The Kalman filter is an optimal estimator with numerous applications in technology, especially in systems with Gaussian distributed noise. Moreover, the adaptive Kalman filtering algorithms, based on the Kalman filter, can control the influence of dynamic model errors. In contrast to the adaptive Kalman filtering algorithms, the H-infinity filter is able to address the interference of the stoch...

Consider the following state space model (signal and observation model). Y t = H t X t + W t , W t ∼ N (0, R) (1) X t = F t X t−1 + U t , U t ∼ N (0, Q) (2)

In this paper, Bayesian nonlinear filtering is considered from the viewpoint of information geometry and a novel filtering method is proposed based on information geometric optimization. Under the Bayesian filtering framework, we derive a relationship between the nonlinear characteristics of filtering and the metric tensor of the corresponding statistical manifold. Bayesian joint distributions ...

In this work we combine ideas from multi-index Monte Carlo and ensemble Kalman filtering (EnKF) to produce a highly efficient method called EnKF (MIEnKF). MIEnKF is based on independent samples of four-coupled estimators hierarchy resolution levels, it may be viewed as an extension the multilevel (MLEnKF) developed by same authors in 2020. Multi-index here refers two-index method, consisting th...

The unscented Kalman filter is a superior alternative to the extended Kalman filter for a variety of estimation and control problems. However, its effectiveness for improving human motion tracking for virtual reality applications in the presence of noisy data has been unexplored. In this paper, we present an empirical study comparing the performance of unscented and extended Kalman filtering fo...

Kalman filtering is introduced as a rational means for developing a monitoring strategy for concrete structures. The mathematics and utility of linear Kalman filters are presented briefly, and the use of linear filters is demonstrated for Fickian diffusion. The nonlinear extended Kalman filter is introduced and its utility in estimating a transport parameter is demonstrated. The concrete servic...