Acoustic and ultrasonic propagation results in a Linear Invariant Filter (LIF). Its complex gain is most often described by a ‘frequency power law’. Equivalently, the complex gain is the characteristic function (c.f.) of a ‘stable probability law’. This strong property justifies a modelization by ‘random propagation times’, which together predict the measured attenuations and obey the principle of energy balance. Except for a Gaussian component, propagation through the atmosphere has no connection with ‘frequency power laws’. In this paper, we show that other components are c.f. of probability laws linked to Poisson and exponential random variables (r.v). Consequently, random propagation times are able to explain propagation losses in the atmosphere.

We address the problem of partitioning a network of nano-satellites to distribute fairly the network load under energy consumption constraints. The study takes place in a context where this swarm of nano-satellites orbits the Moon and works as, but not limited to, a distributed radio-telescope for low-frequency radio interferometry. During an interferometry mission, each nano-satellite collects observation data, then shares them with the other swarm members to compute a global image of space. However, the simultaneous transmission of large volumes of data can cause communication issues by overloading the radio channel, leading to potential packet loss. In this context, we investigate three division algorithms based on graph sampling techniques. We prove that random walk-based algorithms overall perform the best in terms of conservation of graph properties and fairness for group sizes down to 10% of the original graph.

In the last decade, it has been quickly recognized that backhauling Low Power Wide Area Networks (LPWAN) through Low Earth Orbit (LEO) satellites paves the way to the development of novel applications for a truly ubiquitous Internet of Things (IoT). Among LPWAN communications technologies, Narrowband IoT (NB-IoT) does not suffer from interference by other concurrent technologies since it works on a licensed frequency spectrum. At the same time, thanks to its medium access scheme based on contention resolution and resource allocation, NB-IoT is a key enabler for the specific market slice of IoT applications requiring a good level of reliability. In the architectural configuration analyzed throughout this contribution, an NB-IoT low power User Equipment (UE) can communicate with a LEO satellite equipped with an Evolved Node B (eNB) for a time limited to the visibility window of that satellite from the UE position on the Earth. However, the Doppler effect inherent to the time-varying relative speed of the eNB needs to be dealt with additional resources. The solutions proposed until now are non-trivial, thus making the use of NB- IoT for ground-to-satellite communications still expensive and energetically inefficient. Timely, this contribution proposes a procedure for a UE to infer the future values of the Doppler shift from the beacon signals so that frequency pre-compensation can be easily applied in the following interactions during the visibility time. The presented simulation results show that a UE needs to listen to about 10 beacon signals in 1 second to accurately and robustly predict the Doppler curve, thus enabling a lightweight (and eventually truly energy-efficient) implementation of NB-IoT over ground-to-satellite links.

In this communication, we derive a new intrinsic Cramér-Rao bound for both parameters and observations lying on Lie groups. The expression is obtained by using the intrinsic properties of Lie groups. An exact expression is obtained for the case where parameters and observations are in SE(2), the semi-direct Lie group of 2D rotation and 2D translation. To support the discussion, the proposed bound is numerically validated for a Lie group Gaussian model on SE(2).

This paper aims to characterize the estimation precision at the output of the GNSS receiver tracking stage. We define an original statistical modelling of the GNSS tracking loop, which can then be exploited by an optimal linear Kalman Filter (KF) in order to obtain an analytical expression of the steady-state regime. The latter is designed to encompass dynamic information of the GNSS receiver. Two observation models are of interest: the first one considers the propagation delay and Doppler parameters, and the second one also including the Doppler rate, i.e., the acceleration, which is known to be relevant for high dynamics scenarios and can easily be included into the acquisition step. Within this context, the steady-state asymptotic performance of the tracking stage is obtained by solving an algebraic discrete Riccati equation. In both cases, simulation results are provided to show the validity of the proposed approach and the resulting steady-state performance.

Global Navigation Satellite Systems (GNSS) are a key player in a plethora of applications. For navigation purposes, interference scenarios are among the most challenging operation conditions, which clearly impact the maximum likelihood estimates (MLE) of the signal synchronization parameters. While several interference mitigation techniques exist, a theoretical analysis on the GNSS MLE performance degradation under interference, being fundamental for system/receiver design, is a missing tool. The main goal of this contribution is to introduce a mathematical tool to evalute the effect of any type of interference on any GNSS signal. Regarding such tool, we provide closedform expressions of the misspecified Cram´er-Rao (MCRB) bound and estimation bias, for a generic GNSS signal corrupted by an interference. The proposed expressions are used to analyze the GNSS performance degradation induced by the distance measuring equipment (DME) system.

This paper tackles the problem of missing data imputation for noisy and non-Gaussian data. A classical imputation method, the Expectation Maximization (EM) algorithm for Gaussian mixture models, has shown interesting properties when compared to other popular approaches such as those based on k-nearest neighbors or on multiple imputations by chained equations. However, Gaussian mixture models are known to be non-robust to heterogeneous data, which can lead to poor estimation performance when the data is contaminated by outliers or follows non-Gaussian distributions. To overcome this issue, a new EM algorithm is investigated for mixtures of elliptical distributions with the property of handling potential missing data. This paper shows that this problem reduces to the estimation of a mixture of Angular Gaussian distributions under generic assumptions (i.e., each sample is drawn from a mixture of elliptical distributions, which is possibly different for one sample to another). In that case, the complete-data likelihood associated with mixtures of elliptical distributions is well adapted to the EM framework with missing data thanks to its conditional distribution, which is shown to be a multivariate t-distribution. Experimental results on synthetic data demonstrate that the proposed algorithm is robust to outliers and can be used with non-Gaussian data. Furthermore, experiments conducted on real-world datasets show that this algorithm is very competitive when compared to other classical imputation methods.

The aviation Minimum Operational Performance Standard defines the SBAS protection levels as the product of the estimated standard deviation of the positioning error and a scaling factor called K-factor. The K-factor depends on the time window of interest and on the correlation between errors in the time window. The K-factors defined in aviation are difficult to generalize to other specifications in other domains, such as rail and maritime applications. This article presents a simple formula to calculate the K-factor for any value of integrity risk and time interval. The resulting K-factor is shown to be mathematically rigorous under the hypothesis of Gaussian error distribution but without any assumption on the correlation structure of the successive position estimates. The Gaussian assumption can be relaxed and replaced by overbounding with a Gaussian distribution with a very good approximation. This formula can be used in any GNSS application where integrity is needed.