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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
905 
(-x J ,r J ,z J ) „ 
dtr. 
is the satellite 3D speed, 
is the variation of receiver clock offset, 
dt : 
// = 
is the variation of GPS clock offset, 
. j 
is variation of atmosphere delay, 
X i -X j , Y-Y j , Z,-Z y 
— ,mj = ,nj 
Pi 
Pi 
Pi 
On the other side, satellite 3D speed can be obtained with the 
navigation data. Based on equation(4), if no considering on the 
variation of satellite clock offset, variation of atmosphere delay, 
there are four unknown parameters as 
(XX,z,) and du 
If GPS antenna can receive four or more satellite signals 
simultaneously, these parameters can be resolved. In the single 
receiver’s Doppler measurement, no base is needed, and 
because the error from satellite and atmosphere factors can be 
not considered, its speed accuracy is limited as 0.1 meter/s. The 
higher accuracy solution should turn to differential GPS 
2.2 GPS dynamic speed calculation based on differential 
GPS 
According to equation (4), GPS base station’s speed calculation 
can be described as: 
X0 
V 
. j 
Yo 
j 
Po =Ui m iK X \ 
-timin'] 
Y 
Zo 
Z 
d to 
- 
J ' (5) 
■ d t + Ao+£ 
p° 
Base station is always stationary and its 3D speed is zero, and 
variation of atmosphere delay can be regarded as the same in 
base and rover, so equation (4)-(5) can get the differential 
Doppler basic speed calculation equation as following: 
SPio+Sal 
. j 
Xi 
X 
j 
Yi 
Y 
= [// mj ni 1] 
. j 
Zi 
Z 
- 
d ti dto 
+ A*. < 6 > 
P 
Where 
. j . j j 
A Pio - Pi ~ Pq and 
Aa L =U! ~H m ! m i «/ -»ol 
Then if differential again in different satellites to the same 
position of rover, the unknown value of receiver clock offset 
dti-d to can a j so b e erase( i an( j the following equation can 
be derived: 
VAp n +Aa£,-V J -Sa\ o -V k =[//-/* m* -rrt t rt> -«*] 
. jk . j k 
where V A p i0 = A p iQ - A p i0 , 
j j r T 
V J = 
(7) 
+VAf 
j j j 
x , Y , Z 
In Doppler speed calculation equations above, the 
measurements are obtained based on GPS phase carrying-wave, 
which has quite high accuracy and noise is only 0.01 Hz. 
Totally, speed calculation based on differential Doppler would 
reach the accuracy of mm/s level. Besides, the common 
question of GPS ambiguity resolution does not exist in the 
speed calculation. 
2.3 Network RTK filtering by 3D kinetic state from 
Doppler or DGPS 
In fact, DGPS can provide 0.1s interval’s positioning data with 
good position accuracy, thus also reflect the mobile platform’s 
dynamic characteristic in time compared to the network RTK’s 
Is interval position data sampling. The following is the 3D 
speed calculation by DGPS sequential data. 
Zi =[(Z, -z,_,)-f 2 it\ + (Z, -Z/j-/1 7 JHt { +l 2 ) 
In equation (8), (Xi_i,Yj_j,Zi_j) and (X i+1 ,Y i+ i,Z i+1 ) are the nearest 
before and after points of (X,Y,Z), t! and t 2 are the time 
intervals. 
Positioning data from different GPS have the same time-tagged 
in the same spatial place of mobile mapping field work. Thus, 
the actual mobile platform characteristic (at least, more reliable 
and accurate description than the original network RTK 
reflected) such as instant 3D speed can be indexed from 
Doppler measurement or DGPS for corresponding network 
RTK sequential positioning data. Supposed the seed points in 
network RTK is correct by pre-check in the mobile route, the 
other points can be predicted by speed integrated gradually. 
Then check the whole network RTK data and filter the error 
points with certain 3D spatial distance thresholds, which are 
expressed as following equations: