Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos
Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos
Antti Lehtinen Doppler Positioning with GPS - Matematiikan laitos
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The matrix G(x), that is the derivative matrix calculated at the true position<br />
and drift point x, is called <strong>Doppler</strong> geometry matrix. Sometimes the <strong>Doppler</strong><br />
geometry matrix G(x) will be written <strong>with</strong>out the argument as G.<br />
4.6 Problem Specific Iterative Methods<br />
It would appear that the first algorithm for <strong>GPS</strong> <strong>Doppler</strong> positioning was invented<br />
by Jonathan Hill. In his paper [Hill], presented in ION <strong>GPS</strong> 2001, he discusses the<br />
feasibility of <strong>Doppler</strong> positioning. He describes an iterative algorithm that uses<br />
least squares technique after an algebraic manipulation of the set of equations<br />
4.16.<br />
The Hill algorithm does not use the derivative matrix G at all. This has the<br />
advantage of somewhat lighter computation. On the other hand, the derivative<br />
matrix could be beneficial when analysingthe positioningerror, as will be shown<br />
in the followingchapter. There is no documented testingof the convergence<br />
properties of the Hill algorithm.<br />
Probably other iterative algorithms suitable for <strong>Doppler</strong> positioning can be found.<br />
Decidingwhich algorithm to use requires extensive numerical testingand depends<br />
on user’s needs. At least computational efficiency, reliability, convergence properties<br />
and error estimation have to be considered when choosingthe algorithm.<br />
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