Topic
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.
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Dissertation•
15 Sep 2015
TL;DR: In this article, the authors explore the use of non-linear state errors to devise extended Kalman filters (EKFs) for non-invariant systems and derive mathematical properties of the invariant EKF under standard observability assumptions.
Abstract: The present thesis explores the use of non-linear state errors to devise extended Kalman filters (EKFs). First we depart from the theory of invariant observers on Lie groups and propose a more general yet simpler framework allowing to obtain non-linear error variables having the novel unexpected property of being governed by a (partially) linear differential equation. This result is leveraged to ensure local stability of the invariant EKF (IEKF) under standard observability assumptions, when extended to this class of (non-invariant) systems. Real applications to some industrial problems in partnership with the company SAGEM illustrate the remarkable performance gap over the conventional EKF. A second route we investigate is to turn the noise on and consider the invariant errors as stochastic processes. Convergence in law of the error to a fixed probability distribution, independent of the initialization, is obtained if the error with noise turned off is globally convergent, which in turn allows to assess gains in advance that minimize the error's asymptotic dispersion. The last route consists in stepping back a little and exploring general EKFs (beyond the Lie group case) relying on a non-linear state error. Novel mathematical (global) properties are derived. In particular, these methods are shown to remedy the famous problem of false observability created by the EKF if applied to simultaneous localization and mapping (SLAM), which is a novel result.
36 citations
08 Jun 2015
TL;DR: The paper should be viewed as a proof-of-principle and it is shown by measurements that phase based positioning can be a promising solution for movement tracking in cellular systems with extraordinary accuracy.
Abstract: High resolution radio based positioning and tracking is a key enabler for new or improved cellular services. In this work, we are aiming to track user movements with accuracy down to centimeters using standard cellular bandwidths of 20–40 MHz. The goal is achieved by using phase information from the multi-path components (MPCs) of the radio channels. First, an extended Kalman filter (EKF) is used to estimate and track the phase information of the MPCs. Each of the tracked MPCs can be seen as originating from a virtual transmitter at an unknown position. By using a time difference of arrival (TDOA) positioning algorithm based on a structure-of-motion approach and translating the tracked phase information into propagation distances, the user movements can be estimated with a standard deviation of the error of 4.0 cm. The paper should be viewed as a proof-of-principle and it is shown by measurements that phase based positioning can be a promising solution for movement tracking in cellular systems with extraordinary accuracy.
36 citations
TL;DR: In this paper, the Kalman filter is introduced for linear systems on time scales, including the discrete and continuous versions as special cases, and it is shown that the duality of the KF and the LQR is preserved in their unification.
36 citations
TL;DR: In this paper, a cubature Kalman filter (CKF) + extended Kalman filters (EKF + EKF)-based hybrid filtering method was proposed to reduce the computational burden of the PPP/IMU tightly coupled navigation system by applying a linear filtering method to estimate the linear states mainly GPS related states, while a nonlinear filtering method for estimating nonlinear states such as IMU related states.
Abstract: Implementing the global positioning system (GPS) total carrier phase observations based on the precise point positioning (PPP) technique in a navigation Kalman filter can improve the position accuracy of a GPS/inertial measurement unit (IMU) tightly coupled navigation system to the sub-meter level. However, the carrier phase implementation introduces extra states such as ambiguities, to the Kalman filter state vector, which increases the computational burden especially when nonlinear filtering methods are applied. In this paper, in order to reduce the computational burden of the PPP/IMU tightly coupled navigation system, a cubature Kalman filter (CKF) + extended Kalman filter (EKF) hybrid filtering method by applying a linear filtering method to estimate the linear states mainly GPS related states, while a nonlinear filtering method to estimate the nonlinear states such as IMU related states, is proposed. The hybrid filtering method can make a balance between keeping the CKF benefits in dealing with nonlinear problems and reducing the computational time. The simulation and experiment results show the effectiveness of the method.
36 citations
TL;DR: In this paper, a particle filtering approach was proposed for the assimilation of nonlinear Lagrangian trajectories into a point-vortex system, which does not impose Gaussianity on either the prior or the posterior distributions at the update step.
36 citations