Statistical Modeling of Insect Trajectories Using a Kalman Filter

Abstract

This thesis investigates the foraging behavior of the beetle Scarabaeus zambesianus using state-space models (SSM) and the Kalman filter. The study focuses on tracking the beetle’s trajectory from video footage, employing an iterative algorithm that combines image processing techniques with the Kalman filter to estimate the beetle’s location and velocity while minimizing measurement noise. The methodology involves converting video frames into a sequence of images and applying a Kalman filter to estimate the beetle’s true state (location and velocity) while accounting for measurement noise. An iterative tracking algorithm is developed, combining video processing techniques with the Kalman filter to continuously update the beetle’s location as it moves across frames. The algorithm begins by detecting the beetle’s initial position using a sliding window approach, which evaluates intensity changes between consecutive frames. The Kalman filter is then employed to refine the trajectory estimates by integrating predictions from the state-space model with noisy observations. The results show that the Kalman filter significantly improves trajectory accuracy, though challenges emerge when the beetle moves into areas with similar background colors, such as a dung pile. Sensitivity and residual analyses are conducted to evaluate the algorithm’s robustness and performance. Furthermore, linear regression models are used to analyze the relationship between the beetle’s velocity and its distance from the burrow, revealing a weak but statistically significant negative correlation. This research demonstrates the effectiveness of statistical modeling in studying insect behavior and provides a foundation for future work on insect movement dynamics.