An Optimal Quantization-based Unscented Kalman Filter on SE(2): Application to Trajectory Tracking

This paper introduces an Unscented Kalman Filter (UKF) on the Special Euclidean group SE(2) based on optimal quantization, integrating it within the Invariant Linear Quadratic Gaussian (ILQG) regulator to solve trajectory tracking featuring high-angle variations. Traditional trajectory tracking methods like the Linear Quadratic Gaussian (LQG) regulator often face limitations due to linearization, especially under highly nonlinear model, high-angle maneuvers and/or stochastic uncertainties. The proposed approach overcomes these limitations by employing a sigma-point filter, the Unscented Kalman Filter on Lie groups (UKF-LG) enhanced with optimal quantization. This method improves the accuracy of the covariance computation during the filter’s prediction step, enabling better estimation performances to provide robust trajectory tracking in scenarios with significant angular deviations. Simulations demonstrate the effectiveness of the proposed Optimal Quantization-based Left-UKF-LG (OQ-Left-UKF-LG) over the IEKF and standard UKF-LG in complex tracking scenarios. The approach offers promising potential for applications requiring precise tracking in dynamic environments, such as autonomous mobile robots or Unmanned Aerial Vehicles (UAVs).