Cécile Durieu

Ellipsoidal estimation under model uncertainty

Abstract Ellipsoidal outer-bounding under model uncertainty is a natural extension of state estimation for models with unknown-but-bounded errors. The technique described in this paper applies to linear discrete-time dynamic systems. Many difficulties arise because of the non-convexity of feasible sets. Analytical optimal or suboptimal solutions are presented, which are counterparts in this context of uncertainty to classical approximations of the sum and intersection of ellipsoids.

Set-Membership Estimation with the Trace Criterion made Simpler than with the Determinant Criterion

Abstract The problem considered is outer ellipsoidal bounding of the state of a MIMO linear discrete-time model with bounded process perturbations and measurement noise. In the literature, two main measures of the size of bounding ellipsoids have been considered, namely the determinant and trace criteria. The determinant criterion is directly related to the volume of the ellipsoid and has been employed most frequently. It may, however, lead to narrow elongated ellipsoids. The trace algorithm tends to avoid this drawback, but has earned a reputation for complexity. We show that it can be made even simpler globally than the determinant algorithm. A complete filter based on the trace criterion is presented.

Low-Computational Cost Estimation Algorithm for Adaptive Optics Systems*

Abstract Astronomical images received by ground-based telescopes are affected by atmospheric turbulence leading to optical deformations. Hence, adaptive optics systems have been developed as a way to compensate for these optical deformations before images arrive to the telescope high resolution camera. The advent of very large telescopes leads to adaptive optics systems requiring a large computational load and leading to an important time delay that deteriorates performances. Through this paper, a novel solution is explored to overcome the high computational cost of the estimation process while still attaining good performances. The aim of the proposed method is to synthesize a reduced-order filter gain using a turbulence model with large number of Zernike modes. Since the algorithm does not synthesize a full-order gain, the computational cost is significantly reduced for the synthesis and the estimation.

Unique criterion to estimate the performances of some laser diode range finders

The purpose of this paper is to present a general method to estimate the intrinsic performances of some laser range finders based on flight time measurement. Classically this flight time can be measured directly, or after a conversion into a phase shift, or into a beat frequency. We prose here a criterion based on signal processing notions, as matched filtering to get the best detection, and ambiguity function to estimate the quality of the detection. The concept of characteristic length is introduced and applied to the different kind of laser range finders, which suggest a new possibility for flight time measurement.

Guaranteed ellipsoidal state estimation for uncertain MIMO models

Abstract This paper extends to uncertain models the classical ellipsoidal outer-bounding of the set of all feasible state vectors with unknown but bounded state perturbations and measurement noise. The technique applies to linear discrete-time dynamic systems and could be extended to weakly non-linear systems. Combined quadratic constraints on model uncertainty and additive disturbances are considered in order to simplify analysis and to allow an analytical solution of the basic problems involved in parameter or state estimation. The results obtained for combined quadratic constraints are extended to other types of model uncertainty.

A Fourier transform spectrometer based on a birefringent interferometer and spectral analysis methods

A compact and without moving parts Fourier Transform spectrometer is presented. The interferometer associates two identical spath Wollaston prisms and a CCD line sensor. Modern spectral analysis methods lead to improve significantly the spectrum estimation.