# Reliable Non-Linear State Estimation Involving Time Uncertainties

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Simon Rohou, Luc Jaulin, Lyudmila Mihaylova, Fabrice Le Bars, Sandor M. Veres

Published in Automatica, 2018 | Bibtex

**Abstract.**
This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded observation of a continuous-time non-linear system, it is assumed that neither the values of the observed data nor their acquisition instants are known exactly. For systems described by state-space equations, we prove theoretically and demonstrate by simulations that the proposed constraint propagation approach enables the computation of bounding sets for the systems' state vectors that are consistent with the uncertain measurements. The bounding property of the method is guaranteed even if the system is strongly non-linear. Compared with other existing constraint propagation approaches, the originality of the method stems from our definition and use of bounding tubes which enable to enclose the set of all feasible trajectories inside sets. This method makes it possible to build specific operators for the propagation of time uncertainties through the whole trajectory. The efficiency of the approach is illustrated on two examples: the dynamic localization of a mobile robot and the correction of a drifting clock.

**Keywords:**
state estimation, time uncertainties, non-linear systems, tubes, robotics, constraints, contractors

## Tubex library

See the Tubex project.

## Paper examples

Paper examples are available in the Tubex library:

### Localization among low-cost beacons

See: **tubex-lib/examples/cpp/06_lowcost_beacons**

### Reliable correction of a drifting clock

See: **tubex-lib/examples/cpp/07_drifting_clock**