Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 23

Foghorn 3

R3

A

Foghorn 1

Foghorn 2

R2

R1

Figure 2.3 Position ambiguity removal by additional measurement. ( After: [1].)

2.1.1.1 Common Clock Offset and Compensation
This development assumed that the vessel's clock was precisely synchronized with
the foghorn time base. However, this might not be the case. Let us presume that the
vessel's clock is advanced with respect to the foghorn time base by 1 second. That is,
the vessel's clock believes the minute mark is occurring 1 second earlier. The propa-
gation intervals measured by the mariner will be larger by 1 second due to the offset.
The timing offsets are the same for each measurement (i.e., the offsets are common)
because the same incorrect time base is being used for each measurement. The tim-
ing offset equates to a range error of 335m and is denoted as in Figure 2.4. The
separation of intersections C, D, and E from the true vessel position, A, is a function
of the vessel's clock offset. If the offset could be removed or compensated for, the
range circles would then intersect at point A.

2.1.1.2 Effect of Independent Measurement Errors on Position Certainty
If this hypothetical scenario were realized, the TOA measurements would not be
perfect due to errors from atmospheric effects, foghorn clock offset from the fog-
horn time base, and interfering sounds. Unlike the vessel's clock offset condition
cited earlier, these errors would be generally independent and not common to all
measurements. They would affect each measurement in a unique manner and result
in inaccurate distance computations. Figure 2.5 shows the effect of independent