Global Positioning System Reference
In-Depth Information
Algorithm 1
Satellite Selection for PML Refinement Approach
for all
pair of neighboring satellites
do
) for the pair
p
j
;
Calculate rank (
p
i
,
p
j
is co-planar with any previous selected pair and (
if
p
i
,
) of present pair is lower
than selected pair
then
Replace the previous co-planar pair with current pair
else
if
Number of selected pair
<
Required number of pairs
then
Add the current pair to the selected pairs
els
Replace the worst ranking selected pair with the current pair
end if
end if
end for
can be run on-demand only when satellite positions are either changed or after considerable
movement of the receiver. Given the small number of visible satellites in range, this will incur
negligible cost.
Finally, as the new PML method itself is an analytical approach, the order of computational
complexity is
O
(
1
)
once satellite selection has been completed.
Summarizing, PML approaches are improvement over basic trilateration in that it considers
noisy
measurement
conditions
in
its
formulation.
Thus,
this
new
strategy
performs
significantly better for real time GPS and tracking performance.
4. Conclusion
This chapter presented a detailed discussion on the analytical approaches for GPS positioning.
Trilateration is the basis for most analytical positioning approaches and hence this chapter
begins with fundamental discussion on trilateration. However, it performs poorly under
noisy conditions which is analyzed in detail from theoretical and simulated scenarios.
We
also showed how di
erence of two range measurements can result in better positioning
formulations. Subsequently, we present existing analytical approaches of Bancroft's method
and Kleusberg's method that uses least squares and vector algebra respectively for solution of
GPS equations. Later we present two newer approaches that are based on using better Locus
Of Position (LOP) for the receiver than customary spherical locus in presence of noise. The
first of these, called Paired Measurement Localization (PML) with single reference satellite
uses hyperboloid planar locus of positions. The solution of these non-linear hyperboloids are
found by linearizing with reference to a single satellite. The other PML approach obtains a
better LOP from ordinary planar LOPs using a LOP refinement technique. Both of the PML
based approaches have the advantage that they can utilize all the available satellites using
least squares solution.
ff
three LOPs are used for PML single reference or PML
LOP refinement respectively, the receiver position can be calculated by simple algebra. This
has the advantage of avoiding matrix inversion for least squares solution and particularly
suitable when the receiver has constraint computational support such as mobile embedded
GPS receivers. Alternatively, when su
If only four
/
cient computational resources are available and better
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