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RNAV Training Manual - Keilir

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How does GPS work?<br />

9. Illustration of the GPS navigation calculation<br />

Stage 2: The accurate fix<br />

Two dimensional illustration of the GPS navigation calculation<br />

Determining pseudorange from 3 satellites results in<br />

3 equations with 3 unknowns: the x,y position of the<br />

receiver and t, the local clock bias<br />

Satellite position known from<br />

Navigation Message ephemeris data<br />

Pseudoranges g calculated from<br />

PRN correlation time shift<br />

Clock bias unknown,<br />

thus receiver position<br />

unknown<br />

The navigation processor solves these equations to<br />

determine a clock bias which gives the best intersect<br />

between the three bias-adjusted true range arcs<br />

Pseudorange arc<br />

True range arc<br />

Best fit local clock bias<br />

(all three black arrows represent<br />

the same clock bias)<br />

Best fit position p<br />

solution<br />

The actual method used is analogous to this; 4 satellites provide 4 range spheres spheres, and thus<br />

4 equations to solve for the unknown 3D x,y,z position of the receiver and its clock bias<br />

48

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