IEEE Geoscience and Remote Sensing Magazine - June 2020 - 97

of PolInSAR forest parameter inversion. There are many common temporal decorrelation processes, such as wind-induced
vegetation movement, vegetation growth, rain and snow
events, human activities, natural disasters, and so on. Therefore, it is very difficult to accurately model the decorrelation
caused by different changing events. To avoid the performance limitations caused by temporal decorrelation, singlepass InSAR mission scenarios have been suggested. China is
developing the next-generation spaceborne TwinSAR-L mission, which is designed for operating in single-pass interferometry and full-polarization mode.
Now, we analyze the impact of decorrelation sources on
the observed coherence. For our single-pass PolInSAR mission scenario, the impact of temporal decorrelation can be
ignored, that is, cu Temp = 1. Other nonvolume decorrelation
sources change only the interferometric correlation coefficient but not the interferometric phase. For simplicity, we
use one decorrelation coefficient, c SNR , to represent the total effect of all nonvolume decorrelation sources as
c SNR % c SNR $ c Quant $ c Amb $ c Coreg $ c Geo $ c Az.

(61)

According to (22) and (61), we can give the observed coherence affected by the decorrelation sources as
v , c SNR h = c SNR $ exp^iz 0 h
cu Vol ^w

v)
cu V + m(w
v) .
1 + m(w

(62)

Compared with the original forest RVoG scattering model,
the newly observed coherence in (62) is multiplied by a
decorrelation factor c SNR, which still represents a line on the
coherence disk. In Figure 10, we plot a variation diagram of
the coherence values under the impact of the decorrelation
sources; the decorrelation sources shift the blue coherence
points to red ones, which have unchanged phases and decreased amplitudes. Thus, both ground phase and volume
coherence have been changed due to the system errors,
which will certainly cause forest-height estimation error.
FOREST-HEIGHT ESTIMATION ERROR MODEL
In this section, we study the impact of PolInSAR system
errors on the performance of the coherence optimization
technique for forest-height mapping. Finally, we model the
relationship between the forest-height estimation error and
the PolInSAR system parameters. An analytic error model
was developed in [7]. The major conclusion is briefly presented here; technical details can be found in [7].
Cloude studied the effect of residual polarimetric calibration error on forest-height estimation using PolInSAR
and concluded that crosstalk brings no estimation error
for forest height if the coherence optimization technique
is used [120]. We found that this conclusion is valid only
under the condition of high SNR [7]. Thus, a triple-factor
analysis of crosstalk, imbalance, and noise of the PolInSAR
system should be conducted to understand the reverse requirements for the polarimetric system from the end application of PolInSAR forest-height mapping. The coherence
optimization method is assumed to be the default strategy
JUNE 2020

IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE

Im (γ )

O

Re (γ )

FIGURE 10. The impact of decorrelation errors on coherence values.

for forest parameter inversion when discussing a best-case
scenario because it can greatly reduce the estimation error
caused by polarimetric distortions. Considering both the
impact of polarimetric distortions and system noise, the
eigenmatrix K 1^Q, nv 1, nv 2 h in the coherence optimization
method becomes [7]
K 1^Q, nv 1, nv 2 h = Q $ T11·Q H + nv 1 $ nv H1 -1 $ Q $ Ω 12 $ Q H
$ Q $ T22 $ Q H + nv 2 $ nv 2H -1 $ Q $ Ω 12 $ Q H H . (63)
When the system faces serious polarimetric distortions, the
distortion matrix Q becomes ill-conditioned or even noninvertible. Then, even small noise perturbations in the SAR
image lead to incorrect inversion of the matrix T11 ^Q 1, nv 1 h,
as compared with the inversion of the matrix T11 ^I, nv 1 h .
Meanwhile, the presence of system noise leads to changed
optimum coherence values and, finally, causes forest-height
estimation error. Through eigenvalue analysis of the distortion matrix Q (d, f ), we establish the model relationship
between the height estimation error and the polarimetric
distortions as shown in (64) and (65). Then, we can discern
how polarization crosstalk and channel imbalance amplify
the estimation error caused by noise. Here, we directly give
the model relationship between the height estimation error
and polarization crosstalk as well as the amplitude imbalance as follows [7]:
1
1
1
1
Dh V (d, nv ) = 3 $ Th V (nv )·c
+
+
m
(1 + d)4 ^1 - d 2h2 (1 - d)4
1
(64)
.
$ Th V (nv )
(1 - d) 2
1
1
1
+
Th V ^| f | , nv h = 3 ·c 1 +
m $ Th V ^ nv h
|f | 2 |f | 4
1
.
$ Th V ^ nv h,
| f |2

(65)

where Th V ^nv h represents the estimation error caused by
noise alone. In general, the more serious the polarimetric
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IEEE Geoscience and Remote Sensing Magazine - June 2020

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