Robust Moving Horizon Estimation for Autonomous Agricultural Vehicles With GNSS Outliers Using a Robust Loss Function

Abstract

We propose a Moving Horizon Estimator (MHE) for autonomous agricultural vehicles to handle GNSS outliers, a common issue in farming. To improve robustness, we replace the standard L2 stage cost with a loss function based on the square of the derivative of the General Adaptive Robust Loss (GARL). The GARL framework, controlled by parameters α∈[1,2) and c>0, balances between quadratic and outlier-resistant behavior. By using the derivative, we avoid singularities at α=0 and α=2, simplifying tuning and ensuring stable optimization within MHE. This approach retains the flexibility of GARL while narrowing the design space to a singularity-free regime. We prove robust stability under standard assumptions. Simulations show our method outperforms L2-based MHE and state-of-the-art methods, rejecting GNSS outliers. Field experiments validate its practical effectiveness.