Set-membership state estimation with fleeting data

Abstract

Abstract-This paper deals with offline nonlinear state estimation where measurements are available only when some given equality conditions are satisfied. For this type of problems, which are often met in robot localization when sonar or radar are involved, the data are qualified as fleeting because the measurements are available only at some given unknown dates. In this paper, the first approach able to deal with nonlinear estimation with fleeting data is presented. An illustration related to offline robot localization with a laser rangefinder will be given.

Reliable non-linear state estimation involving time uncertainties

“…Assume that a localization of the robot is based on the perception of a wreck for which the highest point w is precisely geolocalized. As pictured in Figure 1, the wreck image W(t) obtained by the sonar may be distorted, stretched and would be highly noisy in practice, depending on the robot navigation [18]. It is a difficult problem for image processing algorithms to detect the highest point w in W to be used as reference for localization.…”

“…A computer representation based on a set of boxes that sample the tube over time has been mentioned in [18,6,26]. …”

“…A tube is defined [17,13] over a domain [t 0 , t f ] as an envelope enclosing an uncertain trajectory x(·). We will use the definition given in [18,6] where Figure 2 illustrates a scalar tube enclosing a trajectory x * (·). For the sake of simplicity, the following tubes mentioned in Sections 2.2-3.1 will be of dimension 1, without loss of generality.…”

“…Hence, the problem becomes much more complex as the uncertainties related to the t i are difficult to propagate through the differential equation. Some attempts of using interval analysis have been proposed in [5,18], but the corresponding observers cannot be considered as guaranteed. Other works, often referred as Out Of Sequence Measurement (OOSM) [9], state problems of time delay uncertainties, which can be somehow related to our problem.…”

Set-Membership Estimation of Hybrid Systems via SAT Modulo ODE

“…SME tech- niques have reached a mature stage when dealing with linear or nonlinear discrete-time models; see a.o. (Milanese and Novara, 2011;Kieffer and Walter, 2011;Jaulin, 2011;Le Bars et al, 2012), and the references therein. Bemporad et al (2005) addressed SME with piecewise affine systems.…”