Invariant extended Kalman filter

About: Invariant extended Kalman filter is a research topic. Over the lifetime, 7079 publications have been published within this topic receiving 187702 citations.

Synchronization through filtering

Abstract: We study the synchronization problem in discrete-time via an extended Kalman filter (EKF). That is, synchronization is obtained of transmitter and receiver dynamics in case the receiver is given via an EKF that is driven by a noisy drive signal from a noisy transmitter dynamics. The convergence of the filter dynamics towards the transmitter dynamics is rigorously shown using recent results in extended Kalman filtering. Two extensive simulation examples show that the filter is indeed suitable for synchronization of (noisy) chaotic transmitter dynamics. An application to private communication is also given.

Dual Kalman Filtering Methods for Nonlinear Prediction, Smoothing and Estimation

Abstract: Prediction, estimation, and smoothing are fundamental to signal processing. To perform these interrelated tasks given noisy data, we form a time series model of the process that generates the data. Taking noise in the system explicitly into account, maximum-likelihood and Kalman frameworks are discussed which involve the dual process of estimating both the model parameters and the underlying state of the system. We review several established methods in the linear case, and propose several extensions utilizing dual Kalman filters (DKF) and forward-backward (FB) filters that are applicable to neural networks. Methods are compared on several simulations of noisy time series. We also include an example of nonlinear noise reduction in speech.

A Neuro-Fuzzy Assisted Extended Kalman Filter-Based Approach for Simultaneous Localization and Mapping (SLAM) Problems

Abstract: Extended Kalman filter (EKF) has been a popular choice to solve simultaneous localization and mapping (SLAM) problems for mobile robots or vehicles. However, the performance of the EKF depends on the correct a priori knowledge of process and sensor/measurement noise covariance matrices (Q and R, respectively). Imprecise knowledge of these statistics can cause significant degradation in performance. The present paper proposes the development of a new neurofuzzy based adaptive Kalman filtering algorithm for simultaneous localization and mapping of mobile robots or vehicles, which attempts to estimate the elements of the R matrix of the EKF algorithm, at each sampling instant when a ldquomeasurement updaterdquo step is carried out. The neuro-fuzzy based supervision for the EKF algorithm is carried out with the aim of reducing the mismatch between the theoretical and the actual covariance of the innovation sequences. The free parameters of the neuro-fuzzy system are learned offline, by employing particle swarm optimization in the training phase, which configures the training problem as a high-dimensional stochastic optimization problem. By employing a mobile robot to localize and simultaneously acquire the map of the environment, under several benchmark environment situations with varying landmarks and under several conditions of wrong knowledge of sensor statistics, the performance of the proposed scheme has been evaluated. It has been successfully demonstrated that in each case, the neuro-fuzzy assistance is able to improve highly unpredictable, degrading performance of the EKF and can provide robust and accurate solutions.