The Kalman filter is the optimal minimum-variance state estimator for linear dynamic systems with Gaussian noise. In addition, the Kalman filter is the optimal linear state estimator for linear dynamic systems with non-Gaussian noise. For nonlinear systems various modifications of the Kalman filter (e.g., the extended Kalman filter, the unscented Kalman filter, and the particle filter) have bee...

In this contribution we extend Kalman-filter theory by introducing a new recursive linear minimum mean squared error (MMSE) filter for dynamic systems with unknown state-vector means. The recursive filter enables the joint MMSE prediction and estimation of the random state vectors and their unknown means, respectively. We show how the new filter reduces to the Kalman-filter in case the state-ve...

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 best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications in...

In this paper principles of extended Kalman filtering theory is developed and applied to simulated on-line electric power systems state estimation in order to trace the operating condition changes through the redundant and noisy measurements. Test results on IEEE 14 - bus test system are included. Three case systems are tried; through the comparing of their results, it is concluded that the pro...

This paper discusses a new Bayesian filter able to estimate the state of static systems (parameter estimation) with any kind of nonlinear measurement equation subject to Gaussian measurement uncertainty. The filter is also applicable to the state estimation for a limited class of dynamic systems. The core idea of the filter is to linearize the process and measurement equation in a higher-dimens...