Intrinsic lower bounds on the intrinsic mean square error are of major importance to characterize the best achievable estimation performance of any unbiased estimator on smooth manifold as Lie group (LG). When the parameter is described by a LG model and the observation noise is with unknown variance, it is also necessary to determine a bound both on the LG parameter and this variance. In this communication, we propose an intrinsic generic Fisher information matrix taking into account this problem. To achieve that, we derive an intrinsic Slepian-Bangs formula on the LG product of the unknown parameter of interest and the LG of positive scalar values in which the variance intrinsically lies. The proposed bound is validated on a Gaussian observation model for unknown parameter lying to SE (3) and variance noise on R+.

In this article, we first derive a general intrinsic Barankin bound (IBB) for unknown parameters lying on Lie groups (LGs), and its intrinsic McAulay-Seidman bound (IMSB) approximation. Second, the IMSB expression is used to revisit the intrinsic Cramér-Rao bound (ICRB) on LGs. Indeed, an analytic expression of the ICRB, which is a special IMSB case, is obtained from the latter. Finally, closed-form expressions for both IMSB and ICRB are obtained for Euclidean and LG observation models depending on parameters lying in SO(3) and SE(3). The validity of the these IMSB and ICRB expressions, with respect to the intrinsic mean square error, is shown via numerical simulations to support the discussion.

The study of ground reflections of Global Navigation Satellite System (GNSS) signals, as in GNSS Reflectometry (GNSS-R) can lead to the receiver height estimation. The latter is estimated by comparing the time of arrival difference between the direct and reflected signals, also called path separation. In ground-based scenarios, this path separation can be very small, inducing important interference between paths, which makes it difficult to correctly obtain altimetry products. The path separation estimation can be obtained by a brute force dual source maximum likelihood estimator (2S-MLE), but this solution has a large computational cost. On the other hand, the path separation is so small that a number of approximations can be done. In this study, a third order Taylor approximation of the dual source likelihood criterion is proposed to reduce its complexity. The proposed algorithm performance is compared to the non approximated 2S-MLE for the estimation of the path separation, and to a standard single source processing for the estimation of the direct signal time-delay. These results, along with the corresponding lower bounds, prove that the proposed approach may be of interest for two applications: ground-based GNSS-R altimetry (or radar with low elevation targets) and GNSS multipath mitigation.

This paper investigates a general framework for the registration of 3D magnetic resonance (MR) and 2D ultrasound (US) images. This framework is divided into a rigid slice-tovolume 3D-2D MR/US registration and a 2D-2D US/MRI fusion algorithm to generate an image having a better resolution than the MR image and a better contrast than the US image. The accuracy of the joint registration and fusion method is analyzed by means of quantitative and qualitative tests conducted on experimental phantom and realistic synthetic data generated from an in vivo MRI volume, with a specific attention to endometriosis treatment.

Interferences are an important threat for applications relying on Global Navigation Satellite Systems (GNSS). Interferences degrade GNSS performance, and can lead to denial of service. The most notable intentional interference family is characterized by its constant envelope, e.g. chirp and tone interferences. Due to its simple structure, the space to search the interference contribution yields to complex circles, allowing the introduction of some latent variables related to those circles. In order to mitigate the interference effect, we compute the maximum likelihood estimator of the parameters of interest (time delay and Doppler shift) in presence of those latent variables. Thus, we resort to the Expectation Maximization algorithm which has already been proved to be efficient in such cases. Experiments conducted on synthetic signals highlight the efficiency of the proposed algorithm.

In this article, we investigate on a new method to jointly design the navigation message with an error correcting scheme. This joint design exploits the "carousel" nature of the broadcasted navigation message and allows both: i) to reduce the Time To First Fix (TTFF) and ii) to enhance the error correcting performances under favorable and challenging channel conditions. We show that the joint design requires error correcting schemes characterized by Maximum Distance Separable (MDS) and the full diversity properties. Those error correcting codes are referred to as Root LowDensity Parity Check (Root-LDPC) codes and they can efficiently operate on block varying channels, enabling the efficient and rapid recovery of information over possibly non ergodic channels. Finally, in order to ensure the data demodulation performance over harsh condition, we propose Root-LDPC codes endowed with the nested property, which allows to inherently adapt the channel coding rate depending on the number of received blocks. The proposed error correcting joint design is then simulated and compared with the well-known GPS L1C subframe 2 structure under several transmission scenarios. Simulations showthatwe can have some enhancement of the error correction performance and a reduction of the TTFF for some scenarios.

State estimation techniques appear in a plethora of engineering fields. Both standard Kalman filter (KF) and its nonlinear extensions, as well as particle filters, consider a known system model (i.e., functions and noise statistics), an assumption which may not hold in practice. A problem of particular interest is how to deal with outliers in the observation model. A possible solution is to resort to the framework of robust statistics, where a robust score function is used to mitigate the impact of outlying measurements, leading to robust M-type KFs. In this contribution, some of these robust filtering results are extended to the case where states may live on a manifold (unit norm quaternion), and propose robust iterated error-state M-type KF solutions. An illustrative example is provided to show the performance of the proposed filter and support the discussion.

Cet article présente un nouvel algorithme de recalage d’images par résonance magnétique (IRM) 3D et d’images échographiques (US) 2D. Le recalage prend en compte une transformation rigide globale caractérisée par des paramètres de rotation et de translation qui est associée à une déformation locale basée sur des fonctions B-splines. Un algorithme de fusion 2D-2D US-IRM est ensuite appliqué pour générer l’image finale qui contient les principales caractéristiques des deux images d’origine. La performance de la méthode de recalage est analysée au moyen de tests quantitatifs et qualitatifs effectués sur un ensemble de données réelles, avec une attention particulière au traitement de l’endométriose.