Journal of Global Positioning Systems (2004)
Vol. 3, No. 1-2: 143-153
Recent Improvements to the StarFire Global DGPS Navigation
Software
Ronald R. Hatch
NavCom Technology, Inc., 20780 Madrona Avenue, Torrance, CA 90744
e-mail: [e-mail], Tel: [phone], Fax: [phone]
Richard T. Sharpe
NavCom Technology, Inc., 20780 Madrona Avenue, Torrance, CA 90744
e-mail: tsharpe@navc omtech.com, Tel: [phone], Fax: [phone]
Received: 6 Dec. 2004 / Accepted: 2 Feb. 2005
Abstract. A general review of NavCom Technology’s
StarFire Global DGPS system is followed by a
description of a number of improvements which have
been either recently introduced or are in the process of
being introduced. These improvements include: (1) an
improved mode switching between various differential
aiding signals and between dual-frequency and single-
frequency operation when the L2 signal is lost; (2) a
high-rate, high-accuracy, and efficient time-difference of
carrier-phase position propagation process, which is used
to generate the position coordinates between the one-
second epochs; (3) an improved RAIM measurement
error detection process; (4) a simplified process of
computing the earth tides caused by both the sun and the
moon; and (5) a built-in RTK capability (referred to as
RTK Extend) which can make use of the synergism
between the Global and RTK correction streams to
continue RTK accuracy for up to 15 minutes when the
RTK corrections are lost due to obstructed line-of-site or
other problems with the local RTK corrections. Each of
these will be addressed at least briefly. The more
significant improvements will be addressed at greater
length.
Key words: Global DGPS, RAIM, RTK, StarFire
1 Introduction
The StarFire Global Differential GPS (GDGPS) system
provides sub-decimeter horizontal navigation accuracy
anywhere in the world other than the two polar regions.
The StarFire GDGPS system was developed at NavCom
Technology and Ag Management Solutions, both John
Deere companies, primarily for agricultural and marine
applications. However, the unprecedented accuracy and
global coverage have resulted in a multitude of
applications, both commercial and military.
The StarFire system depends upon very accurate
corrections to the satellite clocks and to the broadcast
satellite orbits. These corrections make use of orbit
prediction technology developed at the Jet Propulsion
Laboratory (JPL) for the National Aeronautics and Space
Administration (NASA). NavCom has licensed the Real
Time GIPSY (RTG) software developed at JPL for use in
the generation of real-time clock and orbit corrections for
all the GPS satellites. In addition, NavCom has
contracted to receive the data from NASA’s dual-
frequency reference receivers located around the world.
These tracking sites are augmented by more than 23
NavCom installed and maintained sites, bringing the total
number of global tracking sites to more than 60.
The StarFire user navigation receivers are high-accuracy,
dual-frequency receivers. Both the receiver hardware and
the internal navigation software were developed by
NavCom to meet stringent accuracy goals. By using dual-
frequency receivers, the effects of ionospheric refraction
can be removed directly. This eliminates the largest
source of error which competing Wide-Area Differential
GPS (WADGPS) systems suffer.
As indicated above, the root-mean-square (rms)
horizontal accuracy in each axis is better than 10
centimeters. The rms vertical accuracy is normally better
than 20 centimeters, and one of the improvements
described below improves this accuracy significantly. At
NavCom continuing improvements are being made to
enhance the robustness and accuracy. After describing the
overall system, several of these improvements will be

144 Journal of Global Positioning Systems
considered in detail.
2 StarFire Overview
In addition to th e GPS system itself, the StarFire GDGPS
system is composed of seven major components. These
are:
 Reference Network – reference receivers that
continuously provide the raw GPS observables
to the Hubs for processing. These observables
include dual frequency code and carrier
measurements, ephemerides, and other
information.
 Processing Hubs – facilities at which the GPS
observables are processed into DGPS
corrections. There are two geographically
separated, independent Hubs that operate fully in
parallel, with each continually receiving all the
measurement data and each computing
corrections that are sent to the uplink facilities
for the satellites. The Hubs are also the control
centers for StarFire, from which the system
operators monitor and manage StarFire. An
automated Alerts System is used to advise
operators of problem conditions as soon as they
arise so that corrective actions may be taken.
