Aerospace and Electronic Systems Magazine March 2018 - 45

Chu et al.

Figure 5.

Ratio of the Bragg peak at sites A and B varies with time.

pensation is processed according to the characters of the ground
clutter and the directly arriving wave; i.e., the ground clutter is
shifted to zero frequency.

WIND DIRECTION INVERSION WITH AMBIGUITY
The wind direction with ambiguity can be obtained by (5) and (6),
and the parameter β may be determined according to the ratio r of
the experiment data. Figure 5 shows the ratio r of sites A and B
varying with time. We can see that most Bragg peak ratios are between −8 and +8 dB and exceed values of 8 dB only in a rare case.
The hyperbolic secant model [17] can cover the observed firstorder ratios of ±8 dB with β = 0.5, as shown in Figure 2, so the parameter β in (6) can be chosen to be equal to or greater than 0.5. We
find that the influence of choosing parameter β on the estimation of
wind direction is little when β is in the range of 0.5 to 3.0. In subsequent calculations, we select β = 0.5. According to (5) and (6),
the inversion results at sites A and B are shown in Figures 6a and
6b, respectively, versus time; the measurements of the anemometer
are given for comparison. Because of the ambiguity existing in (5),
the extracted results contain two possible wind direction values, as
shown in Figure 6. The results are smoothed using a 10-min average filter in time and a nine-cell (the selected cell and its neighboring eight cells) average filter in space. It is seen that the positive
sign values are closer to the measurements of anemometer, and the
results from site B agree with in situ data better than those from
site A. Because the system has a breakdown at 12:00-13:00, there
are no data in Figure 6a. For the positive sign value, the correlated
coefficient and root mean square error (RMSE) from site A are
0.46 and 34.4°, respectively. In addition, the correlated coefficient
and RMSE from site B are 0.12 and 16.8°, respectively. Although
these results are not as good as the HFSWR [11], considering the
wind speeds below 8 m/s during the experiment and 60% data in
the range of 4 to 6 m/s, the results are accepted. So the wind direction obtained from the HFHSSWR system is feasible.
MARCH 2018

Figure 6.

Comparison between wind directions estimated by radar without ambiguity elimination and those measured by a shipborne anemometer at (a)
site A and (b) site B.

WIND DIRECTION INVERSION WITHOUT AMBIGUITY
As mentioned earlier, the MB method is a simple and useful attempt to resolve the ambiguous wind direction for monostatic radar to eliminate the ambiguity with an assumption of spatial homogeneity on the three radar beams. However, the distribution of the
ionosphere varies with space, and the influence of ionosphere on
the radar backscatter echoes is not uniform. So the assumption of
wind direction homogeneity on the three radar beams is not satisfied easily, and a method like MB is not fit to the inversion of the
wind direction for the HFHSSWR. The ML method is presented
in [14] to eliminate direction ambiguity for single HFSWR. The
method aims to maximize the likelihood of the inversion cell and
the eight locations neighboring it , and then the wind direction of
the inversion cell will be calculated [18]. So this method will be
influenced slightly by the inhomogeneous space distribution of the
ionosphere. Meanwhile, the MB and ML methods are both applied
to calculate the wind directions, and the results show that the ML
method, rather than the MB method, is preferred for our experiment data. In the next section, we apply the MB and ML methods

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