*3.2. Data Filtering*

In this study, after discarding all abnormal values of observations (marked with NaN and negative numbers) and using quality control (QC) flags, a filtering algorithm based on DDM images is proposed. CYGNSS DDM is composed of 11 Doppler rows and 17 delay columns. When the signal condition is poor, the DDMs obtained by GYGNSS will not have an obvious horseshoe shape [14]. Such DDMs are unable to represent the MSS of the reflected surface effectively, and therefore, cannot be used for sea surface wind speed retrieval. In order to analyze the shapes of DDMs more easily, all DDMs are normalized according to:

$$nDDM(\mathbf{r}, f) = \frac{DDM(\mathbf{r}, f)}{DDM\_{\text{max}}} \tag{20}$$

where *nDDM*(*τ*, *f*) represents the measured power of the reflected signal when the time delay and frequency shift are *τ* and *f* in the normalized DDM. *DDMmax* represents the maximum power in the original DDM. CYGNSS compresses the DDM from a 128 × 20 matrix to a 17 × 11 matrix [6]. The red solid box in Figure 6a indicates the selected area of the noise floor part where the signal is absent. All the data whose noise floor maximum powers exceed the threshold value of 0.4 are excluded. This step screens out most of the DDMs influenced by noise without involving much computation. Some remaining DDMs may still be influenced by noise, so it is necessary to verify whether a basic horseshoe-shaped emerges. In order to reduce computation, this paper proposes a parameter called *EdgeA*, i.e., the difference between the mean value of the Edge Box and the mean of the noise floor. The orange and red boxes in Figure 6a indicate the trailing edge part and the floor noise part of the DDMs, respectively. The mean value of the noise floor is derived from Equation (21) [30], and *EdgeA* is derived from Equation (22).

$$Noise\_{floor} = \frac{1}{N\_1} \sum\_{i=1}^{2} \sum\_{j=1}^{11} nDDM(\mathbf{r}\_{i\prime}, f\_j) \tag{21}$$

$$EdgeA = \frac{1}{N\_2} \sum\_{i=\tau\_{\text{max}}}^{2} \sum\_{j=1}^{11} nDDM\left(\tau\_{i\prime}f\_j\right) - Noise\_{floor} \tag{22}$$

where *N*<sup>1</sup> and *N*<sup>2</sup> are the number of all power values in the noise box and edge box. *τmax* is the column number when the power of nDDM is maximum. In this study, *EdgeA* must be greater than 0.1 to ensure that all DDMs have a basic horseshoe shape.

**Figure 6.** (**a**) DDM with a distinct horseshoe shape, (**b**) DDM without a distinct horseshoe shape.
