On the identification of active constraints
SIAM Journal on Numerical Analysis
A robust sequential quadratic programming method
Mathematical Programming: Series A and B
Identifiable surfaces in constrained optimization
SIAM Journal on Control and Optimization
Interior point methods for optimal control of discrete time systems
Journal of Optimization Theory and Applications
On the Accurate Identification of Active Constraints
SIAM Journal on Optimization
Active Sets, Nonsmoothness, and Sensitivity
SIAM Journal on Optimization
Brief paper: A parametric programming approach to moving-horizon state estimation
Automatica (Journal of IFAC)
Brief paper: State estimation for linear systems with state equality constraints
Automatica (Journal of IFAC)
Robust adaptive beamforming based on the Kalman filter
IEEE Transactions on Signal Processing - Part II
The marginal likelihood for parameters in a discrete Gauss-Markovprocess
IEEE Transactions on Signal Processing
Brief Regularization networks for inverse problems: A state-space approach
Automatica (Journal of IFAC)
Hi-index | 22.14 |
Kalman-Bucy smoothers are often used to estimate the state variables as a function of time in a system with stochastic dynamics and measurement noise. This is accomplished using an algorithm for which the number of numerical operations grows linearly with the number of time points. All of the randomness in the model is assumed to be Gaussian. Including other available information, for example a bound on one of the state variables, is non trivial because it does not fit into the standard Kalman-Bucy smoother algorithm. In this paper we present an interior point method that maximizes the likelihood with respect to the sequence of state vectors satisfying inequality constraints. The method obtains the same decomposition that is normally obtained for the unconstrained Kalman-Bucy smoother, hence the resulting number of operations grows linearly with the number of time points. We present two algorithms, the first is for the affine case and the second is for the nonlinear case. Neither algorithm requires the optimization to start at a feasible sequence of state vector values. Both the unconstrained affine and unconstrained nonlinear Kalman-Bucy smoother are special cases of the class of problems that can be handled by these algorithms.