Interval Kalman filter enhanced by positive definite upper bounds

Abstract

A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covariance for all admissible uncertainties. The state estimation is then determined by using interval analysis in order to enclose the set of all possible solutions with respect to the classical Kalman filtering structure.

Fault detection using Upper Bound Interval Kalman Filter for unmaned aerial vehicle

“…As the conventional Kalman filter, the UBIKF can be designed in two steps: prediction and correction. A description of this filter is given in [6] and the main algorithm is recalled below:…”

“…However, an high computational time is required by the proposed algorithm if the considered system is affected by large uncertainties [5]. *This work was not supported by any organization 1 The authors are with LAAS-CNRS, Université de Toulouse, UPS, Toulouse, France cjaubert,sfergani,esaulnier@laas.fr Thus the Minimum Upper Bound of Variance Interval Kalman Filter (UBIKF) has been presented in [6] with two main goals: minimizing an upper bound for the estimation error covariance and enclosing the set of possible solutions of the filtering problem for interval linear systems. Since the gain matrix handled by UBIKF is punctual, this approach encloses all the estimates consistent with the parameter uncertainties in a much less conservative manner than the iIKF.…”

High Integrity Lane Level Localization Using Multiple Lane Markings Detection and Horizontal Protection Levels

“…Assuming that errors are normally distributed is often unrealistic in practice due to outliers [2]. Robust methods have been proposed using more cautious models such as intervals [1], [14] or heavy tail distributions [2], [5]. The aim of these methods is to over-bound the true error distribution resulting in more consistent confidence bounds called protection levels.…”

Robust Iterative Learning Observers Based on a Combination of Stochastic Estimation Schemes and Ellipsoidal Calculus

“…It aims at bounding the arising covariance matrices in both prediction and innovation stages after the specification of desired confidence levels for a quasi-linear state-space representation, i.e., for system and output matrices that may explicitly depend on the state and bounded parameters with unknown probability distributions. In such a way, the use of the ellipsoidal enclosure technique proposed in this paper can be seen as a generalization of the work in [15], where pure parameter uncertainties were accounted for in a time-domain (non-ILO) state estimation.…”