phase measurements separately and update the 
state vector independently. This approach not 
only decreases the dimension of R matrix when 
inverting, but also is convenient for statistical 
quality control. It can be proven that the 
estimated values and corresponding covariance 
matrix obtained by this approach is equivalent to 
that computed by the conventional kalman filter 
which process pseudorange and carrier phase 
data simultaneously. 
2.2 Integer ambiguity search algorithm with 
the optimized Cholesky decomposition 
The real value ambiguities DN= 
(dn 0 , dfi ] , • • • , citi n ) T and its covariance matrix 
q v (sub-matrix of P kJ( ) can be obtained from 
double difference pseudorange/carrier phase 
Kalman filter. Searching the best ambiguity can 
be done by finding the minimum of following 
criterion: 
n* = (DiV - DN) T Qk (DN -DN) = min (J2) 
DN e Z" 
Where, Z n is the n-dimensional space of 
integer numbers, n is the number of integer 
ambiguities. 
Search range of each ambiguity can be defined 
based on q n . Considering a possibly large 
number of combinations (For example, For 6 
integer ambiguities, each with a searching range 
of ±10 cycles, the total number of combinations 
will equal to 8576611), it is necessary to 
rejecting the false combinations as quick as 
possible in search procedure Euler and Landau 
(1992) proposed the optimized Cholesky 
algorithm base on the symmetric positive- 
definite property of matrix Q . Table 1 shows 
a comparison of the search time for one epoch 
on a 586-60 computer between using 
optimized Cholesky decomposition and no 
decomposition It can be seen from the table 
that the improvement of searching speed is 
very significant if using the optimized 
Cholesky decomposition. 
2.3 Validation of ambiguity resolution 
In order to test whether the integer ambiguity 
combination with minimum Q A . is the true 
solution for the integer ambiguities, it is 
necessary to perform following test procedures : 
• Ratio test (Hatch & Euler, 1994) 
• OVT test (Wei Ming & Schwarz, 1995) 
Ratio test is the test of ratio between the next 
minimum Q k (denoted as Q k . ) and the 
minimum Q A . It is come from static 
positioning and used to test the reliability of the 
ambiguity resolution. The optimal solution is 
accepted if Cl k /Q A is larger than a priori given 
number Ratio test is given by: 
Q 
-Q 
> F 
(13) 
Where F is a priori given number or a Fisher 
percentile for a certain confidence level In 
principle, using the ratio test, one can decide 
whether the optimal solution is the true solution 
for integer ambiguity. Practically, it is still risky 
to apply this test to an individual epoch because 
of the existence of various systematic errors A 
reliable validation procedure must apply the 
ratio test to a certain period (for example 10 
seconds) If all epochs during this period pass 
the above test with the same optimal solution, 
the optimal solution can be considered as the 
solution of the true integer ambiguities. This 
validation procedure is called overall validation 
test (OVT). 
2.4 Data procession of kinematic positioning 
after integer ambiguities fixed 
After integer ambiguities fixed by OTF , state 
parameters dn 0 , dn,”\ dn n can be eliminated 
from dynamic equation (1) and integer 
7B-5-3