Moving Horizon State Estimation in Nonlinear Systems
Summary
Moving horizon state estimation (MHE) has emerged as a powerful optimisation-based technique for reconstructing the internal states of nonlinear dynamical systems from noisy and partial measurements. Unlike recursive filters, such as the extended or unscented Kalman filter, MHE solves a constrained optimisation problem over a sliding time window, minimising a cost function that balances fidelity to recent measurements with an arrival cost that summarises prior information. This formulation readily accommodates state and input constraints, non-Gaussian disturbances and complex nonlinearities, thereby enhancing robustness and reliability in practical applications. Over the past decade, theoretical advances have established conditions for stability and convergence of the estimation error under bounded disturbances, while computational innovations in convex programming and proximal algorithms have reduced the associated numerical burden. As a result, MHE has found applications in aerospace navigation, chemical process monitoring, sensorless motor control and infrastructure health diagnostics, where accurate real-time state reconstruction is critical for feedback control, fault detection and predictive maintenance.
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Moving Horizon State Estimation in Nonlinear Systems publication trend
The graph below shows the total number of articles in moving horizon state estimation in nonlinear systems across all publications each year (not limited to Nature Index journals).
Technical terms
Moving horizon estimation (MHE): An optimisation-based state estimation approach that solves a finite-window constrained minimisation problem incorporating recent measurements and prior information.
Arrival cost: A penalty term in the MHE cost function that summarises the influence of data and uncertainty outside the estimation window, ensuring continuity with past estimates.
Bregman distance: A divergence measure generated by a convex function, used in MHE to encode a priori estimate discrepancies while preserving convexity of the optimisation problem.
Takagi-Sugeno (T-S) fuzzy system: A modelling paradigm that represents a complex nonlinear system as a weighted combination of linear submodels, enabling tractable estimation and control design.
Covariance intersection: A fusion algorithm that combines multiple state estimates without requiring knowledge of their cross-covariances, ensuring conservative yet consistent uncertainty bounds.
References
- A filter design for T-S fuzzy systems based on moving horizon estimator with measurement noise. PeerJ Computer Science (2023).
- A proximity moving horizon estimator for a class of nonlinear systems. International Journal of Adaptive Control and Signal Processing (2020).
- Distributed Moving Horizon Fusion Estimation for Nonlinear Constrained Uncertain Systems. Mathematics (2023).
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