# A Long Time Span-Specific Emitter Identification Method Based on Unsupervised Domain Adaptation
## 3 Methodology
### Optimization Method of LTS-SEI  
The parameters of the feature extractor, classifier, and domain discriminator of LTS-SEI can be updated through (22), (23), and (24), respectively:  
\[\theta_{f}^{t+1}=\theta_{f}^{t}-\mu(\frac{\partial L_{\text{C}}^{t}}{\partial \theta_{f}^{t}}-\lambda\frac{\partial L_{D}^{t}}{\partial\theta_{f}^{t}}) \tag{22}\]  
\[\theta_{c}^{t+1}=\theta_{c}^{t}-\mu\frac{\partial L_{\text{C}}^{t}}{\partial \theta_{c}^{t}} \tag{23}\]  
\[\theta_{d}^{t+1}=\theta_{d}^{t}-\mu\frac{\partial L_{D}^{t}}{\partial\theta_{ d}^{t}} \tag{24}\]  
Algorithm 1 provides the optimization and testing process of the LTS-SEI framework. When obtaining the optimal network parameter \((\hat{\theta}_{c},\hat{\theta}_{c},\hat{\theta}_{d})\), LTS-SEI can learn features with interclass separability, domain invariance, and intraclass compactness. The multiple experiments in Section 5 indicate that these features are beneficial to solving the long time span SEI problem.  
```
Input: Source domain signal \(\mathbf{X}_{S}\), Source domain signal label \(\mathbf{Y}_{S}\), Target domain signal \(\mathbf{X}_{T}\), Source domain label \(d_{S}\), Target domain label \(d_{T}\). Output: Optimal network parameter \((\theta_{c},\theta_{c},\theta_{d})\), Target domain sample label \(Y_{T}\).
1. Obtain source domain sample \(X_{S}\), target domain sample, \(X_{T}\) and source domain sample label \(Y_{S}\). (See data-preprocessing module.)
2. Forward propagation: (1) From feature extractor to classifier:  Input \(X_{S}\) and \(X_{T}\) into the feature extractor to obtain shallow features \(F_{S}\) and \(F_{T}\). (See Equation (4)) Input \(F_{S}\) and \(F_{T}\) into the classifier to obtain deep features \(\mathbf{f}_{S}\) and \(\mathbf{f}_{T}\), prediction label \(y_{S}\), and prediction probability \(\mathbf{p}_{S}\) of \(X_{S}\). (See Equations (5)-(7)) Compute Softmax Loss \(L_{SL}\) using \(g_{S}\) and \(Y_{S}\). (See Equation (8)) Compute Counter Loss \(L_{CL}\) using \(\mathbf{f}_{S}\) and \(Y_{S}\). (See Equation (9)) Compute HOMM3 Loss \(L_{FM}\) using \(\mathbf{f}_{S}\) and \(\mathbf{f}_{T}\). (See Equation (16)) Compute the hybrid loss \(L_{\text{C}}\) of the classifier. (See Equation (17)) (2) From feature extractor to domain discriminator:  Input \(X_{S}\) and \(X_{T}\) into the feature extractor to obtain shallow features \(F_{S}\) and \(F_{T}\). (See Equation (4)) Compute domain discrimination loss using \(F_{S}\), \(F_{T}\), \(d_{S}\) and \(d_{T}\). (See Equation (18)) (3. Back propagation: (1) Calculate gradient information \(\frac{\partial L_{\text{C}}}{\partial\theta_{c}}\), \(\frac{\partial L_{\text{C}}}{\partial\theta_{c}}\), \(\frac{\partial L_{\text{D}}}{\partial\theta_{d}}\) and \(\frac{\partial L_{\text{D}}}{\partial\theta_{f}}\). (2) Update \(\theta_{c},\theta_{f}\), and \(\theta_{d}\) through random gradient descent. (See Equations (22)-(24)) 4. Repeat Step 2 and 3 until the maximum number of iterations is met. 5. Save the optimal parameter \((\hat{\theta}_{f},\hat{\theta}_{c},\hat{\theta}_{d})\) after completing the LTS-SEI training. 6. Input \(X_{T}\) into the feature extractor \((\hat{\theta}_{f})\) and classifier \((\hat{\theta}_{c})\). 7. Output target domain sample label \(Y_{T}\).
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**Algorithm 1** The optimization and testing process of the LTS-SEI framework