## 4 FDA-SSD Network  
### Improved Model  
The original SSD design was to use multi-layer convolution to obtain feature extraction of different scales, perform a large number of anchors on each scale, and finally screen the optimal detection by non-maximum suppression. The advantage of this algorithm is that it can adapt to the detection of targets at different scales, while it also has the problem of a large amount of calculation. Regarding each type of target, the smallest-scale detector in SSD needs 4332 anchors; the second-smallest scale needs 2166 anchors, followed by 600, 150, 54, and 6, with a total of 8732 anchors to be detected.  
Considering that the depth of the target related to the camera-coordinate system in the target-tracking problem can be solved, a Fast Depth-Assisted Single-Shot MultiBox Detector for 3D tracking based on monocular vision was designed in this study based on the strong correlation between adjacent frames in the video tracking problem. Figure 4 exhibits a schematic diagram of the Fast Depth-Assisted Single-Shot MultiBox Detector (FDA-SSD) proposed in this study. The part in the red box represents the depth-assisted training model. Regarding the FAD-SSD model, in addition to the image input, we increased the depth value \(D_{norm}\) of the target sample relative to the camera-coordinate system. Besides, the scale correlation information of the sample with the depth value was learned through a Feedforward Neural Network (FNN) and a SoftMax module to determine the detection layer that obtains the most-reliable detection result.  
With respect to the target spatial-positioning algorithm, a suitable detector can be selected for target recognition and extraction instead of searching in every scale. This method can significantly reduce the amount of calculation in the detection part. The deep  
Figure 4: Structure of Fast Depth-Assisted Single-Shot MultiBox Detector.  
conv-layer computing cost in the backbone structure can be saved. The FNN structure is provided in Figure 5.  
Among them, the input layer \(x\) corresponds to the depth information \(D_{norm}\) obtained by the tracking algorithm; the number of hidden layer units was set to 20; the maximum confidence probability \(p_{i},i=1,2,3,4,5,6\) of the detection anchor frame obtained by the six different scale detectors of the SSD corresponding to the output layer \(y_{i},i=1,2,3,4,5,6\) after SoftMax is:  
\[y_{i}=\frac{exp(p_{i})}{\sum_{j=1}^{6}exp(p_{j})},\,i=1,2,3,4,5,6, \tag{1}\]  
The loss function \(L\) used by FNN in this algorithm is cross-entropy:  
\[L=\frac{1}{\text{N}}\sum_{i}L_{i}=\frac{1}{\text{N}}\sum_{i}-[y_{i}\times log( p_{i})+(1-y_{i})\times log(1-p_{i})], \tag{2}\]  
where \(y_{i}\) denotes the probability that the detector correctly detects the sample under six detection scales, and \(p_{i}\) represents the predicted probability under different input depth values. The FDA-SSD training method is consistent with the original SSD. The structure of FNN combined with the SoftMax decision-making scheme was adapted on the increased depth channel, allowing the model to self-learn from end to end if it matches the optimal scale. There was no need to manually mark which scale to use.