 Communication Links – provide reliable
transport mechanisms for the GPS observables
and for the computed corrections. A wide
variety of links are used to ensure that data are
continuously available at the Hubs and that
corrections can always be provided to the Land
Earth Stations (LES) upli n k sites.
 Land Earth Stations – satellite uplink facilities
that send the correction data received from the
Hubs to the geostationary satellites. The
StarFire equipment at the LESs also makes
decisions on which of several streams of
correction data are best and should be broadcast.
 Geostationary Satellites – used to distribute the
corrections to users via L-band broadcasts. The
corrections from the LESs are broadcast on L-
band frequencies to the users. Three Inmarsat
geostationary satellites are used to provide
correction coverage over most of the Earth (the
areas North of +76 degrees latitude and South of
–76 degrees latitude are not covered by
geostationary satellites).
 Monitors – user receivers distributed throughout
the world that use the broadcast corrections and
provide their navig ation information to th e Hubs
in real time. The Monitors are used by StarFire
to continuously observe the operation of the
system and provide immediate automated
feedback about any problems that may arise.
The Monitors are intended to behave just like
user receivers in the field.
 User Equipment – uses the broadcast corrections
along with local GPS observables to produce
very precise navigation. The user equipment
makes dual frequency GPS observations that
remove ionospheric effects, and these refraction-
corrected observations are combined with the
broadcast corrections in a Kalman filter.
These system elements are illustrated in Figure 1, which
shows in schematic form the overall system architecture.
The monitor sites are collocated with the NavCom
reference sites. The system concept is similar to the
regional augmentation systems being deployed by various
governments, e.g. the FAA’s Wide Area Augmentation
System (WAAS), the European EGNOS and Japan’s
MSAS. The government generated WADGPS
corrections use predicted models of the ionospheric effect
and broadcast data for the user to estimate the ionospheric
effect. Because the StarFire system uses dual-frequency
receivers, the ionospheric effects are measured and
removed. This gives more accurate results and also
requires far fewer reference stations than are required by
the above government run WADGPS corrections.
2.1 StarFire ground reference networks
There are 23 NavCom reference sites located on four
continents. The NavCom sites are configured somewhat
different than the NASA global sites which are receiver
only sites. Each of the NavCom reference sites has an
identical set of equipment including:
a) two redundant NCT 2000D GPS reference receivers
which send a full set of du al frequency observables for all
satellites in view to both of the redundant processing
hubs,
b) a fully packaged production StarFire user equipment
unit which serves as an independent monitor receiver,
c) communications equipment (routers, ISDN modems),
d) a remotely controlled power switch and UPS module.
In the US network the communication lines used to link
the reference sites with the processing hubs are frame
relay private virtual circuits. Each frame relay circuit is
backed up with an ISDN dial-up line, which can be
activated in the event of a frame relay connection failure.
The same implementation is used for the communication
lines to and from the hubs and the uplink facilities, with
the exception that th e backup is automatic for these more
critical links. The other regional networks are essentially

Hatch et al.: Recent Improvements to the StarFire DGPS Navigation Software 145
identical with the US network with the exception that
Internet and satellite links are used rather than frame
relay and ISDN.
A StarFire user set is located at each reference site and is
used as a monitor unit to report the health of the system.
These units receive the broadcast correction stream from
the communications satellite, perform differential GPS
navigation and report their positioning results back to the
processing hubs, using the same communication lines as
the reference receivers. In addition to the DGPS
positioning results, the monitor data includes the received
signal strength of the L-band communications satellite,
packet error statistics, age of differential corrections,
signal strengths for the received GPS satellites, PDOP
and other operating parameters. This data, from all of the
reference sites, is continuously monitored by an Alert
Service processor which automatically generates E-mail
and pager messages to on-call network service engineers
in the event of a DGPS service failure.
Figure 1: Overview o f the StarFire WADGPS and GDGPS system
The global reference sites operated by JPL for NASA,
identified by the red flags in Figure 2, along with the
NavCom reference sites, identified by the gree n flag s, are
used in computing the global corrections. The Internet
and satellite links are used to bring the dual-frequency
measurements from these global references back to the
processing hubs at Torrance and Moline. Since the hubs
receive data from more than 60 reference sites, the
corrections are robust; and the loss of data from one or
more sites would not affect the accuracy significantly.
