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

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 $\mathrm{L_{2}}$ 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 $\alpha \in [1,\,2)$ and $c > 0$, balances between quadratic and outlier-resistant behavior. By using the derivative, we avoid singularities at $\alpha = 0$ and $\alpha = 2$, 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 $\mathrm{L_{2}}$-based MHE and state-of-the-art methods, rejecting GNSS outliers. Field experiments validate its practical effectiveness.