Computationally Efficient Moving Horizon Estimator for Linear Time-Invariant Systems

This paper presents a computationally efficient formulation for cost computation in Moving Horizon Estimation (MHE) applied to Linear Time-Invariant (LTI) systems. MHE is a powerful method for state estimation in dynamic systems, but its performance can be hindered by the computational load associated with solving optimization problems at each time step. By leveraging the inherent properties of LTI systems, we derive an optimized cost function formulation that significantly reduces the computational complexity without compromising estimation accuracy. The proposed method is validated through multiple simulation scenarios, including quadrotor formation flight, demonstrating a 77% to 96% reduction in computational time compared to conventional MHE across various levels of system complexity. Our findings present promising results for enhancing the performance of MHE, especially in applications where computational resources are limited.