The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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0.1s, and network RTK gets data as 1 second interval. Besides, 
data transmit in network RTK depends on wireless 
communication system, e.g. GPRS, and that is also quite 
complex influenced in city. All of these will affect the 
positioning and posing accuracy of mobile mapping compared 
to the usual DGPS mode, thus undermine the reliability of geo 
spatial data surveying. New method should be developed on 
how to do the positioning work with dynamic network RTK in 
city. 
2. PRINCIPLE 
Currently, most GPS receiver can provide the measurement data 
of Doppler frequency variation while recording the pseudo 
range data synchronously. Each GPS satellite’s 3D position and 
speed can be calculated in high accuracy with the given 
ephemeris data anytime. The significant meaning of Doppler 
measurement is that rover’s accurate dynamic state can be 
derived without the known of ambiguity of GPS range 
between satellite and receiver. Furthermore, the Doppler 
frequency variation between satellite and receiver is less 
influenced by the atmosphere compared to pseudo-range signal. 
No base station is needed to obtain the land receiver’s dynamic 
state, just as 3D speed in the accuracy of 0.1 m/s. Besides, the 
accuracy also can be improved to mm/s level while base station 
is used (Sun, 2004; He, 2002; Xiao, 2003). This has important 
meaning about improving the mobile platform track’s accuracy 
with static known point while network RTK positioning data for 
mobile mapping in weak conditions. Following is the concrete 
analysis of how to obtain GPS rover receiver’s 3D speed with 
Doppler measurement data. 
t is the time moment in GPS time system that receiver 
get signal, 
T. 
' is time consumed of signal from satellite to 
receiver, 
~ j 
Pi i 
satellite j, 
is the pseudo-range between receiver i and 
p. . 
ri : 
satellite j, 
is the spatial-range between receiver i and 
r/fj 
is equivalent range in the time offset of satellite 
clock to GPS time system, 
dt 
1 is equivalent range in the time offset of receiver 
clock to GPS time system, 
V 
1 is the equivalent range delayed in ionosphere, 
T j 
1 is the equivalent range delayed in troposphere, 
£ 
c is the light-range of measurement noise. 
Pi 
■ ■ U . T/ . 
Expanding'' and combining ' and ' into one, then get: 
p, +<*, -<*' +q +e c 
(3) 
According to the Doppler kinetic theory, there is: 
P = A-df 
(i) 
where df is the Doppler measurement, 
X is GPS carrying wave’s length and 
p is relative speed vector between satellite and 
receiver antenna (including errors). 
Then, after the satellite sub-speeds along with the global 
coordinate system axis is calculated with the given ephemeris 
data, the receiver antenna’s corresponding sub-speed can also 
be calculated with the Doppler data. Because there are three 
unknown speeds and time variations to receiver, four satellites 
at least are needed together to resolve the unknown variations. 
2.1 GPS dynamic speed calculation based on single 
receiver 
The basic GPS pseudo-range observing equation is: 
where 
(X Y Z) 
v ' ’ 1 ’ '' is receiver’s spatial position, 
(X J Y j Z J ) 
^ ’ ’ 'is satellite spatial position, 
=№ -Xj 2 HY-Tf +(Z, -Z>j 
A j . 
' is the equivalent spatial range of 
atmosphere delayed. 
Then, the basic receiver speed calculating equation of Doppler 
measurement can be derived as the differential coefficient on 
(X,-*'),(} r ,-Y J ),(Z-Z J ) 
as following: 
Pi 
= Vi m i n{ l] 
Xi 
V 
Yi 
j 
-[li mini] 
Y 
Zi 
j 
Z 
dti 
- 
,j . j 
-dt + A i+e. 
p 
(4) 
Pi Pi (0 + dtj(t) dt (t tI ) + // (t) + T/ (t) + € c (t) (2) where ^ 1 is a measurement of pseudo-range variation, 
is the receiver spatial 3D speed, 
where i is number of receiver, 
j is number of satellite,