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 analysis of the divergence problem in the Kalman filter

Abstract: The effect of modeling errors in a linear discrete stochastic system upon the Kalman filter state estimates is investigated. Errors in both plant dynamics and noise covariances are permitted. The errors are characterized in such a manner that a linear recursion relation for the actual estimation error covariances can be derived. Conditions which guarantee that the covariance matrix remains bounded are described in terms of the asymptotic stability of the homogeneous part of the covariance equation and the boundedness of the forcing terms in the inhomogeneous equation.

Accurate Self-Localization in RFID Tag Information Grids Using FIR Filtering

Abstract: Grid navigation spaces nested with the radio-frequency identification (RFID) tags are promising for industrial and other needs, because each tag can deliver information about a local two-dimensional or three-dimensional surrounding. The approach, however, requires high accuracy in vehicle self-localization. Otherwise, errors may lead to collisions; possibly even fatal. We propose a new extended finite impulse response (EFIR) filtering algorithm and show that it meets this need. The EFIR filter requires an optimal averaging interval, but does not involve the noise statistics which are often not well known to the engineer. It is more accurate than the extended Kalman filter (EKF) under real operation conditions and its iterative algorithm has the Kalman form. Better performance of the proposed EFIR filter is demonstrated based on extensive simulations in a comparison to EKF, which is widely used in RFID tag grids. We also show that errors in noise covariances may provoke divergence in EKF, whereas the EFIR filter remains stable and is thus more robust.

Robust Kalman filtering for nonlinear multivariable stochastic systems in the presence of non‐Gaussian noise

Abstract: Summary The presence of outliers can considerably degrade the performance of linear recursive algorithms based on the assumptions that measurements have a Gaussian distribution. Namely, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). Therefore, synthesis of robust algorithms is of primary interest. The Masreliez–Martin filter is used as a natural frame for realization of the state estimation algorithm of linear systems. Improvement of performances and practical values of the Masreliez-Martin filter as well as the tendency to expand its application to nonlinear systems represent motives to design the modified extended Masreliez–Martin filter. The behaviour of the new approach to nonlinear filtering, in the case when measurements have non-Gaussian distributions, is illustrated by intensive simulations. Copyright © 2015 John Wiley & Sons, Ltd.

Dynamic State Estimation With Model Uncertainties Using $H_\infty$ Extended Kalman Filter

Abstract: When implementing Kalman filters to track system dynamic state variables, the dynamical model is assumed to be accurate. However, this assumption may not hold true as power system dynamical model is subjected to various uncertainties, such as varying generator transient reactance in different operation conditions, uncertain inputs, or noise statistics. As a result, the performance of Kalman-type filters can be degraded significantly. To bound the influence of these uncertainties, this letter proposes an $H_\infty$ extended Kalman filter (HEKF) based on the robust control theory. An approach to tune the parameter of HEKF is presented as well. Numerical results on the IEEE 39-bus system demonstrate the effectiveness of the HEKF.