Duplicate processing at both Torrance and Moline is used
so that an automatic switch of the data uploaded to the
communication satellites occurs if a failure is detected in
one of the hubs.
2.2 Hub processing software
As indicated above, the StarFire system provides a set of
corrections for each satellite that is good globally. The
corrections are in the form of a three-dimensional
correction to the satellite position and a correction to the
satellite clock. The algorithms used at the processing
hubs to compute the correction streams use the following
inputs:

Journal of Global Positioning Systems (2004)
Vol. 3, No. 1-2: 143-153
Figure 3: The StarFire N e t w ork of Reference Stations
a) dual frequency measurements, i.e. C/A code
pseudoranges, L1 carrier phase, P2 code pseudoranges
and L2 carrier phase, for all of the GPS satellites tracked
at the reference sites, which are sent to the hubs at 1Hz in
real time from all sites;
b) the broadcast ephemeris records from the reference
receivers, which are delivered in real time;
c) a configuration file defining the precise location
(±2cm) of each of the reference receiver antennas, as
determined from network solutions based on the IGS
worldwide control stations.
The dual-frequency measurements are used to form
smoothed, refraction corrected pseudoranges which are
free of ionosphere delay and, due to extended smoothing
with the carrier phase, virtually free of multipath. The
StarFire processing software used within the processing
hubs at Torrance and Moline is that developed by JPL
and licensed to NavCom. Orbit corrections for each
satellite are generated and transmitted each minute and
clock corrections for each satellite are generated and
transmitted every two seconds. The correction data is
sent via the land-lines to the uplink facility for broadcast
from the geostationary communication satellites.
The StarFire corrections are efficient in that only one set
of corrections per satellite is required. Competing
systems require a multiple set of corrections, which
requires computing a weighted correction at the user set.
This is costly in terms of communication bandwidth and
user computational requirements. In addition,
improvements to the StarFire correction generation can
be made without impacting the thousands of user sets
deployed worldwide.
2.3 StarFire user equipment
Several different implementations of the StarFire user
equipment are available. The most widely sold equipment
is the compact rugged unit with all elements internal to
the package. Three elements are contained in the
package. First, it contains a tri-band antenna, which
receives the L1 and L2 GPS frequencies together with the
L-band Inmarsat frequencies. The gain pattern of the
antenna yields a fairly constant gain even at low elevation
angles. This allows the corrections broadcast over the
Inmarsat channel to be received at high latitudes (low
elevation angle) without requiring extra signal strength

Hatch et al.: Recent Improvements to the StarFire DGPS Navigation Software 147
from the geostationary Inmarsat satellite. Second, it
contains an Inmarsat L-band receiver module to acquire,
decode and send the corrections received to the GPS
receiver. It is frequency agile and, under software control,
can track any frequency in the Inmarsat receive band.
Finally, the package contains a NCT 2000D GPS
receiver, designed and built by NavCom.
An alternate “black box” package contains only the
Inmarsat L-band receiver module and the NCT 2000D
GPS receiver. The antenna is packaged separately for
more flexibility, such as is required for aircraft
installations.
Finally, a new StarFire integrated package is nearing
completion. It consists of a tri-band anten na togeth er with
a new combined Inmarsat L-band module and GPS
receiver module. The new package will also contain an
optional inclinometer used in agricultural applications to
map the GPS antenna position to the ground, i.e. it
adjusts for the varying tilt of the agricultural implement
as it passes over rough ground.
2.3.1 The NCT 200D dual-frequency GPS engine
The NCT 2000D is a compact, high-performance, dual
frequency GPS engine aimed at OEM applications. The
receiver is mounted inside the lower housing and
interfaces to the digital board of the L-band receiver via
an RS232 serial port. The StarFire corrections are input
from the L-band receiver and 1, 5, or 10Hz PVT data is
output via the external interfaces (RS-232 and CAN Bus).
The NCT 2000D has ten full dual-frequency channels and
two WAAS channels. It produces GPS measurements of
the highest quality suitable for u se in the most demand ing
applications, including millimeter level static surveys.
