## 3 Method
### Construction of the New MRMDL Model
If the number of channels is to be changed, an additional \(1\times 1\) convolutional is added to convert the input into the required form before the summation operation. In addition, the DDM dimension of L1b is only \(17\times 11\), and  
Figure 1: Schematic diagram of non-nested function and nested function; (**a**) Schematic diagram of non-nested functions; (**b**) Schematic diagram of the nested functions. pooling layers would prevent the convolutional layers from maintaining sufficient depth. This would result in the loss of a large amount of valuable information, so the pooling layer is discarded. Finally, because the 17 \(\times\) 11 DDM data structure is relatively simple, the original number of channels is too large to increase the computation of the model, so the number of channels should be compressed. Table 2 shows the structure of ResNet before and after the modification. (2) The structure of the new MRMDL model  
A new MRMDL model is schematically structured in Figure 3. It is observed that the new MRMDL model has two input lines. In the first input line, based on the MResNet architecture, features are extracted from the combination of Raw DDM and BRCS DDM \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Layer Name**} & \multirow{2}{*}{**ResNet**} & **ResNet Output Size** & **MResNet** & **MResNet** \\  & & & **Output Size** & **Output Size** \\ \hline Conv1 & \(7\times 7,64\) & \(112\times 112\) & \(3\times 3,16\) & \(15\times 9\) \\ \hline \multirow{3}{*}{Conv2} & \(\begin{bmatrix}3\times 3\text{ max pool}\\ \left[\begin{array}{c}1\times 1,64\\ 3\times 3,64\\ 1\times 1,256\end{array}\right]\times 3\\ \end{bmatrix}\) & \(56\times 56\) & \(\begin{bmatrix}1\times 1,16\\ 3\times 3,16\\ 1\times 1,16\end{bmatrix}\times 3\\ \end{bmatrix}\) & \(13\times 7\) \\ \hline \multirow{3}{*}{Conv3} & \(\begin{bmatrix}1\times 1,128\\ 3\times 3,128\\ 1\times 1,512\end{bmatrix}\times 4\\ \end{bmatrix}\) & \(28\times 28\) & \(\begin{bmatrix}1\times 1,8\\ 3\times 3,8\\ 1\times 1,8\end{bmatrix}\times 3\\ \end{bmatrix}\) & \(11\times 5\) \\ \hline \multirow{3}{*}{Conv4} & \(\begin{bmatrix}1\times 1,256\\ 3\times 3,256\\ 1\times 1,1024\end{bmatrix}\times 6\\ \end{bmatrix}\) & \(14\times 14\) & \(\begin{bmatrix}1\times 1,4\\ 3\times 3,4\\ 1\times 1,4\end{bmatrix}\times 3\\ \end{bmatrix}\) & \(9\times 3\) \\ \hline \multirow{3}{*}{Conv5} & \(\begin{bmatrix}1\times 1,512\\ 3\times 3,512\\ 1\times 1,2048\end{bmatrix}\times 3\\ \end{bmatrix}\) & \(7\times 7\) & \(\begin{bmatrix}1\times 1,4\\ 3\times 3,4\\ 1\times 1,4\end{bmatrix}\times 3\\ \end{bmatrix}\) & \(7\times 1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: ResNet structure and MResNet network structure. Figure 2: Schematic diagram of conventional convolution block and residual block. by several residual blocks with 3 \(\times\) 3 convolution kernels. After the feature extraction process, the two-dimensional DDM data are transformed into one-dimensional numerical data. Heterogeneous data are converted to have the same structure. The second input line is used to input auxiliary parameters. The extracted features are fused with the auxiliary parameters in an additional fully connected layer. The fused data are then predicted in the MHL-NN. Assuming the inputs to the convolutional layer of the new MRMDL model is \(X_{1}\) (i.e., CYGNSS Raw DDM and BRCS DDM) and the inputs to the auxiliary parameters is \(X_{2}\), the model output can be expressed as:  
\[MRMDL_{SSH}=\prod_{i=1}^{L_{GS}}\sigma\Big{[}W_{i}^{N_{GS}}(MRResNet(X_{1})\cup X _{2})+b_{i}\Big{]} \tag{4}\]  
where \(MRMDL_{SSH}\) represents the output of the MRMDL; \(N_{GS}\) and \(L_{GS}\) denote the optimal number of hidden layers and neurons for each layer determined by the grid search algorithm, respectively; \(W_{i}\) and \(b_{i}\) denote the \(i\)-th hidden layer's weight and bias, respectively. ; \(MRResNet(X_{1})\) denotes the features extracted by the MResNet mode; and \(\sigma\) denotes each hidden layer's activation function.