Initial covariance estimation and analysis for EKF localization using route-based experimental data

Reliable initialization of covariance matrices is crucial for accurate state estimation in extended Kalman filter (EKF) applications. However, many previous works did not technically formulate but rather relied on assumed or arbitrary covariance values such as identity matrices or random initialization which led to inconsistent convergence and unstable localization. This paper presents an experimental formulation of initial covariance matrices for EKF using a Turtlebot3 Burger platform evaluated over three navigation routes which are square, curve, and diamond. The covariance values are systematically derived from experimental and simulation data along with the manufacturer parameters, enabling robust and repeatable EKF initialization across different navigation conditions. The formulated initial covariance matrices were tested in EKF implementations and their effects were examined in terms of convergence behavior, outlier patterns, rotation characteristics and overall uncertainty reduction. Results demonstrate that the experimentally derived covariance from the square route provides the most stable and reliable initialization with values of 0.001022847 for position and 0.019544504 for orientation. This configuration produced the lowest uncertainty difference of 450 μm², the shortest rotation time of 62.84 s, and the highest improvement rates of 98.47 % and 99.97 % for position and orientation covariances respectively. The novelty of this work lies in the route-based experimental derivation and comparative validation of covariance matrices, which establish a practical reference for EKF and simultaneous localization and mapping (SLAM) implementations in mobile robot navigation where accurate localization and reduced uncertainty are critical.