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Cooperative Localization for Autonomous Vehicles Sharing GNSS Measurements
Published in Chao Gao, Guorong Zhao, Hassen Fourati, Cooperative Localization and Navigation, 2019
Khaoula Lassoued, Philippe Bonnifait
The set-membership approach is based on the assumption that errors of models and measurements are bounded. It has been successfully applied for the estimation of model parameters [21] and the estimation of robot positions when reliable confidence domains are required [22]. Meizel et al. [23] developed a set inversion method by using interval analysis techniques (set inversion via interval analysis [SIVIA]) based on bounded error observers for the localization of one robot. In [24], an efficient technique has been proposed to accurately compute a point estimate from a subpaving. However, SIVIA is not suitable for real-time applications when the initial area of research is too large, which leads to an increase in the number of bisections in the computation process. One solution is to use SIVIA while simultaneously solving a CSP to limit the calculation time of bisections [25]. Regarding real-time cooperative localization, several recent studies based on set inversion with the CSP techniques were studied. Drevelle et al. [26] operated a group of autonomous underwater vehicles (UAV) to explore a large area. In their application, they used ranging sensors to measure the inter-distance between robots.
Prognosis of uncertain linear time-invariant discrete systems using unknown input interval observer
Published in International Journal of Control, 2020
E. I. Robinson, J. Marzat, T. Raïssi
Set inversion of a given box by a vector function f aims at characterising the set defined by: Usually, the Set Inverter via Interval Analysis (SIVIA) (Jaulin & Walter, 1993) algorithm is used to approximate the inner and outer approximations and of the set defined by Equation (41), given a set , an inclusion function for f, and an inclusion test defined by: The characterisation of the set with SIVIA is based on three main steps: (i) choice of an initial box supposed to contain at least a part of , (ii) inclusion tests and (iii) bisection.
Interval and linear matrix inequality techniques for reliable control of linear continuous-time cooperative systems with applications to heat transfer
Published in International Journal of Control, 2020
Andreas Rauh, Julia Kersten, Harald Aschemann
As it was shown in Rauh et al. (2018a) as well as Rauh, Kersten, and Aschemann (2018b), interval algorithms can be employed to identify parameters effectively for those cooperative system models mentioned in the introduction of this paper. Usually, this type of identification which inherently makes use of the SIVIA algorithm (set inversion via interval analysis on the basis of measured system outputs, cf. Jaulin et al., 2001) leads to a description of the possible system parameters in terms of the union of L interval boxes which are mutually non-overlapping except for selected edges and vertices. Then, each of these parameter boxes is therefore described by its own interval vector If the underlying ODEs are either linear (due to physically motivated reasoning) or if nonlinearities are overapproximated after the derivation of a quasi-linear state-space representation that is typically also employed if gain-scheduled feedback controllers (Baumann, 1988; Baumann & Rugh, 1986) are to be designed, the system dynamics can be described by the linear parameter-dependent state equations Using Equation (9), a bank of L parallel interval observers can be implemented which allow for estimating guaranteed lower and upper bounds of all states that are compatible with the ODEs (9) and the measurements under consideration of the bounded error interval .
Colour level set regularization for the electromagnetic imaging of highly discontinuous parameters in 3D
Published in Inverse Problems in Science and Engineering, 2021
In contrast, the conductivity reconstruction in Figure 11 associated with for the level set inversion using the sample in the right image of Figure 8 does not perform as well as the others. Even though the reconstruction overall captures the true behaviour of the conductivity profile, its resemblance to the true phantom is slightly worse than the other two sampling techniques, as it should be expected. This most likely occurs because the a priori information given to the algorithm overall underestimates conductivity values in large parts of the domain. Though it is encouraging that even in penalized situations like this the algorithm can still capture many characteristics which are truly present.