Clustering and Informative Path Planning for 3D Gas Distribution Mapping: Algorithms and Performance Evaluation

Chemical gas dispersion can represent a severe threat to human and animal lives, as well as to the environment. Constructing a map of the distribution of gas in a fast and reliable manner is critical to ensure accurate monitoring of at-risk facilities and coordinate targeted and swift rescue missions when an emergency occurs. In recent years, robots have been endowed with gas sensing capabilities, and several algorithms to generate gas maps have been studied, often producing a 2D map. Two of the major drawbacks of these studies are concerned with the fact that the robot’s path is often fixed to a predefined route, and that the tridimensionality of the gas dispersion phenomenon is not captured by the final gas maps. In this letter, we study the effect of a random walk and an adaptive path planning approach based on informative quantities to gas mapping in a 3D environment using a micro aerial vehicle with severe flight time constraints. We also introduce a clustering strategy to enhance the exploration of the environment. The strategies are compared to a lawnmower movement and evaluated against a ground truth map of the environment, both in simulation and with physical experiments, in order to assess which ones are able to provide an accurate gas map, while simultaneously achieving satisfactory coverage of the desired volume under time constraints.

Fast high-dimensional Bayesian classification and clustering

Vahid Partovi Nia

We introduce a fast approach to classification and clustering applicable to high-dimensional continuous data, based on Bayesian mixture models for which explicit computations are available. This permits us to treat classification and clustering in a single framework, and allows calculation of unobserved class probability. The new classifier is robust to adding noise variables as a drawback of the built-in spike-and-slab structure of the proposed Bayesian model. The usefulness of classification using our method is shown on metabololomic example, and on the Iris data with and without noise variables. Agglomerative hierarchical clustering is used to construct a dendrogram based on the posterior probabilities of particular partitions, to provide a dendrogram with a probabilistic interpretation. An extension to variable selection is proposed which summarises the importance of variables for classification or clustering and has probabilistic interpretation. Having a simple model provides estimation of the model parameters using maximum likelihood and therefore yields a fully automatic algorithm. The new clustering method is applied to metabolomic, microarray, and image data and is studied using simulated data motivated by real datasets. The computational difficulties of the new approach are discussed, solutions for algorithm acceleration are proposed, and the written computer code is briefly analysed. Simulations shows that the quality of the estimated model parameters depends on the parametric distribution assumed for effects, but after fixing the model parameters to reasonable values, the distribution of the effects influences clustering very little. Simulations confirms that the clustering algorithm and the proposed variable selection method is reliable when the model assumptions are wrong. The new approach is compared with the popular Bayesian clustering alternative, MCLUST, fitted on the principal components using two loss functions in which our proposed approach is found to be more efficient in almost every situation.

EPFL2009

Sparse Source Recovery from Boundary Measurements using an Extension of Prony's Method for the Poisson Equation

Djano Kandaswamy

Electroencephalography (EEG) is a key modality to monitor brain activity with high temporal resolution. EEG makes use of an array of electrodes to measure the electrical potential on the scalp. While most traditional EEG analyses have looked at EEG rhythms in different frequency bands, another important application of EEG is source imaging; i.e., map back the measured scalp potential to the underlying source distribution. However, source localization is an ill-posed problem. Most approaches consider a grid of neurobiologically relevant dipoles with fixed positions and directions of their moments, which makes for many more unknown intensities than the number of measures. To make the solution unique, one needs to add regularization strategies such as smoothness or sparsity. The alternative, which is the approach that we will follow in this work, is to impose a sparse and parametric source model with few unknown parameters, but which include both dipole positions and moments thus rendering the problem solution highly non-linear. The proposed method, for which we coin the term "analytic sensing", is based on two main working principles. First, based on the divergence theorem, the sensing principle relates the boundary potential to a volumetric information about the sources. This principle makes use of a mathematical test function ("analytic sensor") that needs to be a homogeneous solution of the Poisson equation, which is the governing equation of the quasi-static electromagnetic setting. The analytic sensor can be defined for different geometries and conductivity profiles of the domain of interest. We derive closed-form expressions for 3D multi-layer spherical models that are often used as a head model in EEG. Recent advances in signal processing known as "annihilation filter" or "finite rate of innovation", have extended Prony's method to recover sparse sources in a robust way, typically a stream of Diracs. We propose to apply the annihilation principle by imposing a particular choice of multiple analytic sensors; i.e., the virtual measurements obtained with these functions can be annihilated by a filter that allows us to recover the dipoles' positions in a non-iterative way. The dipoles' moments can subsequently be retrieved by solving a linear system of equations. While the application of the sensing principle is intrinsically 2D or 3D, the annihilation principle gives only access to the orthographic projection of the source distribution. Two approaches have been developed. First, using coordinate transformations, one can obtain multiple projections of the sources and recombine them to reconstruct the full 3D information. Second, using a second set of analytic sensors, it is possible to retrieve the missing coordinate by solving another linear system of equations. Successful application of the method requires careful implementation of both principles. For the sensing principle, we project the boundary measurements on a set of spherical harmonics with proper regularization to cover parts of the boundary that are not measured. We also show how the annihilation step can be implemented to be robust to noise and numerically stable. We demonstrate the precision and robustness of the method by both experimental results and theoretical Cramèr-Rao bounds. Finally, we show effective source localization for real-world experimental EEG data; i.e., we identify the underlying sources for several time instants of a visual evoked potential.

EPFL2011

Mitigating Slow Dynamics of Low-Cost Chemical Sensors for Mobile Air Quality Monitoring Sensor Networks

Adrian Arfire, Ali Marjovi, Alcherio Martinoli

The last decade has seen a growing interest in air quality monitoring using networks of wireless low-cost sensor platforms. One of the unifying characteristics of chemical sensors typically used in real-world deployments is their slow response time. While the impact of sensor dynamics can largely be neglected when considering static scenarios, in mobile applications chemical sensor measurements should not be considered as point measurements (i.e. instantaneous in space and time). In this paper, we study the impact of sensor dynamics on measurement accuracy and locality through systematic experiments in the controlled environment of a wind tunnel. We then propose two methods for dealing with this problem: (i) reducing the effect of the sensor's slow dynamics by using an open active sampler, and (ii) estimating the underlying true signal using a sensor model and a deconvolution technique. We consider two performance metrics for evaluation: localization accuracy of specific field features and root mean squared error in field estimation. Finally, we show that the deconvolution technique results in consistent performance improvement for all the considered scenarios, and for both metrics, while the active sniffer design considered provides an advantage only for feature localization, particularly for the highest sensor movement speed.