Optimal stochastic linearization for range-based localization

In range-based localization, the trajectory of a mobile object is estimated based on noisy range measurements between the object and known landmarks. In order to deal with this uncertain information, a Bayesian state estimator is presented, which exploits optimal stochastic linearization. Compared to standard state estimators like the Extended or Unscented Kalman Filter, where a point-based Gaussian approximation is used, the proposed approach considers the entire Gaussian density for linearization. By employing the common assumption that the state and measurements are jointly Gaussian, the linearization can be calculated in closed form and thus analytic expressions for the range-based localization problem can be derived

Information Acquisition with Sensing Robots: Algorithms and Error Bounds

Utilizing the capabilities of configurable sensing systems requires addressing difficult information gathering problems. Near-optimal approaches exist for sensing systems without internal states. However, when it comes to optimizing the trajectories of mobile sensors the solutions are often greedy and rarely provide performance guarantees. Notably, under linear Gaussian assumptions, the problem becomes deterministic and can be solved off-line. Approaches based on submodularity have been applied by ignoring the sensor dynamics and greedily selecting informative locations in the environment. This paper presents a non-greedy algorithm with suboptimality guarantees, which does not rely on submodularity and takes the sensor dynamics into account. Our method performs provably better than the widely used greedy one. Coupled with linearization and model predictive control, it can be used to generate adaptive policies for mobile sensors with non-linear sensing models. Applications in gas concentration mapping and target tracking are presented.Comment: 9 pages (two-column); 2 figures; Manuscript submitted to the 2014 IEEE International Conference on Robotics and Automatio

An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to extend the twisted particle filtering methodology, establish accessible theoretical results which convey its rationale, and provide a demonstration of its practical performance within particle Markov chain Monte Carlo for estimating static model parameters. We derive twisted particle filters that incorporate systematic or multinomial resampling and information from historical particle states, and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise and we apply such approximations to two examples: a range and bearing tracking problem and an indoor positioning problem with Bluetooth signal strength measurements. We demonstrate improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time, and improved tracking performance using estimated parameters.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

On-Manifold Preintegration for Real-Time Visual-Inertial Odometry

Current approaches for visual-inertial odometry (VIO) are able to attain highly accurate state estimation via nonlinear optimization. However, real-time optimization quickly becomes infeasible as the trajectory grows over time, this problem is further emphasized by the fact that inertial measurements come at high rate, hence leading to fast growth of the number of variables in the optimization. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes into single relative motion constraints. Our first contribution is a \emph{preintegration theory} that properly addresses the manifold structure of the rotation group. We formally discuss the generative measurement model as well as the nature of the rotation noise and derive the expression for the \emph{maximum a posteriori} state estimator. Our theoretical development enables the computation of all necessary Jacobians for the optimization and a-posteriori bias correction in analytic form. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated into a visual-inertial pipeline under the unifying framework of factor graphs. This enables the application of incremental-smoothing algorithms and the use of a \emph{structureless} model for visual measurements, which avoids optimizing over the 3D points, further accelerating the computation. We perform an extensive evaluation of our monocular \VIO pipeline on real and simulated datasets. The results confirm that our modelling effort leads to accurate state estimation in real-time, outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions on Robotics (TRO) 201

Organs on chip approach: A tool to evaluate cancer-immune cells interactions

In this paper we discuss the applicability of numerical descriptors and statistical physics concepts to characterize complex biological systems observed at microscopic level through organ on chip approach. To this end, we employ data collected on a micro uidic platform in which leukocytes can move through suitably built channels toward their target. Leukocyte behavior is recorded by standard time lapse imaging. In particular, we analyze three groups of human peripheral blood mononuclear cells (PBMC): heterozygous mutants (in which only one copy of the FPR1 gene is normal), homozygous mutants (in which both alleles encoding FPR1 are loss-of-function variants) and cells from ‘wild type’ donors (with normal expression of FPR1). We characterize the migration of these cells providing a quantitative con rmation of the essential role of FPR1 in cancer chemotherapy response. Indeed wild type PBMC perform biased random walks toward chemotherapy-treated cancer cells establishing persistent interactions with them. Conversely, heterozygous mutants present a weaker bias in their motion and homozygous mutants perform rather uncorrelated random walks, both failing to engage with their targets. We next focus on wild type cells and study the interactions of leukocytes with cancerous cells developing a novel heuristic procedure, inspired by Lyapunov stability in dynamical systems