Optimal estimation theory for dynamic systems with set membership uncertainty: an overview
Automatica (Journal of IFAC)
A Smoothly Constrained Kalman Filter
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Brief paper: State estimation for linear systems with state equality constraints
Automatica (Journal of IFAC)
Brief paper: A set-membership state estimation algorithm based on DC programming
Automatica (Journal of IFAC)
Decentralized robust set-valued state estimation in networked multiple sensor systems
Computers & Mathematics with Applications
A robust null space method for linear equality constrained state estimation
IEEE Transactions on Signal Processing
Robust H∞ finite-horizon filtering with randomly occurred nonlinearities and quantization effects
Automatica (Journal of IFAC)
On Kalman Filtering With Nonlinear Equality Constraints
IEEE Transactions on Signal Processing
Automatica (Journal of IFAC)
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In this paper, our previous results on set-membership state estimation for the systems with linear state equality constraints are extended to the systems with both nonlinear state equality constraints and quantized output measurements. The quantization errors in collecting the system output measurements are treated as bounded uncertainties. To achieve the objective in finding the consistent set of state estimates while removing the conservativeness introduced by the Finsler's Lemma, three main techniques are introduced in this paper. Firstly, an improved linearization technique is performed on the nonlinear equality constraints. Secondly, a system model with reduced dimensions is derived, based on which an ellipsoid set of estimates for the state subspace is obtained. Thirdly, we combine the state subspace estimation result with a full-space estimation result obtained by extending a representative method (called the Yang and Li's method) on state estimation with nonlinear state equality constraints and quantization. The estimation results for the full state space in this paper are finally obtained. It is proved that the final set of state estimates is not only ensured to contain the true state, but also less conservative than that obtained by directly extending the Yang and Li's method. Simulation results are provided to validate the theoretical analysis.