Global Positioning System Reference
In-Depth Information
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10
Beyond Trilateration: GPS Positioning Geometry
and Analytical Accuracy
Mohammed Ziaur Rahman
University of Malaya
Malaysia
1. Introduction
Trilateration
multilateration is the fundamental basis for most GPS positioning algorithms.
It begins by finding range estimates to known satellite positions which provides a spherical
Locus of Position (LOP) for the receiver. Ideally four such spherical LOPs can be solved
to precisely determine the receiver position. Thus, it is an analytical approach that finds
receiver position by solving required number of linear
/
quadratic equations. This method
can determine the receiver position precisely when the equations are perfectly formulated.
However, determining the exact range is nearly impossible in real-life due to many external
factors such as noise interference, signal fading, multi-path propagation, weather condition,
clock synchronization problem etc (Strang & Borre, 1997). Hence, trilateration fails to achieve
su
/
cient accuracy under real world conditions.
It is also argued that GPS algorithms are
not at all tri
/
multi-lateration rather they are di
ff
erence of measurement (time-di
ff
erence or
second order di
ee & Abel, 1994).
However, there are widely used useful range-based algorithms such as Bancroft (1985) method.
Therefore, trilateration is still predominantly associated with positioning (Bajaj et al., 2002).
ff
erence of two ranges) based hyperbolic formulations (Cha
ff
In this chapter, we first discuss about the analytical accuracy of trilateration based positioning
algorithms. Subsequently, we show how noise can impact positioning accuracy in real
world. In Section 3, we present existing analytical algorithms for GPS along with two new
analytical approaches using Paired Measurement Localization (PML) of (Rahman & Kleeman,
2009). PML approaches can cope up with practical improper range based equations and are
computationally e
cient for implementation by conventional and resource constraint GPS
receivers. Section 4 draws some conclusions for this chapter.
2. Trilateration: its problems and alternative approaches
As alluded before, analytical approaches of positioning are based on accurate distance
measurement from geo-stationary satellites.
Trilateration is the basis of these techniques
+
where the range measurements from
n
1 satellites are used for an
n
-dimensional position
estimation (Ca
ff
ery, 2000).
In the ideal scenario when we can measure the precise range estimates of the GPS receiver,
we can formulate a spherical locus of position for the receiver. The fundamental positioning
geometry using three satellites placed in a hypothetical 2-Dimensional space is shown in
Fig. 1(a).
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