Step 5: The fitness
f
(
x
i
) of the
i
th
particle is compared
with the fitness values
f
(
pbest
) and
f
(
gbest
) of the individual
and the global best values, respectively.
f
(
pbest
), the individual best value
pbest
current position
x
i
of the particle. If
f
(
x
i
)
the global best value
gbest
is replaced by
x
i
of the particle.
Step 6: According to Step 4, the velocity and position of
the particle are updated and the fitness value is calculated
until the number of iterations reaches the predetermined
maximum value. The algorithm terminates the operation and
outputs the global optimal solution of the current position
gbest
.
Step 7: The global optimal position vector
gbest
obtained
by the
MPSO
algorithm is mapped to the
BP
neural network.
Then, the weight and threshold of the neural network are up-
dated. Meanwhile, the optimized
BP
neural network is learned
and trained using the measurements and remote sensing data
to retrieve soil moisture.
Results
In this study, the remote sensing data include the horizontal
transmit and horizontal receive (
HH
) and vertical transmit
and vertical receive (
VV
) polarization data of
RADARSAT-2
SAR
image on 29 March 2014 and the green, red, and near-
infrared band data closely related to vegetation information
of Landsat-8 optical image on 24 March 2014. Meanwhile,
the square of correlation coefficient (
R
2
) and
RMSE
are used in
the analysis and estimation (Willmott 1982).
R
and
RMSE
are
calculated as follows:
Cov x X
Var x Var X
i
i
i
i
( , )
| | | |
,
(12)
RMSE
N
x X
i
i
i
N
=
1
2
1
−
(
)
=
∑
,
(13)
where,
x
i
is the estimated value,
X
i
is the field measurements,
and
N
is the number of data. Cov(
x
i
,
X
i
) represents covariance
of
x
i
and
X
i
. Var|
x
i
| is variance of
x
i
and Var|
X
i
| is variance
of
X
i
.
Evaluation of Retrieved Accuracies on
Different Inversion Methods
In this study, three inversion algorithms are selected and com-
pared with the
MPSO
-
BP
method for soil moisture retrieval,
which include multivariate nonlinear regression, support
vector machine (
SVM
) algorithm, and
BP
neural network. The
retrieval process of soil moisture and parameter settings of the
four methods are shown as follows:
Multivariate nonlinear regression: The solution using mul-
tivariate nonlinear regression is to transform it into a linear
multivariate regression. The relationship between the total
backscatter coefficient and the surface soil moisture is deter-
mined by least squares method. The quadratic polynomial is
Figure 3. Flowchart of surface soil moisture retrieval using
MPSO-BP
.
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
November 2019
793
