Re: NEW GPS with the best sensitivity of antenna!!!

From: Sam Wormley (swormley1_at_mchsi.com)
Date: 02/05/05 

Date: Sat, 05 Feb 2005 23:34:11 GMT

Kravets Igor wrote:
> I have head that under tree cover after rain GPS doesn't work. Which GPS has
> the best sensitivity? :(
>
> After reading several reviews I came to conclusion that the best sensetivity
> of its antenna has Lowrance, than Magellan Sportrak Pro (C), than Garmin
> 60C, than Garmin 76C and finally Garmin eTrex....
>
> IS IT GOOD? Please help me... Which GPS has the best sensitivity?
>
> THANKS
>
>

More sensitivity might not be the answer because of wet tree cover
increased multipath...

See: GPS Evaluation: West Coast Test Site
      http://www.fs.fed.us/database/gps/mtdc/96712341/index.htm

      http://www.trimble.com:80/products/pd_gi.htm

My purpose in this posting is to raise the awareness of canopy and
it's resulting attenuation, multipath and obstruction on the performance
of GPS positioning, especially as it applies to trail mapping.

Most authors, including the ones cited below, categorize GPS ranging
errors into two broad categories, the signal source and propagation
path, and the receiver. But inherent in any accuracy estimation is also
the geometry of the satellites being used with respect to receiver
position, and any interference in the reception of those signals such
as attenuation, blockage, and RFI.

Moisture in canopy effects both attenuation and multipath. Because there
is not a convenient way to measure the effects of multipath, most folks
just ignor it, but it is probably the dominant error source under canopy.

Ref: http://www.oc.nps.navy.mil/~jclynch/gpsbtoc.html

"Global Positioning System: Theory and Applications", Volume I

B. Parkinson, J. Spilker Editors.
American Institute of Aeronautics and Astronautics, Washington, DC
1996, ISBN 1-56347-106-X

Chapter
-------
> 14. Multipath Effects 547 - 568 M. Braasch 9 Figs. 3 Refs.
> 15. Foliage Attenuation for Land Mobile Users 569 - 583
           J. Spilker 11 Figs. 14 Refs.

First paragraph of Chapter 15 of the reference above, "Foliage Attenuation
for Land Mobile Users", by J.J. Spilker Jr.:

"Land mobile users are expected to be one of the largest categories of
GPS users, and it is important to examine specific GPS propagation
issues for this environment. It has already been shown that the
optimum geometric dilution of precision (GDOP) is provided when several
of the GPS satellites are at low elevation angle near the horizon.
However, the land mobile user environment differs from that of aircraft
in flight or ships at sea in that the users driving along a road or
freeway [or hiking in the woods] is often subject to shadowing,
diffraction, ans scattering of the satellite signal by trees, utility
poles, buildings, or hills. These effects are accentuated by the need
for operation a low elevation angles for at least some of the GPS
satellites. In addition, the requirement for receiver simplicity, and
the need to track several satellites widely spaced in angle
simultaneously, generally dictates the use of an omni- directional or
hemispherical antenna. Thus, while receiving the direct line-of-sight
ray from the satellite, the user has little means to discriminate
against multipath signals scattered from ground reflections, tree limbs
and foliage, or other scattering elements. In addition, the direct ray
may itself be attenuated by tree foliage".

No matter what quality of L1 C/A receiver, an HDOP (B) that is twice
as great as HDOP (A) will result in increasing a probability error
circle (ellipse) by about a factor of two. If a certain specified
level of accuracy is required for a particular purpose, careful
attention must be paid to the potential obstacles to achieving that
level of accuracy.

The following is adapted from Chapter 11, "GPS Error Analysis", pages
478-483, Global Positioning System: Theory and Applications by Bradford
W. Parkinson, James J. Spilker Jr. Eds.

A. Six Classes of Errors

Ranging errors are grouped into the six following classes:
1) Ephemeris data--Errors in the transmitted location of the
      satellite
2) Satellite clock--Errors in the transmitted clock, including SA
3) Ionosphere--Errors in the corrections of pseudorange caused by
      ionospheric effects
4) Troposphere--Errors in the corrections of pseudorange caused by
      tropospheric effects
5) Multipath--Errors caused by reflected signals entering the receiver
      antenna
6) Receiver--Errors in the receiver's measurement of range caused by
      thermal noise, software accuracy, and interchannel biases

Each class is briefly discussed in the following sections.
Representative values for these errors are used to construct an error
table in a later section of this chapter. A more complete discussion of
individual error sources can be found in succeeding chapters.