The NCT 2000D includes a patented multipath reduction
technique built into the digital signal processin g ASICs of
the receiver. This greatly reduces the magnitude of
multipath distortions on both the CA code and P2 code
pseudorange measurements. When combined with
extended dual-frequency code-carrier smoothing,
multipath errors in the code pseudorange measurements
are virtually eliminated. It also includes a patented
technique used to achieve near optimal recovery of the P
code from the anti-spoofing Y-code, resulting in more
robust tracking of the P2/L2 signals. The compact size
(4” x 3”x 1”) of the NCT 2000D allows it to be readily
integrated into the StarFire package. Finally, a high
resolution 1pps output signal, synchronized to GPS time,
is provided by the NCT 2000D . This same signal is used
by the L-band communications receiver to calibrate its
local oscillator, which aids in the acquisition of the
StarFire correction signal. This technique has been
patented by NavCom.
The measurement processing of the NCT 2000D software
in the StarFire user equipment is somewhat unique. Dual-
frequency code and carrier-phase measurements are used
to form smoothed, refraction corrected, code
pseudoranges. But, unlike competing systems, a greater
reliance is put on the carrier-phase measurements and a
floating ambiguity estimate is made of the whole-cycle
ambiguities. All of the measurement data from all
satellites is used to make this ambiguity estimate as
accurate as possible. In addition, a constrained estimate
of the tropospheric refraction is made, using the data
from all the satellites. This constrained solution removes
some of the unmodeled tropospheric refraction effects.
The resulting PVT estimates are output at either 1, 5, or
10 Hz under software control.
2.4 StarFire positioning accuracy
Figure 3 shows typical position accuracy obtained by
using the global StarFire corrections for 24 hours at an
Australian site. The one-sigma accuracy per horizontal
axis rarely exceeds 10 cm. As expected, the accuracy is
not dependent upon geographical location. The accuracy
obtained by using the StarFire global corrections within a
StarFire receiver is unmatched by any other global
system. Furthermore, very few regional networks can
match these results.
2.5 Applications of the StarFire System
StarFire user equipment is now used in a large number of
agricultural applications. These include yield mapping,
field documentation, operator-assisted steering and
automatic steering. Automatic steering is probably the
most rapidly growing new application. However, it is also
used in a wide variety of other applications. These
include: (1) land survey and geographic information
systems, (2) construction equipment guidance and
control, (3) marine survey and resource exploration, (4)
hydrographic map ping and dr edging systems, ( 5) tr acking
of valuable cargo, (6) high precision airborne survey, and
(7) specialized military applications on land, at sea, and
in the air.
3 Recent improvements to the StarFire user software
A number of improvements to the user positioning
software inside the StarFire unit have been made and are
in the process of being verified and released. These
include: (1) improved mode switching logic to minimize
the loss of accuracy when it is necessary to change the
operating mode of the receiver; (2) use of the change in

148 Journal of Global Positioning Systems
carrier-phase measurements to implement a high-rate,
high-accuracy, and efficient “position change” process
which is used to update the position coordinates between
major epochs; (3) the implementation of a “receiver
autonomous integrity monitoring” (RAIM) process which
makes use of the high-accuracy change in the carrier-
phase to detect measurement errors; (4) a simplified
process for computing earth tides caused by the Sun and
the Moon; and (5) the addition of a “real-time kinematic”
RTK mode which can make use of the synergism
between the global RTG correction stream and the RTK
correction stream. Each of these five improvements are
described in more detail below.
3.1 Improved Mode Switching Logic
There are a large number of conditions under which the
navigation software must provide a position solution.
These include the availability of several different
correction streams made available from the various
government sponsored augmentation systems. In
addition, in some environments, signal blockage may
cause the L2 measurements to be lost, even while the L1
measurements are still retained. If too few measurements
are available or the vertical dilution of precision (VDOP)
is too large, it may be desirable to operate in an “altitude
hold” mode. A complicated hierarchy of modes results
from the interplay of all these factors. In the past the
transition between various modes retained no history
(knowledge of the position variance-covariance matrix)
of the prior mode. Failure to retain knowledge of the
position accuracy during the mode transition allowed
large position jumps during the transition, particularly
when the transition was between dual-frequency and
single-frequency modes while using the RTG correction
stream.
