Reduced Complexity Filtering with Stochastic Dominance Bounds: A Convex Optimization Approach

This paper uses stochastic dominance principles to construct upper and lower sample path bounds for Hidden Markov Model (HMM) filters. Given a HMM, by using convex optimization methods for nuclear norm minimization with copositive constraints, we construct low rank stochastic marices so that the optimal filters using these matrices provably lower and upper bound (with respect to a partially ordered set) the true filtered distribution at each time instant. Since these matrices are low rank (say R), the computational cost of evaluating the filtering bounds is O(XR) instead of O(X2). A Monte-Carlo importance sampling filter is presented that exploits these upper and lower bounds to estimate the optimal posterior. Finally, using the Dobrushin coefficient, explicit bounds are given on the variational norm between the true posterior and the upper and lower bounds

Multi-Object Tracking with Interacting Vehicles and Road Map Information

In many applications, tracking of multiple objects is crucial for a perception of the current environment. Most of the present multi-object tracking algorithms assume that objects move independently regarding other dynamic objects as well as the static environment. Since in many traffic situations objects interact with each other and in addition there are restrictions due to drivable areas, the assumption of an independent object motion is not fulfilled. This paper proposes an approach adapting a multi-object tracking system to model interaction between vehicles, and the current road geometry. Therefore, the prediction step of a Labeled Multi-Bernoulli filter is extended to facilitate modeling interaction between objects using the Intelligent Driver Model. Furthermore, to consider road map information, an approximation of a highly precise road map is used. The results show that in scenarios where the assumption of a standard motion model is violated, the tracking system adapted with the proposed method achieves higher accuracy and robustness in its track estimations

Robust Filtering and Smoothing with Gaussian Processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of "system identification" is more robust than finding point estimates of a parametric function representation. In this article, we present a principled algorithm for robust analytic smoothing in GP dynamic systems, which are increasingly used in robotics and control. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.Comment: 7 pages, 1 figure, draft version of paper accepted at IEEE Transactions on Automatic Contro

Regression modeling for digital test of ΣΔ modulators

The cost of Analogue and Mixed-Signal circuit testing is an important bottleneck in the industry, due to timeconsuming verification of specifications that require state-ofthe- art Automatic Test Equipment. In this paper, we apply the concept of Alternate Test to achieve digital testing of converters. By training an ensemble of regression models that maps simple digital defect-oriented signatures onto Signal to Noise and Distortion Ratio (SNDR), an average error of 1:7% is achieved. Beyond the inference of functional metrics, we show that the approach can provide interesting diagnosis information.Ministerio de Educación y Ciencia TEC2007-68072/MICJunta de Andalucía TIC 5386, CT 30

Glacial cycles drive variations in the production of oceanic crust

Glacial cycles redistribute water between oceans and continents causing pressure changes in the upper mantle, with consequences for melting of Earth's interior. Using Plio-Pleistocene sea-level variations as a forcing function, theoretical models of mid-ocean ridge dynamics that include melt transport predict temporal variations in crustal thickness of hundreds of meters. New bathymetry from the Australian-Antarctic ridge shows significant spectral energy near the Milankovitch periods of 23, 41, and 100 ky, consistent with model predictions. These results suggest that abyssal hills, one of the most common bathymetric features on Earth, record the magmatic response to changes in sea level. The models and data support a link between glacial cycles at the surface and mantle melting at depth, recorded in the bathymetric fabric of the sea floor.Comment: 30 pages, 6 figures (including supplementary information). Resubmitted to Science on 12 December 201