B. Ephemeris Errors

Ephemeris errors result when the GPS message does not transmit the
correct satellite location. It is typical that the radial component of
this error is the smallest: the tangential and cross-track errors may be
larger by an order of magnitude. Fortunately, the larger components do
not affect ranging accuracy to the same degree. This can be seen in the
fundamental error Eq. (12). The AW represents each satellite position
error, but when dot-multiplied by the unit satellite direction vector
(in the A matrix), only the projection of satellite positioning error
along the line of sight creates a ranging error.

Because satellite errors reflect a position prediction, they tend to
grow with time from the last control station upload. It is possible that
a portion of the deliberate SA error is added to the ephemeris as well.
However, the predictions are long smooth arcs, so all errors in the
ephemeris tend to be slowly changing with time. Therefore, their utility
in SA is quite limited.

As reported during phase one, (Bowen, 1986) in 1984,[5] for predictions
of up to 24 hours, the rms ranging error attributable to ephemeris was
2.1 m. These errors were closely correlated with the satellite clock, as
we would expect. Note that these errors are the same for both the P- and
C/A-codes (see Chapter 16 of this volume for a more detailed discussion
of ephemeris and clock errors).

C. Satellite Clock Errors

Fundamental to GPS is the one-way ranging that ultimately depends on
satellite clock predictability. These satellite clock errors affect both
the C/A- and P-code users in the same way. The error effect can be seen
in the fundamental error Eq. (11) as delta-B. This effect is also
independent of satellite direction, which is important when the
technique of differential corrections is used. All differential stations
and users measure an identical satellite clock error.

A major source of apparent clock error is SA, which is varied so as to
be unpredictable over periods longer than about 10 minutes. The rms
value of SA is typically about 20 m in ranging, but this can change
after providing appropriate notice, depending on need. The U.S. Air
Force has guaranteed that the twodimensional rms (2 DRMS) positioning
error (approximately 90th percentile) will be kept to less than 100 m.
This is now a matter of U.S. federal policy and can only be changed by
order of the President of the United States. [Note that SA was removed
May 2, 2000 @4:05 UTC.]

More interesting is the underlying accuracy of the system with SA off.
The ability to predict clock behavior is a measure of clock quality. GPS
uses atomic clocks (cesium and rubidium oscillators),' which have
stabilities of about I part in 10E13 over a day. If a clock can be
predicted to this accuracy, its error in a day (~10E5 s) will be about
10E-8 s or about 3.5 m. The experience reported in 1984 was 4.1 m for
24-hour predictions. Because the standard deviations of these errors
were reported to grow quadratically with time, an average error of 1-2 m
for 12-hour updates is the normal expectation.

D. Ionosphere Errors

Because of free electrons in the ionosphere, GPS signals do not travel
at the vacuum speed of light as they transit this region. The modulation
on the signal is delayed in proportion to the number of free electrons
encountered and is also (to first order) proportional to the inverse of
the carrier frequency squared (1/f squared). The phase of the radio
frequency carrier is advanced by the same amount because of these
effects. Carrier-smoothed receivers should take this into account in the
design of their filters. The ionosphere is usually reasonably
well-behaved and stable in the temperate zones; near the equator or
magnetic poles it can fluctuate considerably. An in-depth discussion of
this can be found in Chapter 12, this volume.

All users will correct the raw pseudoranges for the ionospheric delay.
The simplest correction will use an internal diurnal model of these
delays. The parameters can be updated using information in the GPS
communications message (although the accuracy of these updates is not
yet clearly established). The effective accuracy of this modeling is
about 2-5 m in ranging for users in the temperate Zones.

A second technique for dual-frequency P-code receivers is to measure the
signal at both frequencies and directly solve for the delay. The
difference between L1 and L2 arrival times allows a direct algebraic
solution. This dual-frequency technique should provide 1-2 m of ranging
accuracy, due to the ionosphere, for a well-calibrated receiver.

A third technique is to rely on a near real-time update. An example
would be the proposed Wide Area Differential GPS system (WADGPS). This
should also produce corrections with accuracies of 1-2 m or better in
the temperate zones of the world.

E. Troposphere Errors

Another deviation from the vacuum speed of light is caused by the
troposphere. Variations in temperature, pressure, and humidity all
contribute to variations in the speed of light of radio waves. Both the
code and carrier will have the same delays. This is described further in
the chapter devoted to these effects, Chapter 13 of this volume. For
most users and circumstances, a simple model should be effectively
accurate to about 1 m or better.

