Integration of GPS with Other Sensors and Network Assistance - Understanding GPS: Principles and Applications - page 536

2
cp =

2 2 2

σ

4

σ

cos (

φ

) +

σ

pos el cp time _

~300m=1chip 1 ms = 1,023 chips

(common mode)

1,575 Hz / ppm
(common mode)

~1 Hz / s ~1 Hz / km ~2.3 Hz / mi/h

2
dopp =

2
dopp_time

2
dopp_pos

2
dopp_vel

2
dopp_oscl

+ + +

σ σ σ σ σ

Figure 9.41 Two-dimensional Doppler/code phase search space.

For each satellite, the number of Doppler search bins N dopp is dependent on the total
Doppler uncertainty (in hertz) for each satellite, and the coherent integration (PDI)
period in seconds, which is the same as the PDI period T discussed in Section 5.2.1.

σ

dopp

N = (9.41)

i

()

dopp

k PDI

i

The parameter k is based on the desired overlap of the Doppler search bins and
can generally range between 0.5 and 1. The computation of total Doppler uncer-
tainty

2

for each satellite is then dependent on the contributions of Doppler
uncertainty due to position uncertainty, time uncertainty, reference oscillator uncer-
tainty, and user motion (velocity) uncertainty. Thus, one can write a simple equation
for the total Doppler uncertainty per satellite as:

σ dopp i

2 2 2 2 2

σ = σ + σ + σ + σ (9.42)

dopp dopp _ time dopp _ pos dopp _ vel dop poscl _

i i i i i

The first term, the sensitivity of Doppler uncertainty to time uncertainty, can be
computed for each satellite [74], but as a general rule, it is no larger than 1 Hz per
second of time uncertainty. Likewise, the second term, the sensitivity of Doppler to
initial position error, is about 1 Hz/km worst case. In [74], equations are presented
for the precise computation of

2 for each individual satellite, which is gener-
ally much less than 1 Hz/km. The effects of user platform motion are accounted for
by the third term, which represents the Doppler error induced on the GPS signal due
to user motion. The term

σ dopp

_ pos i

2 is a maximum for low elevation angle satellites if
the user is heading directly at or away from the satellite, and it is very small for high
elevation angle satellites. Worst case,

σ dopp

_ vel i

2 contributes no more than 2.3 Hz/mph
of user motion and can be generally multiplied by the cosine of the elevation angle to
limit its effect.

σ dopp

_ vel i