# Intelligent Detection Method for Satellite TT&C Signals under Restricted Conditions Based on TATR
## 5 Methods
### Signal Detection  
The features obtained from the decoder module undergo global and local adaptive feature selection, mapping through the feed forward network (FFN) to a higher-dimensional feature space. Class labels and the coordinates of detection boxes are predicted through an FFN layer with shared weights. The output dimension of the FFN layer is \(D\times 5\), providing four coordinate predictions and one class prediction, where \(D\) represents the number of set signal query vectors. The traditional post-processing step, based on the NMS algorithm, relies on manually set anchor points [46] and retains the box with the highest probability among \(D\) results using a fixed threshold [47]. This approach is unsuitable for complex and dynamic signal broadband reception scenarios. In this paper, the Hungarian algorithm [11] is employed for bipartite graph matching of signal detection boxes, as illustrated in Figure 7. Where \(\mathcal{O}_{i}\) represents the \(i\)-th signal detection box predicted by TATR, \(\mathcal{T}_{i}\) is the \(i\)-th ground truth detection box, and \(\omega_{ij}\in 0,1\) indicates whether the predicted box \(\mathcal{O}_{i}\) and the true box match. The Hungarian algorithm is used to establish a one-to-one correspondence between the predicted results and the labels to minimize the matching loss. The optimal matching of signal prediction boxes is found by recursively changing the corresponding relationship. The calculation of the matching loss is shown in Equation (9):  
\[ \begin{split}\hat{\sigma}&=\operatorname*{arg\,min} \limits_{\sigma\in\mathcal{D}}\sum_{i}^{D}L_{m}(\mathcal{O}_{i},\mathcal{T}_{ \sigma(i)})\\ L_{m}(\mathcal{O}_{i},\mathcal{T}_{\sigma(i)})&=- 1_{\{c_{i}\
eq\varnothing\}}\hat{\rho}_{\sigma(i)}(c_{i})+1_{\{c_{i}\
eq \varnothing\}}L_{box}(s_{i},s_{\sigma(i)})\end{split}  \tag{9}\]  
where \(\hat{\sigma}\) represents the paired matching indices obtained by minimizing the matching loss through the Hungarian algorithm, and \(L_{m}(\mathcal{O}_{i},\mathcal{T}_{\sigma(i)})\) represents the matching loss between each predicted signal detection box and the padding detection box of the true label. The loss consists of two parts: the bounding box loss \(1_{\{c_{i}\
eq\varnothing\}}L_{box}(s_{i},s_{\sigma(i)})\) minus the category loss \(1_{\{c_{i}\
eq\varnothing\}}\hat{\rho}_{\sigma(i)}(c_{i})\). The matching cost considers both class prediction and the similarity between predicted boxes and true boxes, where \(c_{i}\) is the signal class label, \(c_{i}=\varnothing\) represents the case where the  
Figure 7: Signal prediction box matching using Hungarian algorithm. The features output by TATR decoder are processed through FFN to obtain the predicted signal box, which is then matched with the actual detection box padding results using the Hungarian algorithm to obtain the minimum matching loss result. predicted signal class is not considered as background, \(\hat{p}_{\sigma(i)}(c_{i})\) represents the predicted probability for each signal class \(c_{i}\), and \(s_{i}\in[0,1]^{d=4}\) represents the center coordinates of the true signal box (\(\mathcal{O}_{i}^{x}\) and \(\mathcal{O}_{i}^{y}\)), as well as its height \(h_{i}\) and width \(w_{i}\). After obtaining the optimal match \(\hat{\sigma}\) for the signal prediction box, the loss function of the TATR model is calculated and consists of two parts: the negative log-likelihood loss for signal category prediction \(L_{pre}\) and the bounding box loss \(L_{box}\). The negative log-likelihood loss for signal category prediction is the same as the cross-entropy loss. It measures the goodness of fit between the model and the training data, maximizing the likelihood estimation to obtain a model that is closest to the data distribution, which is defined as  
\[L_{pre}=-\log\hat{p}_{\sigma(i)}(c_{i}) \tag{10}\]  
The bounding box loss measures the difference between predicted bounding boxes and true bounding boxes.