The state space description of some physical systems possess nonlinear equality
constraints between some state variables. In this paper, we consider the problem of applying …

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with
Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear …

This paper considers the state-estimation problem with a constraint on the data-injection
gain. Special cases of this problem include the enforcing of a linear equality constraint in the …

Kalman filters are commonly used to estimate the states of a dynamic system. However, in
the application of Kalman filters there is often known model or signal information that is …

This report presents and derives the Kalman filter and the Extended Kalman filter dynamics.
The general filtering problem is formulated and it is shown that, under linearity and Gaussian …

This paper presents the Smoothly Constrained Kalman Filter (SCKF) for nonlinear
constraints. A constraint is any relation that exists between the state variables. Constraints …

A theoretical analysis is presented of the correction step of the Kalman filter (KF) and its
various approximations for the case of a nonlinear measurement equation with additive …

A simple procedure to include state inequality constraints in the unscented Kalman filter is
proposed. With this procedure, the information of active state constraints influences the state …

We analyze the behavior of the extended Kalman filter as a state estimator for nonlinear
deterministic systems. Using the direct method of Lyapunov, we prove that under certain …

The Kalman filter is the Bayesian optimum solution to the problem of sequentially estimating
the states of a dynamical system in which the state evolution and measurement processes …