# Reliable Non-Linear State Estimation Involving Time Uncertainties

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

**Abstract.**
This paper presents a new approach to bounded-error state estimation involving time uncertainties. For a given bounded observation of the system, it is assumed that neither the value of the data nor the acquisition time are known exactly. We show that if the system is described by a continuous-time state equation, then at each time instant a constraint propagation approach enables us to compute bounding sets for the state vectors consistent with the measurement. The bounding property of our method is guaranteed even if the system is non-linear. Compared to other existing constraint approaches, the originality of our method is to enclose the set of all feasible trajectories inside a tube. This makes it possible to build specific operators for the propagation of time uncertainties through the whole trajectory. The efficiency of our approach is illustrated by two examples: the dynamic localization of a mobile robot and the correction of a drifting clock.

**Keywords:**
state estimation, time uncertainties, observations, tubes, robotics, constraints, contractors

## Paper

Currently submitted to Automatica.

## 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**