Melbourne, Australia, StarFire Monitor Receiver
24 Hour Positioning Resul ts
-3
-2
-1
0
1
2
3
0481216 20 24
GPS Time (seconds in week)
Position Error (meters)
0
6
12
18
24
30
36
DGPS Status and Number of SVs
De
Dn
Nsats
Qual
East NorthUp
Std. Dev. (m.)0.090.060.17
Figure 3 Sample RTG StarFire results in Australia
There is a significant “pull-in” time before the full ten-
centimeter accuracy of the StarFire RTG global DGPS
can be attained. This pull-in time comes from the need to
solve for a floating ambiguity to the refraction-corrected
carrier-phase measurements. Until that floating ambiguity
can be determined with the requisite accuracy, the
position solution will depend in large measure upon the
less accurate refraction-corrected code measurements. It
takes some significant geometry change (movement of
the GPS satellites) before these ambiguities can be
successfully resolved to an accuracy of a few centimeters.
With no accuracy history, if the L2 signals were lost for
even a few seconds, the mode would switch to a single-
frequency mode and a significant loss of accuracy would
result. Thus, when dual-frequency operation was
resumed, the initial poor accuracy would require a new
pull-in time before the full accuracy was again obtained.
In the new logic the change in the carrier-phase
measurements, even if only available on the L1 signals,
allows the propagation of the position accuracy to
degrade only slowly. Thus, if the outage of the L2

Hatch et al.: Recent Improvements to the StarFire DGPS Navigation Software 149
measurements is only brief, when the dual-frequency
measurements are resumed, the position accuracy will be
only and no new pull-in time will be required before full
accuracy is restored.
3.2 Propagation of Position Using the Change in the
Carrier-Phase Measurements
The change in the carrier-phase measurements can be
used as a measure of the change in position (and clock).
This allows a highly-efficient, high-accuracy update of
the position to be computed at a high rate [Hatch, et al.,
2004]. In the new StarFire navigation software, this
technique is used to compute the position at high rates,
e.g. 5 to 10 Hz. At the slower 1 Hz rate the normal least-
squares computation is performed. As part of that low-
rate computation, the gain matrix used during the high-
rate is computed once and applied successively at the
high-rate. An explanation of the fundamental process is
provided below. The above reference gives further details
on how to handle the loss of measurements from one or
more satellites during the interval between the low-rate
epochs. The addition of a measurement from a new
satellite can simply be delayed until the next low-rate
epoch.
The computation of the position during the low-rate
epoch (for a simplified least-squares solution) is derived
below. The fundamental measurement equation for a
specific satellite is given by:
η
+= hxz (1)
Where: x is the state correction vector (change in position
and clock) value to be computed; h is the measurement
sensitivity vector, which characterizes the effect of any
errors in the state vector upon the measurement;  is the
measurement noise; and z is the measurement
innovations, i.e. the difference between the measurement
and the expected value of the measurement given the
current estimate of the state vector (position and time).
The value of z also includes the StarFire corrections to
the measurement.
Equation (1), when expanded into matrix form to
represent the set of equations from all tracked satellites,
becomes:
nHxz += (2)
The least-squares solution to Equation (2), which
minimizes the effect of the noise vector, n, is given by:
zHHHx TT 1 )( − = (3)
where the superscript, T, represents the transpose, and the
superscript, -1, represen ts the inverse.
The matrix operations can be performed to give simpler
forms of Equation (3):
zAHx T
=
(4)
or
Bzx
=
(5)
where: A = (HTH)-1 and B = AHT.
The matrix B has four rows, corresponding to the three
position coordinates and the clock. It has as many
columns as there are satellite measurements available. It
is stored for subsequent use in the high-rate propagation
computation.
The high-rate computation uses the change in the carrier-
phase measurements to compute the change in position
(and clock) over the high-rate epoch intervals. Having
stored the B matrix used in Equation (5) above, the
change in carrier phase over the high-rate epoch can be
used to propagate the position forward in time with high
accuracy and with minimal computations. The high
accuracy is a result of the low noise in the carrier-phase
measurements. The first computation required is to
compute the innovations (pre-fix residuals), z for use in
Equation (5). The change in the measured carrier phase
(delta phase) for each satellite is a major component of
the innovations. Generally, only one correction to the
delta-phase measurements is required to make the
innovations accurate enough to maintain centimeter
accuracy over major epoch intervals of one second.
