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 …

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 …

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 …

The Kalman Filter (KF) is one of the most widely used methods for tracking and estimation
due to its simplicity, optimality, tractability and robustness. However, the application of the KF …

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, rooted in the state‐space formulation of linear dynamical systems,
provides a recursive solution to the linear optimal filtering problem. It applies to stationary as …

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 …

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 …

This paper points out the flaws in using the extended Kalman filter (EKE) and introduces an
improvement, the unscented Kalman filter (UKF), proposed by Julier and Uhlman (1997). A …

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 …