The optimal linear Kalman filters (Kalman, 1960b) and their approximative non-linear
extensions (non-linear Kalman filters) for state estimation of stochastic dynamic systems …

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 …

In this paper, we discuss the Kalman filter for state estimation in noisy linear discrete-time
dynamical systems. We give an overview of its history, its mathematical and statistical …

The Kalman filter is a well-known recursive state estimator for linear systems. In practice, the
algorithm is often used for non-linear systems by linearizing the system's process and …

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 technical note deals with the unscented Kalman filter for state estimation of nonlinear
stochastic dynamic systems with a special focus on the scaling parameter of the filter. Its …

This paper studies semi-stability for Kalman filters in the context of linear time-varying
systems with incorrect noise information. Semi-stability is a key property, as it ensures that …

We propose two variants of the Linearized Kalman Filter (LKF). The model linearization is
made about an auxiliary state estimate that can be seen as an exogenous input to the LFK …

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 …

Stability of the Kalman filter for linear time-invariant systems is studied from the perspective
of divergence of the estimation error under incorrect noise measurement. We provide …