Specifically, one must subtract from the delta phase the
change in the radial distance to the satellite o ver the high-
rate epoch interval. The specific equation to compute the
innovations for each satellite is:
)()( 11 −−
−
−
−
=
iiiii
z
ρ
φ
ρ
φ
(6)
where  represents the phase measurement scaled by the
wavelength and  represents the range to the satellite.
The subscript i indicates the current epoch and i-1 the
prior epoch.
The difference between the current phase measurement
and the range to the satellite can be stored for use in the
subsequent epoch. The satellite position computation
should be optimized for this high-rate computation. There
are a number of methods described in the literature to
optimize this computation.
Most of the normal corr ections to the innovations that ar e
required at the low-rate major epo chs are not required for
the innovations at the high rate. This is because they
generally change by less than the centimeter level over
the one-second interval between the major epochs. This
generally includes: 1) the satellite clock error; (2) the
ionospheric and tropospheric refraction; and 3) the
corrections from StarFire (or any other correction

150 Journal of Global Positioning Systems
source). Of these factors, the largest may well be the
satellite clock errors. They can contribute an error which
can approach one centimeter over a one-second major
epoch interval. But it is quite easy to incorporate the
satellite clock correction if desired. It is simply the clock
frequency offset times the high-rate epoch interval.
Once the innovations are computed using Equation (6),
the values can be used in Equation (5), together with the
stored value of the B matrix, to give the high-rate
correction to the position and clock. This propagates the
position with the high accuracy of the carrier-phase
measurements, and the computational load is minimized.
Once the high-rate propagation of position has been
initialized, the low-rate computation is implemented as a
simple correction to that propagated position.
3.3 Receiver Autonomous Integrity Monitoring
(RAIM)
As indicated in the prior section, the position determined
in the StarFire solution results from the propagation of
the position using the change in the carrier-phase
measurements. The low rate computation is simply a
correction to that propagated position. Because the
measurements of the carrier-phase are so precise, they
open the possibility of a very effective means of detecting
and even correcting measurement errors. The technique
summarized below has been described in detail in Hatch
et al. [2003], along with some sample computations.
To detect an erroneous measurement one needs to
analyze the post-fix residuals. To the extent the solution
is accurate, the residuals become an estimate (the
negative) of the noise in Equation (2). The post-fix
residuals can be computed directly from the innovations
or pre-fix residuals. Given the correction to the state
vector, x, the post-fix residuals, r, are obtained by
rearranging Equation (2 ):
Hxzr −= (7)
But using equation (5) to replace the state update, x, in
equation (7) gives:
HBzzr −= (8)
This in turn can be simplified to:
Szr = (9)
Where: S = (I – HB).
The matrix, S, maps the pre-fix residuals into the post-fix
residuals. S is square and the number of rows and
columns are equal to the number of satellite
measurements.
With the high accuracy of the carrier-phase
measurements, i.e. the low noise in Equation (2) and the
small residuals in Equation (9), a measurement error can
generally be detected by computing the value of the RMS
residuals and comparing them to a threshold value. The
RMS residuals are given by:
n
Trr
= δ
(10)
Where n is the total number of measurements.
Assuming a single fault, which is by far the most
probable situation, the specific measurement at fault can
be determined by forming the correlation between the
residuals and each column (or row) of the S-matrix.
j
i
j
ii
j
sr
sr
∑
= ρ
(11)
In this equation j is the correlation coefficient
associated with the satellite j measurement; ri is the ith
element of the residual vector and j
i
sis the ith element of
the jth column of the S-matrix; r and
j
s are the
lengths of the two column vectors, i.e. the square root of
the sum of the squares of the elements.
