Improved estimation performance using known linear constraints
Automatica (Journal of IFAC)
Brief paper: Optimal control for linear systems with state equality constraints
Automatica (Journal of IFAC)
Improved state estimation of stochastic systems
MATH'07 Proceedings of the 12th WSEAS International Conference on Applied Mathematics
Brief paper: On the constrained small-time controllability of linear systems
Automatica (Journal of IFAC)
Improved estimation of state of stochastic systems via invariant embedding technique
WSEAS Transactions on Mathematics
An inequality constrained nonlinear Kalman-Bucy smoother by interior point likelihood maximization
Automatica (Journal of IFAC)
A robust null space method for linear equality constrained state estimation
IEEE Transactions on Signal Processing
Reparameterization for statistical state estimation applied to differential equations
Journal of Computational Physics
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This paper deals with the state estimation problem for linear systems with linear state equality constraints. Using noisy measurements which are available from the observable system, we construct the optimal estimate which also satisfies linear equality constraints. For this purpose, after reviewing modeling problems in linear stochastic systems with state equality constraints, we formulate a projected system representation. By using the constrained Kalman filter for the projected system and comparing its filter Riccati equation with those of the unconstrained and the projected Kalman filters, we clearly show, without using optimality, that the constrained estimator outperforms the other filters for estimating the constrained system state. Finally, a numerical example is presented, which demonstrates performance differences among those filters.