# Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory
## 3 Method  
### Animal Movement Modeling  
Among numerous different models to predict and model stochastic animal movement behavior, the simplest approach to explain the stochastic nature of the animal movement is the uncorrelated and unbiased random walk based on the Brownian motion. In this model, the animal movement directions are assumed to be uncorrelated--the current heading direction of the animal is not influenced by the previous heading directions and unbiased--the animal movement direction is not influenced by a specific direction or location. The location of the animal at any time is simply influenced by the previous location, and the heading direction at any time is completely random. However, due to the two biological constraints related to most animals: bilateral symmetry and cephalocaudal polarization (responsible for an animal's tendency to move forward) according to [34], this simple random walk model is unable to represent a realistic animal movement behavior. Additionally, in many realistic scenarios, the animals are inclined to go to specific locations for food, shelter, migrations, etc., which also cannot be included in the uncorrelated and unbiased random walk models. To incorporate the aforementioned biological constraints and global directional bias in the animal movement modeling, two separate random walk models were derived from the uncorrelated and unbiased random walk model: the Correlated Random Walk (CRW) and the Biased Random Walk (BRW). The CRW model is developed under the assumption that there exists a correlation between consecutive heading directions of animals, which is defined as 'persistence'. The persistence term explains local directional bias for an animal since the current heading direction is biased by the previous heading angle, which ensures that the animal intends to move in the forward direction. However, there exists some uncertainty associated with the heading directions, which results in making the heading direction different from the initial heading direction and therefore, the effect of the initial heading direction decreases in time. In the BRW model, there exists global directional bias in the animal movement directions, meaning that an animal following the BRW model will intend to move towards a specific direction or a location at all times. This directional bias can be long term (annual migration) or short term (i.e., daily foraging for food) and the specific location for the directional bias be can be either moving (i.e., herd center) or stationary (i.e., food, water, shelter). Similar to the CRW model, there will be some uncertainty regarding the movement direction at any time although the animal will have a higher probability to move towards the target location or direction. Given that there exists some persistence in the direction of the animals while moving towards a specific direction, this special form of BRW is defined as the Biased-Correlated Random Walk (BCRW). Here, the animal movement direction at any time is influenced by both the previous heading direction (local directional bias) and the specific direction (global directional bias). The Correlated Random Walk (CRW) model has been adopted in broad literature to explain individual behavior of stochastic movement for animals, fishes, insects, etc. [34; 35; 36; 37; 38]. In the meantime, this random walk model can hardly be utilized to replicate the group behavior of animal herds since this model cannot establish a link between individual animal movement direction and the overall herd location, which is essential for maintaining the integrity of animal herds. An animal movement strategy to explain the group behavior of animal herds was proposed in [39], where the movement of the animal group centers was modeled using BCRW and the individual animal movements were followed by either CRW or BRW, where the animals for the BRW model were biased to the herd center. This study demonstrated that the group dynamics model can explain the group-influenced behavior of animals.