International audienceIn this paper we generalize the Continuous-Discrete Extended Kalman Filter (CD-EKF) to the case where the state and the observations evolve on connected unimodular matrix Lie groups. We propose a new assumed density filter called Continuous-Discrete Extended Kalman Filter on Lie Groups (CD-LG-EKF). It is built upon a geometrically meaningful modeling of the concentrated Gaussian distribution on Lie Groups. Such a distribution is parametrized by a mean and a co-variance matrix defined on the Lie group and in its associated Lie algebra respectively. Our formalism yields tractable equations for both non-linear continuous time propagation and discrete update of the distribution parameters under the assumption that the posterior distribution of the state is a concentrated Gaussian. As a side effect, we contribute to the derivation of the first and second order differential of the matrix Lie group logarithm using left connection. We also show that the CD-LG-EKF reduces to the usual CD-EKF if the state and the observations evolve on Euclidean spaces. Our approach leads to a systematic methodology for the design of filters, which is illustrated by the application to a camera pose filtering problem with observations on Lie group. In this application, the CD-LG-EKF significantly outperforms two constrained non-linear filters (one based on a linearization technique and the other on the unscented transform) applied on the embedding space of the Lie group
Multipath propagation causes major impairments to global positioning system (GPS) based navigation. Multipath results in biased GPS measurements, hence inaccurate position estimates. In this paper, multipath effects are considered as abrupt changes affecting the navigation system. A multiple model formulation is proposed whereby the changes are represented by a discrete valued process. The detection of the errors induced by multipath is handled by a Rao-Blackwellized particle filter (RBPF).The RBPF estimates the indicator process jointly with the navigation states and multipath biases. The interest of this approach is its ability to integrate a priori constraints about the propagation environment. The detection is improved by using information from near future GPS measurements at the particle filter (PF) sampling step. A computationally modest delayed sampling is developed, which is based on a minimal duration assumption for multipath effects. Finally, the standard PF resampling stage is modified to include an hypothesis test based decision step.
The Internet of Things (IoT) finds widespread applications spanning from consumer services such as smart home or domotic to strategic use cases, including infrastructure or energy management. Different technologies have been proposed to support IoT and this paper aims at analyzing the Long Range (LoRA) one. After introducing the main principles of the physical layer, the main contribution is a theoretical performance analysis. Closed-form expression of the symbol and bit error probabilities are derived that are validated by simulation results.
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