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Title
Proceedings International Workshop on Mobile Mapping Technology
Author
Li, Rongxing

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