Geoscience Reference
In-Depth Information
precision of this algorithm as compared with the measured values and the differ-
ential approximation method.
2.12.3 Method for Parametric Identi
cation
of Environmental Objects
Radiometers determine the brightness temperatures Z
ij
(i =1,
…
, M; j =1,
…
, n)
given by Z
ij
= T
j
+
ʾ
ij
, where M is the number of measurements, n is number of
radiometers, T
j
is the real value of the brightness temperature for wavelength
μ
j
and
ʾ
ij
is the noise with zero mean and dispersion
˃
j
. The problem is to determine the
correlation function T
j
= f
j
(X), where X ={x
1
,
., x
m
} are geophysical, ecological,
biogeochemical or other parameters. There are many algorithms for the de
…
nition of
the function f. As a general rule, the mean-square criterion is used for this purpose.
But such an approach has one defect: the impossibility of taking the dispersion
properties of the noise
ʾ
ij
} into consideration.
Let the function f be linear. Then we have the following system of equations for
parameters A
ij
:
ʕ
={
k
A
ij
k
X ¼ T
þ
E
ð
2
:
28
Þ
It is necessary to solve Eq. (
2.28
) such that its solution has minimum dispersion.
Such a solution is called the
solution.
The ith equation of system (
2.28
) is multiplied by the set of parameters c1i,
1i
,
˃—
…
, c
mi
. An additional condition is given:
X
n
c
ji
A
il
¼
d
jl
ð
2
:
29
Þ
i¼1
where
1
0
for
for
j ¼ l
j
d
jl
¼
ð
l
;
j ¼ 1
; ...;
m
Þ
ð
2
:
30
Þ
6
¼ l
Under the conditions (
2.29
) and (
2.30
) we have
x
1
¼
X
n
c
1i
T
i
ð
2
:
31
Þ
i¼1
From (
2.28
)to(
2.31
) we obtain:
Search WWH ::
Custom Search