9
Differential GPS
9.1 INTRODUCTION
Differential GPS (DGPS) is a technique for reducing the error in GPS-derived
positions by using additional data from a reference GPS receiver at a known
position. The most common form of DGPS involves determining the combined
effects of navigation message ephemeris and satellite clock errors [including the
effects of selective availability (SA), if active] at a reference station and transmitting
pseudorange corrections, in real time, to a user's receiver. The receiver applies the
corrections in the process of determining its position [63]. This results in the
following:
 Some error sources are canceled completely:
(a) selective availability and
(b) satellite ephemeris and clock errors.
 With other error sources, cancelation degrades with distance:
(a) ionospheric delay error and
(b) tropospheric delay error.
 Still other error sources are not canceled at all:
(a) multipath errors and
(b) receiver errors.
265
Global Positioning Systems, Inertial Navigation, and Integration,
Mohinder S. Grewal, Lawrence R. Weill, Angus P. Andrews
Copyright # 2001 John Wiley & Sons, Inc.
Print ISBN 0-471-35032-X Electronic ISBN 0-471-20071-9
9.2 LADGPS, WADGPS, AND WAAS
9.2.1 Description of Local-Area DGPS (LADGPS)
LADGPS is a form of DGPS in which the user's GPS receiver receives real-time
pseudorange and, possibly, carrier phase corrections from a reference receiver
generally located within the line of sight. The corrections account for the combined
effects of navigation message ephemeris and satellite clock errors (including the

nonnavigation users.
WAAS provides improved en route navigation and PA capability to WAAS
certi®ed avionics. The safety critical WAAS system consists of the equipment and
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DIFFERENTIAL GPS
software necessary to augment the Department of Defense (DoD) provided GPS
SPS. WAAS provides a signal in space (SIS) to WAAS certi®ed aircraft avionics
using the WAAS for any FAA-approved phase of ¯ight. The SIS provides two
services: (1) data on GPS and GEO satellites and (2) a ranging capability.
The GPS satellite data is received and processed at widely dispersed wide-area
reference Stations (WRSs), which are strategically located to provide coverage over
the required WAAS service volume. Data is forwarded to wide-area master stations
(WMSs), which process the data from multiple WRSs to determine the integrity,
differential corrections, and residual errors for each monitored satellite and for each
predetermined ionospheric grid point (IGP). Multiple WMSs are provided to
eliminate single-point failures within the WAAS network. Information from all
WMSs is sent to each GEO uplink subsystem (GUS) and uplinked along with the
GEO navigation message to GEO satellites. The GEO satellites downlink this data to
the users via the GPS SPS L-band ranging signal (L
1
) frequency with GPS-type
modulation. Each ground-based station=subsystem communicates via a terrestrial
communications subsystem (TCS). See Fig. 9.1.
In addition to providing augmented GPS data to the users, WAAS veri®es its own
integrity and takes any necessary action to ensure that the system meets the WAAS
performance requirements. WAAS also has a system operation and maintenance
function that provides status and related maintenance information to FAA airway
facilities (AFs) NAS personnel.
WAAS has a functional veri®cation system (FVS) that is used for early
development test and evaluation (DT&E), re®nement of contractor site installation

performance data for the local C&V subsystems.
4. Process Input Data (PID) selects and monitors data from the wide-area
reference equipment (WREs). Data that passes PID screening is repackaged
for other C&V capabilities. PID performs clock and L
1
GPS Precision
Positioning Service L-band ranging signal (L
2
) receiver bias calculations,
cycle slip detection, outlier detection, data smoothing, and data monitoring.
In addition, PID calculates and applies the windup correction to the carrier
phase, accumulates data to estimate the pseudorange to carrier phase bias,
and computes the ionosphere corrected carrier phase and measured slant
delay.
5. Satellite Orbit Determination (SOD) determines the GPS and GEO satellite
orbits and clock offsets, WRE receiver clock offsets, and troposphere delay.
6. Ionosphere Correction Computation (ICC) determines the L
1
IGP vertical
delays, grid ionosphere vertical error (GIVE) for all de®ned IGPs, and L
1
±L
2
interfrequency bias for each satellite transmitter and each WRS receiver.
7. Satellite Correction Processing (SCP) determines the fast and long-term
satellite corrections, including the user differential range error (UDRE). It
determines the WNTand the GEO and WNTclock steering commands [99].
8. Independent Data Veri®cation (IDV) compares satellite corrections, GEO
navigation data, and ionospheric corrections from two independent computa-
tional sources, and if the comparisons are within limits, one source is selected

