## 3 Spatial Location Representation Map Construction  
Based on the physiological properties of each the navigation cells mentioned above, it is known that boundary cells can fire specifically in response to the perception of the environmental boundary by the rat, i.e., the vectorial relationship between the rat and the boundary. Furthermore, the closer the rat is to the environmental boundary, the greater the value of the boundary cell firing response [32]. Grid cells are considered as a coordinate system for characterizing the environment due to their specific spatial metric properties, and when multiple grid cells fire aggregately the current position of the rat can be estimated [33; 34]. A process schematic diagram of constructing a spatial location representation map, using the specific firing responses of these navigation cells and their mapping relationships with each other, is shown in Figure 6. The specific map construction steps are as follows:  
Figure 5: Cell distribution and firing rate in different geometric environments. **(a)** Cell distribution in a trigonal environment. **(b)** Cell distribution in a pentagonal environment. **(c)** Cell distribution in a nine-sided environment. **(d)** Cell firing rate in a trilateral environment. **(e)** Cell firing rate in a pentagonal environment. **(f)** Cell firing rate in a nine-sided environment. Figure 6: Schematic diagram of the spatial location representation map construction. Step 1: As the mobile robot explores the environment, it collects the speed, direction, and distance-aware information needed to construct a spatial location representation map. Step 2: The inputs of the direction and velocity-aware information to the input layer of LAHN are conducted. The output of the grid cell response value is obtained after the learning performed by LAHN. Step 3: Grid cells undergo a competitive Hebb learning network in order to generate place cells that are capable of representing current location information [18]. The mobile robot explores the environment by continuously activating new place cells in response to new location scenarios and jointly constructs a spatial location cell representation map until the robot stops running. The algorithm for the construction of the spatial location representation map is shown in detail in Algorithm 1. In order to avoid the undesirable situation where the number of place cell activations for the same scene is too many due to the small place cell spacing in the operation of the mobile robot (thus resulting in the waste of system computational resources) or the undesirable situation where the place cell spacing is too large (thus resulting in the poor accuracy of position estimation), this paper introduces the place cell distance threshold \(r_{th}\) in order to constrain the place cell activation response. Figure 7 shows the box plot of the localization accuracy of the mobile robot when constructing the spatial location representation map under different values of \(r_{th}\). The localization error in Figure 7 fluctuates upward with the distance threshold, and the localization error is minimized when \(r_{th}\) is taken as 0.06 m, such that \(r_{th}\) is taken as 0.06 \(m\) in this paper.