## 3 Pedestrian Inertial Navigation Algorithm Based on RBCN-Net
### RBCN-Net  
To improve the mapping capability of IMU sequence \([a,w]_{i=1\sim 200}^{n}\) to labels \((v_{x},v_{y})\), further reduce the interference of non-critical information, and make the network focus on more effective information, we modify the ResNet18-NAM 1D framework by adding the CBAM [18] after the maximum pooling layer. The CBAM is formed by serially connecting two attention submodules, CAM and SAM, to enhance the network's ability to learn channel and spatial features, respectively. The network with the addition of CBAM still has limited capability in long-range learning modeling, so the BiLSTM network is added after the 8 th Basicblock-NAM structure in this paper. BiLSTM can realize the network's feature learning for long-range sequences as well as fully learn the temporal correlation of IMU sequences. The framework of the proposed RBCN-Net is shown in Figure 4.  
The network's input IMU sequence is \([a,w]_{i=1\sim 200}^{n}\) whose dimension is 6 \(\times\) 200.The input sequence is first subjected to preliminary feature extraction and dimensionality reduction using a \(7\times 1\) convolutional kernel and a 3 \(\times\) 1 maximum pooling layer to obtain a 64 \(\times\) 50 feature vector \(f_{1}\).  
\[f_{1}=MaxPool(f^{7\times 1}([a,w]_{i=1\sim 200}^{n})) \tag{5}\]  
Then \(f_{1}\) is fed into the CBAM. CAM compresses \(f_{1}\) based on maximum pooling and average pooling for length and width, respectively, to produce two new feature sequences, which are fed into a two-layer perceptron to produce two new feature vectors,  
Figure 4: RBCN-Net Architectures.  
which are activated by the Sigmoid function to produce the module's final output weight coefficients, \(M_{cam}\).  
\[M_{cam}(f_{1})=\sigma(MLP(AvgPool(f_{1}))+MLP(MaxPool(f_{1}))) \tag{6}\]  
Finally, the output feature vector \(f_{cam}\) of CAM is obtained by multiplying the weight \(M_{cam}\) with \(f_{1}\) element by element.  
\[f_{cam}=M_{cam}(f_{1})\bigodot f_{1} \tag{7}\]  
The SAM takes \(f_{cam}\) as input and first compresses it using maximum pooling and average pooling. After compression, the two new feature sequences obtained are spliced by corresponding channels and further dimensional compression is performed using a \(7\times 1\) convolution, and the final compressed features are activated by the sigmoid function to obtain the spatial attention weights \(M_{snm}\).  
\[M_{sam}(f_{cam})=\sigma(f^{7\times 1}[AvgPool(f_{cam});MaxPool(f_{cam})]) \tag{8}\]  
The weights \(M_{sam}\) are multiplied element by element with \(f_{cam}\) to obtain the output of the SAM as well as the output feature vector \(f_{CBAM}\) of CBAM. The dimensionality of \(f_{CBAM}\) is the same as that of \(f_{1}\).  
\[f_{CBAM}=M_{sam}(f_{cam})\bigodot f_{cam} \tag{9}\]  
After passing 8 Basicblock-NAM, the \(f_{CBAM}\) obtains 512 \(\times\) 7 feature vectors, and then input to the BiLSTM layer, which has two hidden layers with input and output dimensions of seven. The fully connected layer connects the 512 \(\times\) 14 feature vectors output from the BiLSTM layer into the final feature vector with the same dimension as the velocity label, and the physical meaning represents the pedestrian's velocity vector in the navigation coordinate system. In the fully connected layer, the dropout layer parameter of 0.5 is used to prevent overfitting. The mathematical expression of the proposed RBCN-Net is shown in Equation (10).  
\[\widetilde{v}(\widetilde{v}_{x},\widetilde{v}_{y})=f_{\theta}([a,w]_{i=1\sim 2 00}^{n}) \tag{10}\]