includes a set of WRS and at least one WMS, which enable monitoring the integrity
status of GPS and the determination of wide-area DGPS correction data. Each WRS
has three dual frequency GPS receivers to provide parallel sets of measurement data.
The presence of parallel data streams enables Independent Data Veri®cation and
Validation (IDV&V) to be employed to ensure the integrity of GPS data and their
corrections in the WAAS messages broadcast via one or more GEOs. With IDV&V
active, the WMS applies the corrections computed from one stream to the data from
the other stream to provide veri®cation of the corrections prior to transmission. The
primary data stream is also used for the validation phase to check the active (already
broadcast) correction and to monitor their SIS performance. These algorithms are
continually being improved. The latest versions can be found in references [48, 96,
97, 137, 99] and [98, pp. 397±425].
9.3 GEO UPLINK SUBSYSTEM (GUS)
Corrections from the WMS are sent to the ground uplink subsystem (GUS) for
uplink to the GEO. The GUS receives integrity and correction data and WAAS
speci®c messages from the WMS, adds forward error correction (FEC) encoding,
and transmits the messages via a C-band uplink to the GEO satellites for broadcast
to the WAAS user. The GUS signal uses the GPS standard positioning service
9.3 GEO UPLINK SUBSYSTEM(GUS)
269
waveform (C=A-code, BPSK modulation); however, the data rate is higher (250
bps). The 250 bps of data are encoded with a one-half rate convolutional code,
resulting in a 500-symbols=s transmission rate.
Each symbol is modulated by the C=A-code, a 1:023 Â 10
6
-chips=s pseudo
random sequence to provide a spread-spectrum signal. This signal is then BPSK
modulated by the GUS onto an IF carrier, upconverted to a C-band frequency, and
uplinked to the GEO. It is the C=A-code modulation that provides the ranging
capability if its phase is properly controlled.

sign
and the received
pseudorange from the L
1
downlink as measured by the WAAS GPS Receiver PR
geo

and adjusted for estimated ionospheric delay PR
iono
. The equation for the range
measurement is then
z 
1
2
PR
geo
À PR
iono
PR
sign
ÀT
Cup
À T
L1dwnS
;
where T
Cup
 C-band uplink delay m
T
L1dwnS

9.3.2 In-Orbit Tests
Two separate series of in-orbit tests (IOTs) were conducted, one at the COMSAT
GPS Earth Station (GES) in Santa Paula, California with Paci®c Ocean Region
(POR) and Atlantic Ocean Region-West (AOR-W) I-3 satellites and the other at the
COMSAT GES in Clarksburg, Maryland, using AOR-W. The IOTs were conducted
Iono delay
rate
estimator
PR
iono
PR
iono
Range, rate
acceleration
estimator
Code control
loop
Frequency
control
loop
GUS signal
generator
Iono delay
estimate
Iono delay
estimate
Range & rat
e
estimates
WAAS GPS

Fig. 9.2 GUS control loop block diagram.
9.3 GEO UPLINK SUBSYSTEM(GUS)
271
to validate a prototype version of the GUS control loop algorithm. Data was
collected to verify the ionospheric estimation and code±carrier coherence perfor-
mance capability of the control loop and the short±term carrier frequency stability of
the I-3 satellites with a prototype ground station. The test results were also used to
validate the GUS control loop simulation.
Figure 9.3 illustrates the IOTsetup at a high level. Prototype ground station
hardware and software were used to assess algorithm performance at two different
ground stations with two different Inmarsat-3 satellites.
9.3.3 Ionospheric Delay Estimation
The GUS control loop estimates the ionospheric delay contribution of the GEO C-
band uplink to maintain code±carrier coherence of the broadcast SIS. Figures 9.4±
9.6 provide the delay estimates for POR using the Santa Paula GES and AOR-W
using both the Santa Paula and Clarksburg GES. Each plot shows the estimated
ionospheric delay (output of the two-state Kalman ®lter) versus the calculated delay
using the L
1
and C pseudorange data from a WAAS GPS receiver. Calculated delay
is noisier and varying about 1 m=s, whereas the estimated delay by the Kalman ®lter
is right in middle of the measured delay, as shown in Figures 9.4±9.6. Delay
measurements were calculated using the equation
Ionospheric delay 
P
RL1
À P
RC
À tau L
1

Frequency
reference
WAAS phase 1 equipment
Processor/
controller
• prototype
algorithm
software
WAAS GPS
receiver
FTS
atomic
clock
IF
Fig. 9.3 IOT test GUS setup.
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DIFFERENTIAL GPS
where P
RL1
 L
1
pseudorange m
P
RC
 C pseudorange m
tau L
1
 L
1
downlink delay m

f
code
1:023 MHz
À
f
carrier
1575:42 MHz








< 5Â 10
À11
Fig. 9.6 Measured and estimated ionospheric delay, Clarksburg.
TABLE 9.1 Observed RMS WAAS Ionospheric Correc-
tion Errors
In-Orbit Test RMS Error (m)
Santa Paula GES, Oct. 10, 1997, POR 0.20
Santa Paula GES, Dec. 1, 1997, AOR-W 0.45
Clarksburg GES, Mar. 20, 1998, AOR-W 0.34
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DIFFERENTIAL GPS