Analog Devices AN-540 Application Notes

AN-540

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APPLICATION NOTE

Understanding Global Positioning System Receiver Specifications

Dilution of Precision

Dilution Of Precision (DOP) is a measure of the contribu­tion of the relative geometry of the user and the satel­lites to the error in the location/navigation data
generated, making use of the satellites. GPS receivers
choose the combination of satellites to be used for posi­tion computation based on their geometric location with
respect to the user. The lesser the DOP resulting from a
particular combination of satellites, the better the accu­racy that can be achieved. When the receiver is tracking
more than four satellites, it computes the DOP associ­ated with each possible combination of four satellites
and chooses the combination with the least DOP for use
in computation of the user’s position.

The DOP is inversely proportional to the volume of the
tetrahedron formed with the user and the four satellites
at the five corners. Generally a combination of satellites
where, in each of the satellites there is a different azi­muth angle with respect to the user and as much spread
apart as possible from each other, results in a very good
DOP.

The effect of DOP can be resolved into HDOP, VDOP,
PDOP and TDOP.

HDOP is the contribution of the relative
(Horizontal Dilution geometry of the satellite con-
Of Precision) stellation and the user’s posi-

tion to the computed horizontal
position coordinates, that is, the
2D position.

VDOP is the contribution of the relative
(Vertical Dilution geometry of the satellite con-
Of Precision) stellation and the user’s position

to the computed height above
sea level, that is, the altitude.

TDOP is the contribution of the relative
(Time Dilution geometry of the satellite constel-
Of Precision) lation and the user’s position to

the computed time.

PDOP is the contribution of the relative
(Position Dilution geometry of the satellite constel-
Of Precision) lation and the user’s position to

the computed in 3D position
coordinates, that is, the 2D
position as well as the altitude.

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PDOP

= HDOP2 + VDOP

GDOP is the contribution of the relative
(Geometric Dilution geometry of the satellite constel-
Of Precision) lation and the user’s position

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GDOP

= PDOP2 + TDOP

Number of Channels

To compute the user’s position, speed, heading and
time, the GPS Receiver needs a minimum of four paral­lel correlation channels. GPS receivers have evolved
to incorporate six, eight or twelve channels in their
architectures.

The following factors influence the necessity/effective­ness of the number of channels in a receiver:

Satellite Visibility

Studies show that most of the time, at most places, eight
to ten satellites will be visible above the horizon (above
zero degrees of elevation angle). Above 10 degrees of
elevation, not more than eight satellites are visible. Above
20 degrees, six or fewer satellites are usually visible.

When installed on a ship, a GPS receiver is likely to
acquire/track signals from satellites at very low eleva­tion angles (nearing zero degrees), because in marine
applications, the sky is very open with little to obstruct
the antenna’s view.

In contrast, a GPS installed in an automobile does not
usually enjoy such a view of the sky. Signals from satel­lites below elevation angles of 10 degrees are very hard

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to the computed position coordi­nates and time.

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AN-540

to track, and even more difficult to acquire, due to build­ings, trees, etc. In city areas and in thickly wooded ter­rain, this problem becomes worse and the visibility
mask is more than 20 degrees.

Geometrical Dilution of Precision

The relative geometry of the satellites, and the user,
greatly influence the accuracy obtainable in the user’s
position computed from GPS satellites. The accuracy
obtainable is directly proportional to the volume of
the tetrahedron formed by the user and the four satel­lites chosen for position computation. This is called
Geometric Dilution of Precision. The receivers achieve
better accuracy in computed position by choosing the
right combination of satellites from among the visible
satellites.

With more channels, and when visibility is good, the re­ceiver has a better choice of satellite combinations. In
this respect, a higher number of channels is desirable.
But again, more channels than the number of visible sat­ellites do not help.

Dynamic Loss of Satellite Signals

In terrain where the antenna’s view of the sky is
dynamically obstructed and cleared frequently, more
channels improves the percentage of time for which
GPS-computed position data is generated by the re­ceiver. Here again, an increase in the number of chan­nels helps to a point when the number of channels
becomes equal to the number of visible satellites above
visibility mask angle.

Time-to-First-Fix

When the receiver is powered ON/initialized, it relies on
the initial estimates of position and time as well as the
age of the almanac data to compute the satellite visibil­ity data. With more channels, the receiver’s time to first
fix will improve. This is even more true when the re­ceiver is switched ON and left to itself to find the posi­tion, without an estimate data. In the case of GPS
receivers incorporating hardware correlators, increas­ing the number of channels considerably improves the
time-to-first-fix. However, in the case of Accord/ADI so­lution, where a soft correlator approach is employed
and FFT techniques are used for acquisition of satellite
signals, initial estimates of data are of less importance
than in the case of receivers using hardware correlators.
Since the time taken by our correlator to scan the entire
visible sky for a satellite signal is much less than the
time taken by other receivers, eight parallel channels
are sufficient to give time-to-first-fix in a time of better
than two minutes in Autonomous Cold Start.

Computational Assets

Every extra correlation channel imposes additional
computational load on the Navigation Processor in the
receiver, therefore, more channels than the number of
visible satellites are a disadvantage.

Ephemeris Collection

Availability of Ephemeris Data from a visible satellite
qualifies the satellite to be considered by the receiver for
use in its position computation. The receiver is likely to
provide GPS-computed position data for a better per­centage of time when it has collected ephemeris data
from most/all visible satellites. This is especially true
when the user’s vehicle is moving in obstructed terrain.
More channels help in this regard too, but again only to
a point where they are not more than the number of vis­ible satellites above the mask angle of elevation. From
all of the above considerations, eight parallel channels
is the optimum number.

FFT Techniques

FFT—Fast Fourier Transform—converts the time do­main samples of a signal to frequency domain. This
technique is used in GPS signal processing to improve
satellite signal acquisition time and hence Time-to-First­Fix (TTFF).

The background for using FFT technique in GPS receiver
is explained below:

GPS satellites continually transmit unique pseudoran­dom (PN) codes, phase modulated on an L-band carrier
at 1575.42 MHz, to users all over the world. These PN
codes available for civilian users are known as C/A
(Coarse Acquisition) codes. The C/A codes provide
single peak correlation properties and low cross correla­tion properties.

As the GPS satellite signal travels in space from the sat­ellite to the user equipment, there is a time delay due to
transit. This transit time is a measure of the range be­tween satellite and user equipment. Four such range
measurements to four satellites are required in the com­putation of user’s position.

The transit time is manifested as phase change in the
received PN code, which is measured using correlation
technique. These measurements are performed on the
signals received from all visible satellites.

To make range measurements more complicated, con­tinuous motion of GPS satellites and the user equipment
bring about a shift in the frequency of received signal
due to Doppler effect. Thus, the signal processing sec­tion of GPS receiver will have to perform a search for
received C/A code in both time domain (phase) and fre­quency domain (Doppler).

One method is to perform a “Cell-by-Cell” search. This
approach involves generating local C/A codes to per­form correlation in time domain with received C/A codes
from all visible satellites. The process is repeated by
changing frequency of local code in small steps.

If the search domains—both in time and frequency—are
unknown, the acquisition process will take a very long

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