Note that the two lengths can be obtained from simple
alternate equations:
nr δ = (12)
j
j
jss = (13)
Given that a fault has been detected by the size of the rms
residuals, the faulty satellite will be identified by the
correlation coefficient from Equation (11) with absolute
value closest to one. This test will fail to identify the
faulty measurement if there are only five measurements
in the total set. When only five measurements are
available, all of the correlation coefficients from equation
(13) will be very close to one or minus one. Only the
lengths of the columns (or rows) of the S-matrix will vary
when measurements to only five satellites are available.
When there are more than five measurements available,
the faulty satellite can be identified by the largest
correlation value; and the size of the error (i.e. the
number of cycle slips) can be computed from the ratio of
the residual vector length (Equation 12) to the length of
the associated column of the S-matrix (Equation 13).
j
j
j
s
n
e
δ
=
(14)

Hatch et al.: Recent Improvements to the StarFire DGPS Navigation Software 151
The sign of the error in Equation (14) is obtained by
using the associated sign of the correlation value. This
error in the measurement from the jth satellite can be
tested to see if it is very close to an exact integer. If it is, a
correction to the measurement can be made. The revised
residuals can be computed from the following equation:
jjesrr+=
′ (15)
where sj is the jth column of the S-Matrix.
The revised rms residuals computed from this new
residual vector should now pass the threshold test and
indicate that the fault has been removed.
A discussion of unusual situations, where the error
detection and removal described above might fail or
require special logic, is found in the more detailed paper
[Hatch et al. 2003].
3.4 Removing the effects of solar and lunar earth
tides
While the StarFire orbit and clock computations licensed
from JPL included adjustments for the earth tides caused
by the sun and the moon, no corresponding adjustment
was included in the initial StarFire navigation software
developed by NavCom. For almost all farming
applications the small cyclic v ariation in height over a 12
hour period was of little consequence or interest.
However, in other applications precise height location is
desired. That small but significant height variation caused
by the earth tides was confirmed by computing daily
values of the RMS height variation over a complete 24
hour period. It was found that this daily RMS height
variation was a strong function of the phase of the moon.
Figure 4 shows that when the sun and the moon are not
aligned the RMS height variation is generally between 10
and 15 centimeters. When the sun and moon are aligned,
either on the same side of the earth (new moon) or on
opposite sides of the earth (full moon), the RMS variation
is about twice as big. Because the plane of the moon’s
orbit is not aligned with the ecliptic (earth’s orbital
plane), the tides can be larger at one of the two
alignments than at the other.
Torrance, California
56
39
26
12
0
5
10
15
20
25
30
35
0 10203040506070
Sequential D ays
RMS Height Variation (cm)
Figure 4 RMS height variation over 60 days at Torrance, California
Having determined that the solid earth tides were
significant, a computationally efficient method of
removing them within the navigation software was
undertaken. The algorithms developed by Sinko [1995]
were selected, and four relatively minor modifications
were implemented to improve their computational
efficiency. The concept of the modifications was
relatively simple. First, the equations were updated to
use the initial epoch of 2000 rather than the 1900
epoch. Second, to cut down on the computational load,

152 Journal of Global Positioning Systems
the equations were separated into those requiring
frequent update (every few minutes) from those
requiring only daily updates. Third, at the general cost
of less than a centimeter in accuracy, it was found that
a spherical earth model could be used rather than a
flattened ellipsoid. This significantly simplified some
of the higher rate computations. Finally, the equations
were modified to avoid where possible the computation
of the specific angular values. Instead, the sine and
cosine of angular values were retained. This allowed
the subsequent computation of the sine and cosine of
sums (or differences) of angles to use the product rule
for sines and cosines rather than computing the sine
and cosine for the sum (or difference) directly. Using
this process a large number of trigonometric functions
and their inverses were avoided.
Testing the simplified Sinko model within the software
with external off-line computations of the earth tides
verified that the implementation was generally within
one centimeter of the more precise off-line
computations. The latest release of the StarFire
navigation software now incorporates this earth-tide
computation.
3.5 Extending the RTK performance
As one of many options, the StarFire navigation
software has for some time included a high-accuracy
RTK capability. This past year a significant
improvement was made to the RTK performance.
Specifically, the short-term accuracy performance of
the StarFire GDGPS can be used to augment the RTK
performance when the RTK corrections are lost for any
reason. This capability is of particu lar benefit in rolling
hills or other conditions in which the line of sight
between RTK reference receiver and the RTK
navigation receiver is often obstructed.
