19 mars 2019

Catégorie : Doctorant

Titre : Statistical learning on manifolds for attitude and position inference

Sujet de thèse au Gipsa-Lab en traitement du signal

**Contexte :**

Attitude and position estimation as well as tracking is a crucial problem that occurs in a wide range of applications. It has attracted continuous attention in the last decades in satellite positioning, radar, robotics, to name just a few. Being able to track a vectorial quantity/direction with a real-time algorithm is still not a completely solved problem and only approximate solutions are available today.

In the context where the recording sensors are inside a moving vehicle or inside of a building, many external perturbations add up and performing a thorough estimation of the time-varying state of the body and of the magnetic heading is an even more complicated challenge. Among the possibly recorded datas, the magnetic field is exposed to many non-stationary noise sources and a smart denoising scheme needs to be developed to fully exploit the signal.

Developing algorithms which are able to accurately track, in a noisy environment, the true magnetic north is thus a challenging problem with many potential applications. When the measurements (magnetic and inertial) are made inside a building, external sources of noise are the ones that alter the most the recorded signals. In addition, as the recorded quantities are vectorial by nature (magnetic field and motion), the extension of classical optimal tracking filters/algorithms (Kalman) is not trivial. One needs to take into account the non-linear nature of the system evolution to tackle the problem, together with a high robustness to error model and/or variability. Extended Kalman filter (EKF) is a known approximate solution that allows to deal with non-linearity \cite[ref1,ref2,ref3]. Some authors have also incorporated the directional nature of the measurement by using different noise model based on directional statistics (von-Mises Fisher) rather than Gaussian.

The proposed work will consist in exploring different approaches to estimate the attitude and position of the body by using magnetic, inertial and vision measures. Vision and depth measures are given by algorithms written in C/C+, whereas the other measures are physical sampled signals. Each type of measure has its own bias, drift, and possible perturbation, but we aim at designing new estimation algorithms. A possible track will consist in developing a thorough model of the measured signals (continuous time and discrete time) in the context of developing a filtering algorithm to track accurately the magnetic north, the attitude and the position in this very noisy/perturbed environment. This could be done using global linearization in the EKF (using the anti-development technique), or by refining the model using directional statistics rather that projected distributions. An other possible way to tackle this problem will be to make use of geometric and spectral description of trivariate signal to filter and estimate the time-varying vector valued signal.

The simultaneous use of different sensors output will need to be taken into account to take advantage of the signal redundancy and noise decorrelation between sensors. Choices will need to be made during the algorithm development to account for efficiency and rapid convergence, together with real-time implementation.

This work will be conducted in collaboration between an academic lab (Gipsa-Lab) and the SYSNAV company. Real datasets acquisition will be made using SYSNAV facilities and will be used to benchmark the developed algorithms. Attention will be paid to applicability of the proposed algorithms and real-time issues, both on simulated and real datasets.

**Compétences attendues :** Master 2R en traitement du signal, mathématiques appliquées, science des données.

**Encadrement : **Nicolas Le Bihan (DR CNRS, Gipsa-Lab) et Christophe Prieur (DR CNRS, Gipsa-Lab)

**Lieu : **Gipsa-Lab, Grenoble

Candidature : Envoyer un CV au format pdf à Nicolas Le Bihan (nicolas.le-bihan@gipsa-lab.fr) et Christophe Prieur (christophe.prieur@gipsa-lab.fr)

**Références :**

[1] D.O. Anderson and J.B. Moore, Optimal filtering, Dover Books on Electrical Engineering, Mineola, N.Y., Dover Publications, 2005.

[2] J. Boulanger, S. Said, N. Le Bihan and J.H. Manton, Filtering from Observations on Stiefel Manifolds, Signal Processing, Vol. 122 , pp. 52-64, 2016.

[3] C.-I. Chesneau, M. Hillion, and C. Prieur, Motion estimation of a Rigid Body with an EKF using Magneto-Inertial Measurements, 7th Conf. on Indoor Positioning and Indoor Navigation (IPIN’16), Madrid, Spain, 2016.

[4] C.-I. Chesneau, M. Hillion, and C. Prieur, Improving magneto-inertial attitude and position estimation by means of a magnetic heading observer, 8th Conf. on Indoor Positioning and Indoor Navigation (IPIN’17), Sapporo, Japan, 2017.

[5] K.V. Mardia and P.E. Jupp, Directional Statistics, Wiley series in probability and statistics, 2008.

(c) GdR 720 ISIS - CNRS - 2011-2019.