There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The simultaneous localization and map building (SLAM) problem asks if it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and then to incrementally build a map of this environment while simultaneously using this map to compute absolute vehicle location. Starting from estimation-theoretic foundations of this problem, the paper proves that a solution to the SLAM problem is indeed possible. The underlying structure of the SLAM problem is first elucidated. A proof that the estimated map converges monotonically to a relative map with zero uncertainty is then developed. It is then shown that the absolute accuracy of the map and the vehicle location reach a lower bound defined only by the initial vehicle uncertainty. Together, these results show that it is possible for an autonomous vehicle to start in an unknown location in an unknown environment and, using relative observations only, incrementally build a perfect map of the world and to compute simultaneously a bounded estimate of vehicle location. The paper also describes a substantial implementation of the SLAM algorithm on a vehicle operating in an outdoor environment using millimeter-wave radar to provide relative map observations. This implementation is used to demonstrate how some key issues such as map management and data association can be handled in a practical environment. The results obtained are cross-compared with absolute locations of the map landmarks obtained by surveying. In conclusion, the paper discusses a number of key issues raised by the solution to the SLAM problem including suboptimal map-building algorithms and map management.

/pdf/a-solution-to-the-simultaneous-localization-and-map-building-2pp3i7uhdj.pdf

A solution to the simultaneous localization and map building (SLAM) problem

In this paper, a multi-level approach to intention, activity, and motion recognition for a humanoid robot is proposed. Our system processes images from a monocular camera and combines this information with domain knowledge. The recognition works on-line and in real-time, it is independent of the test person, but limited to predefined view-points. Main contributions of this paper are the extensible, multi-level modeling of the robot's vision system, the efficient activity and motion recognition, and the asynchronous information fusion based on generic processing of mid-level recognition results. The complementarity of the activity and motion recognition renders the approach robust against misclassifications. Experimental results on a real-world data set of complex kitchen tasks, e.g., Prepare Cereals or Lay Table, prove the performance and robustness of the multi-level recognition approach.

/pdf/combined-intention-activity-and-motion-recognition-for-a-4h1cczrcap.pdf

Combined intention, activity, and motion recognition for a humanoid household robot

Human action and activity recognition from videos has attracted an increasing number of researchers in recent years. However, most of the works aim at multimedia retrieval and surveillance applications, but rarely at humanoid household robots, even though the robotic perception of human activities would allow a more natural human-robot interaction (HRI). To encourage future studies in this domain, we present in this work a novel data set specifically designed for the application in HRI scenarios. This Robo-kitchen data set consists of 14 typical kitchen activities recorded in two different stereo-camera setups, and each performed by 17 subjects. To establish a baseline for future work, we extend a state-of-the-art action recognition method to be applicable on the activity classification problem and evaluate it on the Robo-kitchen data set showing promising results.

/pdf/the-kit-robo-kitchen-data-set-for-the-evaluation-of-view-1nlesha3f4.pdf

The KIT Robo-kitchen data set for the evaluation of view-based activity recognition systems

This paper addresses a systematic method for the reconstruction and the prediction of a distributed phenomenon characterized by partial differential equations, which is monitored by a sensor network. In the first step, the infinite-dimensional partial differential equation, i.e. distributed-parameter system, is spatially and temporally decomposed leading to a finite-dimensional state space form. In the next step, the state of the resulting lumped-parameter system, which provides an approximation of the solution of the underlying partial differential equations, is dynamically estimated under consideration of uncertainties both occurring in the system and arising from noisy measurements. By using the estimation results, several additional tasks can be achieved by the sensor network, e.g. optimal sensor placement, optimal scheduling, and model improvement. The performance of the proposed model-based reconstruction method is demonstrated by means of simulations.

Bayesian estimation of distributed phenomena using discretized representations of partial differential equations

A new Gaussian filter for estimating the state of nonlinear systems is derived that relies on two main ingredients: i) the progressive inclusion of the measurement information and ii) a tight coupling between a Gaussian density and its deterministic Dirac mixture approximation. No second Gaussian assumption for the joint density of state and measurement is required, so that the performance is much better than that of Linear Regression Kalman Filters (LRKFs), which heavily rely on this assumption. In addition, the new filter directly works with the generative system description. No Likelihood function is required. It can be used as a plug-in replacement for standard Gaussian filters such as the UKF.

PGF 42: Progressive Gaussian filtering with a twist

This paper introduces a novel recursive Bayesian estimator for the center and radius of a circle based on noisy points. Each given point is assumed to be a noisy measurement of an unknown true point on the circle that is corrupted with known isotropic Gaussian noise. In contrast to existing approaches, the novel method does not make assumptions about the true points on the circle, where the measurements stem from. Closed-form expressions for the measurement update step are derived. Simulations show that the novel method outperforms standard Bayesian approaches for circle fitting.

/pdf/a-novel-bayesian-method-for-fitting-a-circle-to-noisy-points-1nxumcth1o.pdf

Uwe D. Hanebeck

Papers

Combined intention, activity, and motion recognition for a humanoid household robot

The KIT Robo-kitchen data set for the evaluation of view-based activity recognition systems

Bayesian estimation of distributed phenomena using discretized representations of partial differential equations

PGF 42: Progressive Gaussian filtering with a twist

A novel Bayesian method for fitting a circle to noisy points