**A PROPOSED GPS METHOD WITH
MULTI-ANTENNAE AND SINGLE RECEIVER FOR THE IMPROVEMENT OF BASELINE HEIGHT COMPONENT**

**It is well known that GPS (ellipsoidal) height determination is weaker than that
of horizontal coordinates. The weakness of GPS height determination can explained by the
following facts: i).a high degree of correlation exists between the vertical coordinate
and the clock parameters, as well as with the tropospheric delay parameters; ii) GPS
satellites are only visible above the local horizon.**

**With
the standard GPS field operation, clock parameters may be explicitly estimated in a GPS
least squares adjustment with between-receiver single difference observations or they may
be implicitly taken into account with a double difference observations processing scheme.
The standard field operation consists of two or more receivers operating simultaneously
without physical links between them. The proposed GPS method consists of two or more
antennae connected to the same receiver for use in small monitoring networks (e.g., dam
deformation monitoring) with baselines a few kilometres in length. In this scenario, the
between-antenna single difference observations do not contain receiver clock errors, but
careful calibration of the relative signal delay throughout the hardware (especially
antenna cables) has to be performed. Because these single difference observations are free
of clock parameters, more geometrical strength remains to determine the baseline
components.**

**This
paper is a theoretical study to demonstrate the feasibility of the proposed method
and its usefulness to improve baseline height determination. In this study, the following
topics are addressed. First, the observation equations are reviewed along with a
discussion about error modelling with emphasis on intercable bias calibration. Simulation
results for ambiguities-fixed solutions are presented and analysed for equatorial,
mid-latitude and polar sites. For the proposed method, the impact of the propagation of
intercable bias into station coordinates is studied. The propagation of systematic
tropospheric errors and random measurement errors into GPS station coordinates for the
proposed method is compared to standard data processing. The next paragraphs summarize the
results of this study.**

**To
determine height component to the mm-level, intercable biases must be calibrated at the
same level. With the proposed GPS method, zero baseline tests (1 antenna, 2 cables and 1
receiver) are well suited to calibrate intercable biases. The change of cable length due
to temperature variations can be taken into account with the knowledge of the thermal
coefficient of delay of the cables and with the measurements of temperature at different
points along the cable routes. For the proposed method, fiber optic cables would be
preferred to coaxial cables because they have lower thermal coefficients and lower
attenuation, they are unaffected by electromagnetic interference and they have excellent
stability properties.**

**The
tropospheric delay error is the main error source affecting baseline height components for
small networks. For the standard method, the tropospheric zenith delay error is mainly
magnified in the height component by a factor ranging between 2.6 and 6.5 (for elevation
mask angles of 20° and 10° and for different latitude sites). For the proposed method,
the magnification factor ranges between -1.9 to -4.6. If relative tropospheric zenith
delay are suspected to remain after data modelling, a relative tropospheric zenith delay
parameter must be estimated. This parameter will absorb the tropospheric error, but this
has the consequence to amplify the propagation of measurement noise (random error) into
the height component.**

**For
standard data processing (without a tropospheric delay parameter), the height standard
deviation is 2.3 to 2.7 times larger than the standard deviation of the horizontal
coordinates, for equatorial sites and 2.6 to 3.0 times larger for mid-latitude sites. The
ratio is 4.1 to 5.7, for polar sites. Moreover, for mid-latitude sites the standard
deviation of the north component is 1.4 times larger than the standard deviation of
the east component.**

**The
height standard deviation varies quite significantly for different parameter combinations.
If a tropospheric parameter is estimated with the standard data processing the height
standard deviation becomes 2.4 to 3.7 times larger, for equatorial and mid-latitude
sites and 3.0 to 5.5 times larger for polar sites. For the proposed method (without a
tropospheric delay parameter) the height standard deviation is smaller (with respect to
standard method without a tropospheric delay parameter) by a factor 2.7 to 3.6 for
equatorial sites, 2.5 to 3.3 for mid-latitude sites and 3.1 to 5.1 for polar sites.
Finally, even if a tropospheric parameter is estimated together with the proposed method,
the height standard deviation is still 2 times smaller than the one associated to
standard data processing (without a tropospheric delay parameter), for all sites and
elevation mask angles. In other words, for the proposed method, the height standard
deviations are comparable to those of the horizontal components, even if a tropospheric
parameter is solved for (exception of polar sites).**

**It
is shown that the proposed field operation and its associated data processing
significantly improve GPS height determinations compared to standard GPS data processing
schemes. The proposed field procedure is more cumbersome (long physical link between
antennae and receiver) and requires careful relative cable calibration. However, for
special precise applications (e.g., small networks with permanently installed cables)
additional efforts can be justified. The benefit is the substantial improvement of GPS
height determination. It is hoped that this work will stimulate further, hardware
oriented, research along the same lines.**