Global Positioning System Reference
In-Depth Information
FIGURE 8.12
Shift the input data relative to the three codes.
8.12 FINE TIME RESOLUTION THROUGH CURVE FITTING
The discussion in the previous section is based on an ideal correlation of the
C/A code. The correlation output is triangle shaped with values varying from
0 to 1,023. The actual correlation of the C/A signal does not start from zero
and the shape is not a triangle. In an actual receiver, since the bandwidth is
limited, the correlation does not have a sharp peak as shown in Figure 8.10, but
is a smooth one as shown in Figure 8.13. The top of the correlation output is
rounded due to the limited bandwidth. To take this shape of correlation function
into consideration, a quadratic equation can be used to model it. In order to
perform the curve fitting, the correlation data must contain the highest value and
the two values on either side of it. If this situation does not occur, a wrong
result can be drawn. In order to guarantee that this situation occurs, usually more
than three correlation values are needed. In general, five correlation peaks with
two early and two late codes should be sufficient. The two early and late codes
are obtained by shifting the prompt code by
±
d
and
±
2
d
. The highest
y
value
and its two adjacent neighbors are used in the following equation. The quadratic
equation to model the correlation peak can be written as
ax
2
y
=
+
bx
+
c
(
8
.
46
)
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