In this communication, we propose a new Bayesian framework to characterize the concentration parameter of the von Mises distribution. To achieve this, we equip this parameter with a Lie group structure. We design a Lie group (LG) estimator by incorporating prior information modeled by a Gaussian distribution on$\mathbb{R}^{+}$. This estimator is determined using a dedicated optimization algorithm on$\mathbb{R}^{+}$. The performance of this estimator is then evaluated by computing a new expression of the Bayesian Cramér-Rao bound on the Lie group (LG-BCRB)$\mathbb{R}^{+}$. The consistency between the proposed estimator and the LG-BCRB is validated through numerical simulations by comparing it with the Bayesian Mean Squared Error.

International audience

This contribution explores the optimality properties of integrity monitoring fault detectors by exploiting the hypothesis testing invariance theory. The focus is on three fault detectors widely used in GNSS: the Generalized Likelihood Ratio Test (GLRT), the Least Squares (LS) residuals method, and the Solution Separation (SS) test statistics. The GLRT has been shown to be uniformly most powerful invariant for linear Gaussian models, and the single-state SS test statistic has been proven to be the optimal detector which minimizes the so-called worst-case integrity risk, if the LS estimator is used to estimate the unknown state vector. This work aims i) to make the connection between these two optimal detectors within the invariance framework, and ii) to establish the conditions for their equivalence in the case of a single alternative faulty hypothesis.

Accurate and real-time position estimates are cru-cial for mobile robots. This work focuses on ranging-based positioning systems, which rely on distance measurements between known points, called anchors, and a tag to localize. The topology of the network formed by the anchors strongly influences the tag's localizability, i.e., its ability to be accurately localized. Here, the tag and some anchors are supposed to be carried by robots, which allows enhancing the positioning accuracy by planning the anchors' motions. We leverage Bayesian Cramer-Rao Lower Bounds (CRLBs) on the estimates' covariance in order to quantify the tag's localizability. This class of CRLBs can capture prior information on the tag's position and take it into account when deploying the anchors. We propose a method to decrease a potential function based on the Bayesian CRLB in order to maintain the localizability of the tag while having some prior knowledge about its position distribution. Then, we present a new experiment highlighting the link between the localizability potential and the precision expected in practice. Finally, two real-time anchor motion planners are demonstrated with ranging measurements in the presence or absence of prior information about the tag's position.

Position estimation in Multi-Robot Systems (MRS) relies on relative angle or distance measurements between the robots, which generally deteriorate as distances increase. Moreover, the localization accuracy is strongly influenced both by the quality of the raw measurements but also by the overall geometry of the network. In this paper, we design a cost function that accounts for these two issues and can be used to develop motion planning algorithms that optimize the localizability in MRS, i.e., the ability of individual robots to localize themselves accurately. This cost function is based on computing new Cramér Rao Lower Bounds characterizing the achievable positioning performance with range and angle measurements that deteriorate with increasing distances. We describe a gradient-based motion-planning algorithm for MRS deployment that can be implemented in a distributed manner, as well as a non-myopic strategy to escape local minima. Finally, we test the proposed methodology experimentally for range measurements obtained using ultra-wide band transceivers and illustrate the improvements resulting from leveraging the more accurate measurement model in the robot placement algorithms.

This paper addresses the problem of restoring standing in paralegia via functional electrical stimulation (FES) and investigates the relashionship between body posture and voluntary upper-body movements. A methodology is presented for upper-body posture estimation in the sagittal plane from force and torque measurements exerted on handles during human standing, in the hypothesis of quasi-static equilibrium. The method consists in setting up constraints related to the geometric equations and the hand-handle interaction. All measured quantities are subject to an uncertainty assumed unknown but bounded. The set membership estimation problem is solved via interval analysis. Guaranteed uncertainty bounds are computed for the estimated postures. The methodology is validated experimentally with spinal cord injured patients with lesions between T5 and T12. Possible applications of the developed methodology are lower limbs function rehabilitation within clinical centers, walk assistance and independent mobility for spinal cord injured patients.