# Artificial Intelligence-Empowered Doppler Weather Profile for Low-Earth-Orbit Satellites
## 2 Methodology
### AI Model Framework for Doppler Weather Profile Analysis
#### 2.4.2 The Proposed IIS-LSTM Modelling Approach  
The model consists of a hybrid involving an IIS algorithm that functions as a feature selector and LSTM as a deep learning algorithm. IIS streamlines the input space dimensions by identifying the most important input variables (features) that enhance the model's performance. It identifies the most advantageous attributes within the innovative hybrid integrated model. The channel matrix is transformed into a three-dimensional tensor \(\beta\) with dimensions of  
\[F_{n}=\beta(W_{m}.(LH_{n-1},NI_{n})+V_{m}) \tag{9}\]  
\(\beta\) is the input tensor that takes on the appearance of a dual channel. After feature extraction, a component of Recurrent Neural Networks (RNNs), LSTM, was utilised, which possesses the capability to capture long-term dependencies. These models have recently attracted increasing interest. The chief advantage of LSTM networks lies in their ability to consider the sequential progression of events in a forecasting period, rendering them well suited for sequential AI methodologies. In Long Short-Term Memory networks, there are input, output, and forget gates within memory blocks that effectively update and regulate the flow of information in distinct blocks. This unique feature of LSTM is beneficial as it facilitates the continual updating of future predictions. If \(LH_{n-1}=\) last hidden state, \(NI_{n}=\) new input, \(FG_{n}=\) forget gate, \(W_{m}=\) weight matrices, \(V_{m}\)= bias vector, \(ig_{n}=\) input gate, \(\theta(..)=\) logistic sigmoid activation functions, \(tanh(..)=\) hyperbolic tangent. Further to \(S_{n-1}\) and \(NI_{n}\), LSTM can determine the information that is to be excluded or thrown away from the cell state represented by  
\[CS_{n}=\tanh(W_{c}.(LH_{n-1},NI_{n})) \tag{10}\]  
Deciding what information will be stored in the cell state, we need another candidate cell state \(CS_{n}\) that is generated and scaled by  
\[ig_{n}=(W_{i}.(LH_{n-1},NI_{n})+V_{i}) \tag{11}\]  
\[CS_{n}=(F_{n}*C_{n-1}+NI_{n}*C_{n}) \tag{12}\]  
\(CS_{n}\), which is the latest state of a cell, is updated by merging the earlier state of the cell \(CS_{n-1}\) and the latest state of the cell \(CS_{n}\). The earlier cell is affected by the 'forget gate' \(FG_{n}\) and the latter by 'input gate' \(ig_{n}\):  
\[\partial_{n}=\sigma(W_{\partial}.(LH_{n-1},NI_{n})+b_{\partial}) \tag{13}\]  
The output process is conducted sequentially, comprising two distinct steps. A newly introduced gate, referred to as the 'output gate' \(\partial_{n}\), is employed to determine the specific elements of the cell state (the \(C_{n}\) that is to be outputted). The activation of the cell state through the tanh function is refined by the application of the 'output gate' \(\partial_{n}\). The resultant product of this multiplication operation yields the anticipated output, denoted as Sn. \[LH_{n}=\partial_{n}\tanh(C_{n}) \tag{14}\]  
Benchmarking is performed with two other machine and deep learning models (Table 2), Extreme Gradient Boosting (XGBoost), and Convolutional Neural Network (CNN) which have been covered in our earlier studies [31; 32]. With precise calculations for Doppler shift and additional data extracted related to Doppler, we also took care of the trajectory of its variation. The data output for Doppler includes relative velocity and Doppler rate. See Figures 5-12. Figures 5 and 9 illustrate the Doppler shift, Figures 6 and 10 show the Doppler rate, Figures 7 and 11 describe latency, and Figures 8 and 12 discuss the latency rate corresponding to the Globalstar and ISS with initial satellite data. The original Doppler shift possesses a dynamic range deemed too vast for effective training with Mean Squared Error (MSE) loss. By converting the values to a normalised scale, our proposed model achieved improved training precision and accuracy. We have optimised the training process to minimise the error for enhanced performance. \[\text{Loss}=\frac{1}{N}\sum_{g=1}^{N}\abs{DS_{g}-\tilde{D}S_{g}}^{2} \tag{15}\]