goldovsky, M.Luria, Frequency Standard and Oscillators Calibration at the
National Physical Laboratory of Israel, Proceedings of the 14-th International
Conference on the Israel Society for Quality, Jerusalem, November 2002, pp. 394399.
[15] N.Goldovsky, M.Luria, Ionospheric delay contribution to the uncertainty of time
and frequency measurement by one-way satellite time transfer method,
Measurement, 35, 2004, pp. 353-362.
[16] D.W.Allan, Statistics of Atomic Frequency Standards, Proc. IEEE, vol. 54,
February 1966, pp. 221-230.
[17] D.W.Allan, The Measurement of Frequency and Frequency Stability of Precision
Oscillators, NBS Tech. Note 669, July 1975.
[18] F.L.Walls and D.W.Allan, Measurements of Frequency Stability, Proc. of the
IEEE, vol. 74, №1, January 1986, pp. 162-168.
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UTC and SI
Second (BIPM)
D
UTC(NMI)
C
Broadcast GPS
signal monitored by
NMI
B
User’s GPS receiver
A
Measurement
instrument
Fig. 1. The traceability chain for time and frequency measurements.
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Monitor
Printer
Commutator
Distrib
Ampl.
Microprocessor
5 MHz
GPS
Pulse
Distrib
Ampl.
1 pps
start
1 pps
stop 5 MHz
5 MHz
1 pps 5 MHz
ICR
INPL GPS Receiver
1 pps
Cs-Standard
PC1
5 MHz
ICR
1 pps 5 MHz
Time Interval Counter
PC2
start
UUT
GPS Receiver
stop
1 pps Generator
(Optionally)
Fig. 2. Block diagram of GPS receiver calibration system.
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12.000
11.800
Microsecond
11.600
11.400
D1 = UTC (INPL) - UUT time
11.200
D2 = UTC (INPL) - GPS time
11.000
10.800
10.600
10.400
0
1
2
3
4
5
6
Days
Fig. 3. The time difference D3 between the user’s GPS receiver and the GPS time
scales.