F. Multipath Errors

Multipath is the error caused by reflected signals entering the front
end of the receiver and masking the real correlation peak. These effects
tend to be more pronounced in a static receiver near large reflecting
surfaces, where 15 m in or more in ranging error can be found in extreme
cases. Monitor or reference stations require special care in siting to
avoid unacceptable errors. The first line of defense is to use the
combination of antenna cut-off angle and antenna location that minimizes
this problem. A second approach is to use so-called "narrow correlator,
receivers which tend to minimize the impact of multipath on range
tracking accuracies. With proper siting and antenna selection, the net
impact to a moving user should be less than 1 m under most
circumstances. See Chapter 14 of this volume for further discussion of
multipath errors.

G. Receiver Errors

Initially most GPS commercial receivers were sequential in that one or
two tracking channels shared the burden of locking on to four or more
satellites. With modem chip technology, it is common to place three or
more tracking channels on a single inexpensive chip. As the size and
cost have shrunk, techniques have improved and five- or six-channel
receivers are common. Most modem receivers use reconstructed carrier to
aid the code tracking loops. This produces a precision of better than
0.3 m. Interchannel bias is minimized with digital sampling and
all-digital designs.

The limited precision of the receiver software also contributed to
errors in earlier designs, which relied on 8-bit microprocessors. With
ranges to the satellites of over 20 million meters, a precision of
1:10E10 or better was required. Modem microprocessors now provide such
precision along with the co-requisite calculation speeds. The net result
is that the receiver should contribute less than 0.5 ms error in bias
and less than 0.2 m in noise. Further information on receiver errors is
available in Chapters 3, 7, 8, and 9 of this volume.

V. Standard Error Tables

These overview discussions on error sources and magnitudes, as well as
the effects of satellite geometry, can be summarized with the following
error tables. Each error is described as a bias (persistence of minutes
or more) and a random effect that is, in effect "white" noise and
exhibits little correlation between samples of range. The total error in
each category is found as the root sum square (rss) of these two
components.

Each component of error is assumed to be statistically uncorrelated with
all others, so they are combined as an rss as well. The receiver is
assumed to filter the measurements so that about 16 samples are
effectively averaged reducing the random content by the square root of
16. Of course, averaging cannot improve the bias-type errors.

Finally, each satellite error is assumed to be uncorrelated and of zero
mean, so the application of HDOP and VDOP are justified as the last
step. Despite these limiting assumptions, the resulting error model has
proved to be surprisingly valid. Of course, the assumptions on
uncorrelated errors is almost always violated to some degree. For
example, if the estimate of zenith ionosphere delay is in error, a
proportional error is induced in all measurements through the obliquity
calculation. Clearly, such an error would be correlated. These and other
correlations have not caused serious problems in the use of this model.

A. Error Table without SA: Normal Operation for C/A Code

Table 2 assumes that SA is not operating. Consequently, the residual
satellite clock error, at 2.1 m, is not the dominant error; in fact, the
largest error is expected to be the mismodeling of the ionosphere, at
4.0 m. Thus, the worldwide civilian positioning error for GPS is
potentially about 10 m (horizontal), as shown in Table 2.

B. Error Table with SA

A second example shows the impact of SA on these errors. Because the
deliberately mismodeled clock so dominates the ranging error, all other
effects could be safely ignored in the error budget. The results of
Table 3 have been repeatedly corroborated by actual measurements. Note
that SA is listed as a bias because it cannot be averaged to zero with a
1 s (or less) filter. Selective availability is expected to be zero
mean, but only when averaged over many hours or perhaps days. Of course,
such averaging is not practical for a dynamic user who only sees the
satellite for a portion of the orbit. If differential corrections are
used, they will eliminate the SA error entirely (if corrections are
passed at a sufficiently high data rate) as discussed in Chapter 21,
this volume.

The 41-m horizontal error is a one-sigma result; under the existing
agreement between the U.S. Department of Transportation (DOT) and the
U.S. Department of Defense (DOD), the 2 DRMS horizontal error is to be
less than 100 m. The impact on the vertical error is probably greater,
because the VDOP value usually exceeds the HDOP value.

   Table 2 Standard error model - L1 C/A (no SA)

                                   One-sigma error, m
   Error source Bias Random Total DGPS
   ------------------------------------------------------------
   Ephemeris data 2.1 0.0 2.1 0.0
   Satellite clock 2.0 0.7 2.1 0.0
   Ionosphere 4.0 0.5 4.0 0.4
   Troposphere 0.5 0.5 0.7 0.2
   Multipath 1.0 1.0 1.4 1.4
   Receiver measurement 0.5 0.2 0.5 0.5
   ------------------------------------------------------------
   User equivalent range
     error (UERE), rms* 5.1 1.4 5.3 1.6
   Filtered UERE, rms 5.1 0.4 5.1 1.5
   ------------------------------------------------------------

   Vertical one-sigma errors--VDOP= 2.5 12.8 3.9
   Horizontal one-sigma errors--HDOP= 2.0 10.2 3.1

*This is the statistical ranging error (one-sigma) that represents the
total of all contributing sources. The dominant error is usually the
ionosphere. A horizontal error of 10 m (one-sigma) is the expected
performance for the temperate latitudes using civilian (C/A-code)
receivers.

