Differential GPS - Understanding GPS: Principles and Applications - page 442

To account for tropospheric delays, the user equipment is required to apply a
tropospheric delay correction to each raw pseudorange measurement. The UNB3
algorithm presented in Section 7.2.4.2 is employed. After applying all specified cor-
rections, SBAS user equipment computes user position using a WLS algorithm.
In addition to application of the SBAS differential corrections, user equipment
for safety applications must also compute position error bounds, referred to as the
HPL or VPL in the local horizontal and vertical directions, respectively. These levels
represent the user position errors that will not be exceeded without a timely warning
with the associated probability levels and time to alerts listed in Table 8.3. The HPLs
and VPLs are continually compared to the applicable horizontal alert limit (HAL)
and vertical alert limit (VAL) for the current phase of flight, and a warning is issued
to the pilot if HPL > HAL or VPL > VAL pertaining to that operation. For instance,

for APV-I approaches, VAL 40m, and the time to alert is 10 seconds.

An SBAS system is designed so that the probability is less than 2

= 50m, HAL =

10 −7 per approach

×

that an aircraft conducting an APV-I approach computes VPL <

40m when the true vertical or horizontal position errors are greater than these levels
for longer than 10 seconds without a warning being issued.
The user equipment computes HPL and VPL using variances that are broadcast
in message types 2-6 for the SBAS fast and long-term corrections and in message type
26 for the SBAS ionospheric corrections. A set of complicated rules is also applied to
adjust these variances for latency, missed messages, and other factors [52]. Variances
for receiver noise, multipath, and residual tropospheric errors are computed based
upon the elevation angles of the visible satellites. The individual error variances are
summed to form overall residual pseudorange error variances for the visible satellite.
Finally, the geometry matrix and known weighting matrix for the WLS solution are
used to bound the standard deviation of horizontal and vertical position errors.
Under the assumption that all errors are Gaussian, multipliers for the horizontal and
vertical position error standard deviations are applied to determine HPL and VPL.
Although it is well known that the true residual errors are not Gaussian, the variances
in the broadcast message and the variances for receiver noise, multipath, and tropo-
spheric errors are inflated by design to represent Gaussian distributions that
overbound the true errors for the probabilities of interest (e.g., see [55]).

< 50m and HPL

SBAS GEOs
The current SBAS geostationary constellation consists of the five Inmarsat-3 satel-
lites, the European Space Agency (ESA) Artemis satellite, and the MTSAT-1R satel-
lite. The four primary Inmarsat-3 satellites are located at approximately the
following longitudes in a geostationary orbit: 178ºE for the POR, 64.5ºE for the
IOR, 55.5ºW for the AORW), and 15.5ºW for the AORE. The fifth Inmarsat-3 sat-
ellite was launched to location 25ºE as an in-orbit spare. The ESA Artemis satellite is
located at 21.5ºE, and the MTSAT-1R satellite is at 140ºE.
At present, the U.S. WAAS uses the Inmarsat-3 AORW and POR satellites with
coverage as shown in Figure 8.33. In the near future, AORW is anticipated to be
moved to 98ºW. Additionally, the FAA is leasing transponders on two GEOs that
will be launched in the near future. These include Telesat Canada's Anik F1R satel-
lite, which will be located at 107ºW and PanAmSat's Galaxy XV satellite to be
located at 133ºW (see Figure 8.34).