## 3 Algorithm Design
### Combination of BP Neural Network Optimized by BBO Algorithm and EKF  
#### 3.3.1 BBO Algorithm  
In an attempt to imitate the migratory behavior of biological groups in nature, [PERSON] [20] originally put forward a biogeography optimization method in 2008, which was centered on the migration operation of a linear model. The algorithm is uncomplicated in principle, easy to implement, contains fewer parameters, and has good global search capability and robustness. It is extensively applied in engineering [20; 31; 32], data analysis [33], and image processing [34]. The BBO algorithm mainly realizes the exchange of information through species migration and mutation between habitats. It then calculates the fitness value after exchange, and finally searches for the optimal solution through continuous iteration. Because the BP neural network is prone to falling into a local optimal solution in the training process, the application of the BBO algorithm to optimize the initial weight and threshold of a BP neural network can solve this problem to a certain extent, which helps to improve the optimization performance of a BP neural network and increase the number of opportunities to find a global optimal solution. Because the core of the BBO algorithm is a migration operation, the traditional BBO algorithm is a linear mobility model (LMM) (see expression (14)), which has shortcomings in terms of its global search ability. This paper proposes a nonlinear mobility model, the arc curve mobility model (ACMM), as shown in expression (15), which advances the global search ability of the BBO algorithm. \[\left\{ \begin{array}{l}\lambda_{n}=I(1-\frac{n}{m})\\ \mu_{n}=E\cdot\frac{n}{m}\end{array} \right. \tag{14}\]\[\left\{ \begin{array}{l}\lambda_{n}=\left\{\begin{array}{l}\frac{l}{2}+\sqrt{ \left(\frac{l}{2}\right)^{2}-\left(\frac{n}{m}\right)^{2}}\,\ 0\leq n<\frac{m}{2}\\ \frac{l}{2}-\sqrt{\left(\frac{l}{2}\right)^{2}-\left(\frac{n}{m}-1\right)^{2}} \,\ \frac{m}{2}\leq n\leq m\\ \end{array}\right.\\ \mu_{n}=\left\{\begin{array}{l}\frac{E}{2}-\sqrt{\left(\frac{E}{2}\right)^{2 }-\left(\frac{n}{m}\right)^{2}}\,\ 0\leq n<\frac{m}{2}\\ \frac{E}{2}+\sqrt{\left(\frac{E}{2}\right)^{2}-\left(\frac{n}{m}-1\right)^{2}} \,\ \frac{m}{2}\leq n\leq m\\ \end{array}\right.\\ \end{array} \right. \tag{15}\]  
Above, \(\lambda_{n}\) and \(\mu_{n}\) are the immigration rate and emigration rate when the quantity of biological populations in the current habitat is \(n\), and their respective maximum values are equal to \(I\) and \(E\). \(m\) is the maximum quantity of biological populations that the habitat can accommodate. When the maximum quantity of biological populations \(m=50\), \(I=1\) and \(E=1\), as shown in Figure 5, can be obtained. It can be observed from the above expression or figure that the immigration rate \(\lambda\) and emigration rate \(\mu\) will change with the change in the quantity of species \(n\). When there are few species in the ecosystem, the circular arc curve mobility model can increase the immigration rate and slow decline, and the emigration rate will become small and slowly rise, which can increase the exchange of species information between habitats as well as boost the algorithm's capacity for global search; when the quantity of species in the habitat is large, the immigration rate is small and the emigration rate is large, which also enhances the algorithm's capacity for global search; when the quantity of species in the habitat is equal to half of the maximum quantity of species, the immigration rate is equal to the emigration rate, thus reaching a balance state. Please refer to Figures 5 and 6 for further information. The habitat suitability index (HSI) is a metric utilized to assess whether an area is suitable for a species' existence. The larger the value, the more suitable the habitat is for species survival. The HSI is composed of many factors, including temperature, rainfall,  
Figure 5: Linear/Arc curve mobility model diagram.