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.

An improved quaternion-based Kalman filter for real-time tracking of rigid body orientation

Abstract: This paper presents an improved Kalman filter for real-time tracking of human body motions. An earlier version of the filter was presented at IROS 2001. Since then, the filter has been substantially improved. Real-time tracking of rigid body orientation is accomplished using the MARG (magnetic, angular rate, and gravity) sensors. A MARG sensor measures the three-dimensional local magnetic field, three-dimensional angular rate, and three-dimensional acceleration. A Kalman filter is designed to process measurements provided by the MARG sensors, and to produce real-time orientation represented in quaternions. There are many design decisions as related to choice of state vectors, output equations, process model, etc. The filter design presented in this paper utilizes the Gauss-Newton method for parameter optimization in conjunction with Kalman filtering. The use of the Gauss-Newton method, particularly the reduced-order implementation introduced in the paper, significantly simplifies the Kalman filter design, and reduces computational requirements.

Skewed approach to filtering

Abstract: The dynamics of many physical system are nonlinear and non- symmetric. The motion of a missile, for example, is strongly determined by aerodynamic drag whose magnitude is a function of the square of speed. Conversely, nonlinearity can arise from the coordinate system used, such as spherical coordinates for position. If a filter is applied these types of system, the distribution of its state estimate will be non-symmetric. The most widely used filtering algorithm, the Kalman filter, only utilizes mean and covariance and odes not maintain or exploit the symmetry properties of the distribution. Although the Kalman filter has been successfully applied in many highly nonlinear and non- symmetric system, this has been achieved at the cost of neglecting a potentially rich source of information. In this paper we explore methods for maintaining and utilizing information over and above that provided by means and covariances. Specifically, we extend the Kalman filter paradigm to include the skew and examine the utility of maintaining this information. We develop a tractable, convenient algorithm which can be used to predict the first three moments of a distribution. This is achieved by extending the sigma point selection scheme of the unscented transformation to capture the mean, covariance and skew. The utility of maintaining the skew and using nonlinear update rules is assessed by examining the performance of the new filter against a conventional Kalman filter in a realistic tracking scenario.

Observability-based consistent EKF estimators for multi-robot cooperative localization

Abstract: In this paper, we investigate the consistency of extended Kalman filter (EKF)-based cooperative localization (CL) from the perspective of observability. We analytically show that the error-state system model employed in the standard EKF-based CL always has an observable subspace of higher dimension than that of the actual nonlinear CL system. This results in unjustified reduction of the EKF covariance estimates in directions of the state space where no information is available, and thus leads to inconsistency. To address this problem, we adopt an observability-based methodology for designing consistent estimators in which the linearization points are selected to ensure a linearized system model with observable subspace of correct dimension. In particular, we propose two novel observability-constrained (OC)-EKF estimators that are instances of this paradigm. In the first, termed OC-EKF 1.0, the filter Jacobians are calculated using the prior state estimates as the linearization points. In the second, termed OC-EKF 2.0, the linearization points are selected so as to minimize their expected errors (i.e., the difference between the linearization point and the true state) under the observability constraints. The proposed OC-EKFs have been tested in simulation and experimentally, and have been shown to significantly outperform the standard EKF in terms of both accuracy and consistency.

Sequential parameter estimation for stochastic systems

Abstract: . The quality of the prediction of dynamical system evolution is determined by the accuracy to which initial conditions and forcing are known. Availability of future observations permits reducing the effects of errors in assessment the external model parameters by means of a filtering algorithm. Usually, uncertainties in specifying internal model parameters describing the inner system dynamics are neglected. Since they are characterized by strongly non-Gaussian distributions (parameters are positive, as a rule), traditional Kalman filtering schemes are badly suited to reducing the contribution of this type of uncertainties to the forecast errors. An extension of the Sequential Importance Resampling filter (SIR) is proposed to this aim. The filter is verified against the Ensemble Kalman filter (EnKF) in application to the stochastic Lorenz system. It is shown that the SIR is capable of estimating the system parameters and to predict the evolution of the system with a remarkably better accuracy than the EnKF. This highlights a severe drawback of any Kalman filtering scheme: due to utilizing only first two statistical moments in the analysis step it is unable to deal with probability density functions badly approximated by the normal distribution.

Adaptive robust extended Kalman filter for nonlinear stochastic systems

Abstract: The authors analyse the error behaviour of the robust extended Kalman filter (REKF) for nonlinear stochastic systems. On the basis of some standard results about the boundedness of stochastic processes, it is specified that stability of the REKF cannot be guaranteed. In order to solve this problem, a novel method is proposed to design the REKF so that the sufficient conditions to ensure filter stability will be fulfilled. Furthermore, an adaptive scheme is adopted to automatically tune the error covariance matrix in response to the changing environment. Numerical example shows the superiority of the proposed adaptive REKF over the usual extended Kalman filter (EKF), the REKF and the adaptive EKF.