Fully Adaptive Gaussian Mixture Metropolis-Hastings Algorithm

Markov Chain Monte Carlo methods are widely used in signal processing and communications for statistical inference and stochastic optimization. In this work, we introduce an efficient adaptive Metropolis-Hastings algorithm to draw samples from generic multi-modal and multi-dimensional target distributions. The proposal density is a mixture of Gaussian densities with all parameters (weights, mean vectors and covariance matrices) updated using all the previously generated samples applying simple recursive rules. Numerical results for the one and two-dimensional cases are provided

EAGLE multi-object AO concept study for the E-ELT

EAGLE is the multi-object, spatially-resolved, near-IR spectrograph instrument concept for the E-ELT, relying on a distributed Adaptive Optics, so-called Multi Object Adaptive Optics. This paper presents the results of a phase A study. Using 84x84 actuator deformable mirrors, the performed analysis demonstrates that 6 laser guide stars and up to 5 natural guide stars of magnitude R<17, picked-up in a 7.3' diameter patrol field of view, allow us to obtain an overall performance in terms of Ensquared Energy of 35% in a 75x75 mas^2 spaxel at H band, whatever the target direction in the centred 5' science field for median seeing conditions. The computed sky coverage at galactic latitudes |b|~60 is close to 90%.Comment: 6 pages, to appear in the proceedings of the AO4ELT conference, held in Paris, 22-26 June 200

Resource-Constrained Adaptive Search and Tracking for Sparse Dynamic Targets

This paper considers the problem of resource-constrained and noise-limited localization and estimation of dynamic targets that are sparsely distributed over a large area. We generalize an existing framework [Bashan et al, 2008] for adaptive allocation of sensing resources to the dynamic case, accounting for time-varying target behavior such as transitions to neighboring cells and varying amplitudes over a potentially long time horizon. The proposed adaptive sensing policy is driven by minimization of a modified version of the previously introduced ARAP objective function, which is a surrogate function for mean squared error within locations containing targets. We provide theoretical upper bounds on the performance of adaptive sensing policies by analyzing solutions with oracle knowledge of target locations, gaining insight into the effect of target motion and amplitude variation as well as sparsity. Exact minimization of the multi-stage objective function is infeasible, but myopic optimization yields a closed-form solution. We propose a simple non-myopic extension, the Dynamic Adaptive Resource Allocation Policy (D-ARAP), that allocates a fraction of resources for exploring all locations rather than solely exploiting the current belief state. Our numerical studies indicate that D-ARAP has the following advantages: (a) it is more robust than the myopic policy to noise, missing data, and model mismatch; (b) it performs comparably to well-known approximate dynamic programming solutions but at significantly lower computational complexity; and (c) it improves greatly upon non-adaptive uniform resource allocation in terms of estimation error and probability of detection.Comment: 49 pages, 1 table, 11 figure