Real-Time Moving Horizon Estimation for Nonlinear Systems With Unknown Inputs

Moving horizon estimation (MHE) is a well-known alternative to Kalman-like filtering due to its superior performance in terms of estimation accuracy, convergence speed, and robustness to poor initial state guesses. However, most MHE methods cope with unknown inputs by introducing a random walk model, which is unsuitable for fast-varying unknown inputs. To address this issue, we propose an unknown input moving horizon estimator (MHE-UI) that does not require any prior knowledge of the dynamic behavior of unknown inputs. To solve the associated nonlinear least squares problem in real time, we develop a computationally efficient Gauss-Newton iterative algorithm by exploiting the block pentadiagonal structure of the resulting Karush-Kuhn-Tucker (KKT) matrix. A numerical case study demonstrates that the proposed real-time MHE-UI algorithm achieves higher estimation accuracy than the unknown input unscented Kalman filter (UKF-UI) and significantly reduces the computational cost compared to the exact MHE-UI algorithm.