Data Processing for Positioning - A Software-Defined GPS and Galileo Receiver: A Single-Frequency Approach - page 123

Z

P

h

Q

ϕ

X , Y

N ϕ

(ϕ, λ, h ) ( X , Y , Z )

FIGURE 8.9. Conversion between and Cartesian .

UTC on January 6, 1980, but is not incremented by UTC leap seconds. According
to Table 8.7 there has been a total of 14 leap seconds since January 6, 1980, so
that in early 2006

GPST = UTC + 14 s .

GPS week numbers and seconds of week Along with GPST, from the very be-
ginning was introduced the GPS week numbers. Since January 6, 1980, any week
has been designated its own number. At the time of writing we have week number
1315. To identify a given epoch within the week, the concept of seconds of week
(SOW) is used. This number counts from midnight between Saturday and Sunday,
which is also the beginning of the GPS week.
Furthermore, for convenience the individual days of the week are numbered:
Sunday 0, Monday 1, Tuesday 2, Wednesday 3, Thursday 4, Friday 5, and Satur-
day 6.
Professional GPS softwares use the day of week for numerical reasons. SOW
may be as large as 7 604,800 s. In order to keep track of the mm

in a point position we have to know time at the level of 0.01 nanosecond. Using
seconds of week with 12 decimals is beyond the limits of most computers. So
either you may split the real number holding the seconds of week into an integer
part and a decimal part or you may compute time in terms of GPS week number,
day of week, and seconds of day.

× 24 × 60 × 60 =

8.7 Coordinate Transformations

The immediate result of a satellite positioning is a set of X -, Y -, Z -values, which
we most often want to convert to latitude , and height h , refer to

Figure 8.9. We start by introducing the relation between Cartesian

ϕ , longitude λ

( X , Y , Z ) co-