The StarFire performance, as illustrated in Figure 3,
looks pretty noisy. However, if one were to amplify the
horizontal scale by 144 to look at any fifteen-minute
segment, the performance would appear to be virtually
noise free but with a small very slowly changing bias.
The new “RTK Extend” feature embedded within the
navigation software takes advantage of this “low noise,
but biased” characteristic of the StarFire GDGPS
performance. Specifically, the offset between the RTK
performance and the StarFire performance is
continually computed when both the RTK and StarFire
navigation are enabled. Applying this offset to the
StarFire navigation when the RTK correction link is
lost allows the navigation to proceed with virtually no
loss in accuracy.
The process is a little more complicated than indicated
above only becau se of the normal pull-in time requ ired
of the StarFire navigation. To avoid the pull-in time on
the navigation receiver, the RTK solution is used to
“quick start” the StarFire navigation. The quick start
capability depends upon initializing the position to an
accurate absolute position with an associated small
valued variance-covariance matrix. Unfortunately, the
RTK navigation solution is not an absolute position
unless the RTK base position is an accurate absolute
position. This problem can be resolved by using a
StarFire receiver at the base station. Requiring that the
base station operate 15 to 30 minutes before the RTK
extend feature is enabled is generally not an onerous
requirement. This allows the base station sufficient
pull-in time to determine the absolute offset of the
initialized RTK base station. This offset is transmitted
along with the RTK correction stream to allow the
StarFire navigation to be initialized with the absolute
position, i.e. with the RTK solution offset by the
measured absolute error at th e base is used to initialise
the StarFire navigation within the user set.
4 Conclusion s
The StarFire Global DGPS was reviewed and its
performance illustrated. Recent improvements to the
navigation software were described. These included
five new features. The first was to avoid losing the
historical information of position and its associated
accuracy when switching between modes in the
receiver. This simple improvement provides a much
more accurate solution under constrained visibility
situations where switching between single-frequency
and dual-frequency operation is quite common.
The second improvement was the implementation of an
effective high-rate propagation of position using the
change in the carrier-phase measurements. The
accuracy of the carrier-phase measurements, combined
with the ability to use the same gain matrix generated
at the low-rate epochs, allows the technique to be both
very efficient and very accurate.
The accuracy of the carrier-phase measurements used
in the prior improvement allows those same
measurements to be used to implement a very simple
and effective RAIM and measurement correction
scheme. With five or more satellites, small errors or
carrier cycle slips can be detected. With six or more
satellites, carrier cycle slips of a single cycle can
normally be isolated to the specific satellite and
corrected.
The implementation of an earth tides algorithm has
improved the height accuracy significantly and
improved the horizontal position marginally. The
Sinko [1995] algorithm was simplified and
implemented within the navigation software.

Hatch et al.: Recent Improvements to the StarFire DGPS Navigation Software 153
Comparison with off-line computations of the earth
tides were generally at the centimeter level.
Finally, the synergistic characteristics of the StarFire
Global DGPS solution and the RTK solution were
exploited to give a “quick start” to th e StarFire so lution
and an accurate “RTK extend” to the RTK solution.
This capability allows the StarFire RTK solution to
continue without interruption for up to 15 minutes
when the RTK base station corrections are lost. This
capability is particularly useful for where the line-of-
site communications link is obstructed by rolling hills
or other obstacles.
Acknowledgements:
The developments described herein were largely
funded by and performed for the Ag Management
Solutions group of John Deere. The initial earth-tides
development was stimulated by feedback from C&C
Technologi es, Inc.
References
Hatch RR, Sharpe RT, and Yang Y (2003): A simple RAIM
and fault isolation scheme, Proceedings of the 16th Int.
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Hatch RR, Sharpe RT, and Yang Y (2004): An innovative
algorithm for carrier-phase navigation, Proceedings of
the 17th Int. Tech. Mtg. of the Satellite Division of the
U.S. Inst. of Navigation, Long Beach, California, 21-24
Sept.
Sinko J (1995): A compact earth tides algorithm for
WADGPS, Proceedings of 8th Int. Tech. Mtg. of the
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