# Brain-Like Navigation Scheme based on MEMS-INS and Place Recognition
## 2 Proposed Solution
### Proposed Brain-Like Navigation Model Based on Vision and INS  
As indicated by research on physiology, the phenomenon that the animal's place cells are activated in the environment is determined by path integration, which is a consequence of integrating internal cues include directional heading and distance computations. Naturally, errors in path integration accumulate over time. When rats are placed in a familiar environment, the path integrator will be reset to be adapted to the external environment information perceived by the eyes. It has been demonstrated by these studies that rats can integrate the internal and external information for accurate navigation in various environments. In a familiar environment, the positioning error can be corrected with the external perceptive information as an absolute reference, and the same is true for human beings. Figure 3: Actual speed and the results of linear decoders. Figure 2: Response curve of firing of a head-direction (HD) cell. By simulating the navigation mechanism of these species, we put forward an intelligent brain-like navigation model based on vision and INS. The attractor network model of place cells constructs a measurement model corresponding to the relative position in the actual external environment. The place cells model adopts continuous attractor networks, where the place cells on the fringe are connected to the ones on the other fringe and form an annular shape. The continuous attractor networks model creates a stable activity packet via the wraparound excitatory connections on the same neural plate. This attractor network is driven by the path integration system and reset by the graphic information derived from the current position. By using two-dimensional Gaussian distribution to construct \(\chi_{x,y}\) which is the weight connection matrix of excitability, \(\chi_{x,y}\) is expressed by:  
\[\chi_{x,y}=e^{-(x^{2}+y^{2})/E}, \tag{1}\]  
where \(x\) and \(y\) are the distances between units in \(X\) and \(Y\) coordinate respectively, and \(E\) is the width constant for position distribution. The place cell activity matrix \(P\) is used to describe the activity in the place cells. The variable quantity of place cells' activities induced by local excitation is given by:  
\[\Delta P(X,Y)=\sum_{i=0}^{S_{X}-1}\sum_{j=0}^{S_{Y}-1}P(i,j)\chi_{x,y}, \tag{2}\]  
where \(S_{X}\),\(S_{Y}\) are the dimensions of the two-dimensional matrix of the place cells in the space and represent the attractor sub-model's range of activity on the neural plate. The precondition for the iteration of place cells and the matching of the visual template is to pinpoint the relative position of place cells attractors in the neural plate. The relative position coordinates are expressed by the subscript of the weight matrix, which is calculated by the equations:  
\[x=(X-i)(\text{mod}S_{X}), \tag{3}\]  
\[y=(Y-j)(\text{mod}S_{Y}). \tag{4}\]  
Each place cell receives the global inhibitory signal in the same manner as an entire network. The symmetry of the excitatory and inhibitory connection matrix is a guarantee for proper neural network dynamics, which keeps the attractors in the space from unrestricted excitability. The variable quantity of place cells' activities induced by inhibitory connection weight is given by the equation:  
\[\Delta P(X,Y)=\sum_{i=0}^{S_{X}}\sum_{j=0}^{S_{Y}}P(i,j)\Psi_{x,y}-\xi, \tag{5}\]  
where \(\Psi_{x,y}\) is the inhibitory connection weight, \(\xi\) controls the level of global inhibition. The activities of all place cells are nonzero and have undergone the normalization procedure. \(P^{t+1}(X,Y)\), the firing rate of place cells with path integration is given by:  
\[P^{t+1}(X,Y)=\sum_{i=\Delta X}^{\Delta X+1}\sum_{j=\Delta Y}^{\Delta Y+1} \alpha_{i,j}P^{t}(i+X,j+Y), \tag{6}\]  
where \(\alpha_{i,j}\) is the residual. \(\Delta X\) and \(\Delta Y\) are the offset values via rounding down, which is determined by speed and direction, as shown in Equation (7):  
\[\left[ \begin{array}{c}\Delta X\\ \Delta Y\end{array} \right]=\left[