   Table 3 Standard error model - L1 C/A (with SA)

                                   One-sigma error, m
   Error source Bias Random Total DGPS
   ------------------------------------------------------------
   Ephemeris data 2.1 0.0 2.1 0.0
   Satellite clock (dither) 20.0 0.7 20.0 0.0
   Ionosphere 4.0 0.5 4.0 0.4
   Troposphere 0.5 0.5 0.7 0.2
   Multipath 1.0 1.0 1.4 1.4
   Receiver measurement 0.5 0.2 0.5 0.5
   ------------------------------------------------------------
   User equivalent range
     error (UERE), rms* 20.5 1.4 20.6 1.6
   Filtered UERE, rms 20.5 0.4 20.5 1.5
   ------------------------------------------------------------

   Vertical one-sigma errors--VDOP= 2.5 51.4 3.9
   Horizontal one-sigma errors--HDOP= 2.0 41.1 3.1

C. Error Table for Precise Positioning Service (PPS Dual-Frequency P/Y
Code)

The errors for dual-frequency PN code are similar to those above except
that SA errors are eliminated because the authorized user can decode the
magnitude as part of a classified message. An expected horizontal error
is less than 10 m. The ionosphere error is reduced to 1-m bias and about
0.7 m of noise by the dual-frequency measurement. The dominant sources
are the satellite ephemeris and clocks. This is illustrated in Table 4.

   Table 4 Precise error model, dual-frequency, P(Y) code

                                  One-sigma error, m
   Error source Bias Random Total DGPS
   ------------------------------------------------------------
   Ephemeris data 2.1 0.0 2.1 0.0
   Satellite clock 2.0 0.7 2.1 0.0
   Ionosphere 1.0 0.5 1.2 0.1
   Troposphere 0.5 0.5 0.7 0.1
   Multipath 1.0 1.0 1.4 1.4
   Receiver measurement 0.5 0.2 0.5 0.5
   -----------------------------------------------------------
   User equivalent range
     error (UERE), rms* 3.3 1.5 3.6 1.5
   Filtered UERE, rms 3.3 0.4 3.3 1.4
   -----------------------------------------------------------

   Vertical one-sigma errors--VDOP= 2.5 8.3 3.7
   Horizontal one-sigma errors--HDOP= 2.0 6.6 3.0

VI. Summary

Excluding the deliberate degradation of SA, the dominant error source
for satellite ranging with single frequency receivers is usually the
ionosphere. It is on the order of four meters, depending on the quality
of the single-frequency model. For dual-frequency (P/Y-code) receivers
(which eliminate SA) the Standard Error Model of Table I has one
principal change (in addition to the elimination of the SA error). The
ionospheric error is reduced from four meters to about one meter.

Greater variations in the errors are due to geometry, which are
quantified as dilutions of precision or DOPs. While geometric dilutions
of 2.5 are about the worldwide average, this factor can range up to 10
or more with poor satellite geometry. Reduced satellite availability
(and consequent increases in DOP) could be caused by satellite outages,
local teff ain masking, or user antenna tilting (for example due to
aircraft banking). Typical normal accuracy (one-sigma) for welldesigned
civil equipment under nominal operating conditions with SA off should be
about 10 m horizontal and 13 m vertical.

References

Martin, E. H., "GPS User Equipment Error Models," Global Positioning
System Papers, Vol. I, Institute of Navigation, Washington, DC, 1980,
pp. 109-118.

Milliken, R. J., and Zollar, C. J., "Principle of Operation of NAVSTAR
and System Characteristics," Global Positioning System Papers, Vol. 1,
Institute of Navigation, Washington, DC, 1980, pp. 3-14.

Copps, E. M., "An Aspect of the Role of the Clock in a GPS Receiver,"
Global Positioning System Papers, Vol. 111, Institute of Navigation,
Washington, DC, 1986.

Massat, P., and Rudnick, K., "Geometric Formulas for Dilution of
Precision Calculations," Navigation, Vol. 37, No. 4, 1990-1991.

Bowen, R., et al., "GPS Control System Accuracies," Global Positioning
System Paapers, Vol. III, Institute of Navigation, Washington, DC, 1986,
pp. 241-247.

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