Global Positioning System Reference
In-Depth Information
where
ˆ
A
is the geoid height computed with the polynomial or ANFIS
N
model
, and
A
is the
mean value of observations, and
j
is the number of observations (Sen and Srivastava, 1990).
Coefficient of determination indicates how closely the estimated values (
ˆ
A
) from an
approximation model corresponds to the actual data (
ℓ
), and takes values between 0 and 1
(or represented as percentage, and the closer the R
2
is to 1, the smaller the residuals and
hence the better the model fit).
µ
B1
µ
A1
w
1
f
1
=
p
1
x
+
q
1
y
+
r
1
wf
+
w f
X
Y
( )
fxy
,
=
11
2 2
ww
wf
+
1
2
f
2
=
p
2
x
+
q
2
y
+
r
2
µ
A2
=
+
w f
11
2 2
w
2
µ
B2
x
y
Y
X
(a)
w
1
(
x,y
)
μ
A1
(
x
)
w
Π
⊗
w
=
1
ww
x
1
+
1
2
μ
A2
(
x
)
f
1
(
x,y
)
wf
11
f
(
x,y
)
Σ
f
2
(
x,y
)
wf
μ
B1
(
y
)
22
w
Π
⊗
y
w
=
2
ww
2
+
1
2
μ
B2
(
y
)
w
2
(
x,y
)
Layer 4
Layer 5
Layer 1
Layer 2
Layer 3
(b)
Fig. 9. (a) type 3 fuzzy reasoning, (b) a simple two-input, two-rule and single-output ANFIS
structure (Jang, 1993)
3.1.3 Test results
In the results of the tests, repeated with the varying polynomial orders from first to sixth
order, a 5
th
and 4
th
order polynomial models (having 21 and 15 coefficients) were
determined as optimal for the Istanbul and Sakarya data, respectively. The significance tests
of the polynomial parameters revealed the final forms of the models. Evaluation of these
polynomials at the reference and test benchmarks, separately, in Istanbul and Sakarya
Search WWH ::
Custom Search