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

© 2014 International Society of Information Fusion. This work proposes a novel way to represent uncertainty on the Lie group of rigid-body motions in the plane. This is achieved by using dual quaternions for representation of a planar rigid-body motion and proposing a probability distribution from the exponential family of distributions that inherently respects the underlying structure of the representation. This is particularly beneficial in scenarios involving strong measurement noise. A relationship between the newly proposed distributional model and the Bingham distribution is discussed. The presented results involve formulas for computation of the normalization constant, the mode, parameter estimation techniques, and a closed-form Bayesian measurement fusion.

A new probability distribution for simultaneous representation of uncertain position and orientation

This paper addresses the problem of sequence-based controller design for Networked Control Systems (NCS), where control inputs and measurements are transmitted over TCP-like network connections that are subject to random transmission delays and packet losses. To cope with the network effects, the controller not only sends the current control input to the actuator, but also a sequence of predicted control inputs at every time step. In this setup, we derive an optimal solution to the Linear Quadratic Gaussian (LQG) control problem and prove that the separation principle holds. Simulations demonstrate the improved performance of this optimal controller compared to other sequence-based approaches.

Optimal sequence-based LQG control over TCP-like networks subject to random transmission delays and packet losses

We introduce the unscented von Mises–Fisher filter (UvMFF), a nonlinear filtering algorithm for dynamic state estimation on the $n$ -dimensional unit hypersphere. Estimation problems on the unit hypersphere occur in computer vision, e.g., when using omnidirectional cameras, as well as in signal processing. As approaches in literature are limited to very simple system and measurement models, we propose a deterministic sampling scheme on the unit hypersphere, which allows us to handle nonlinear system and measurement models. The proposed approach can be seen as a hyperspherical variant of the unscented Kalman filter (UKF). The advantages of the novel method are shown by means of simulations.

Unscented von Mises–Fisher Filtering

This paper considers state estimation for dynamic systems in the case of non-white, mutually correlated noise processes. Here, the problem is complicated by the fact, that only the individual covariances are known; cross covariances between random variables obtained by taking individual noise processes at different time steps and between different noise processes are completely unknown. New estimator equations for solving this problem are derived in feedback form for both the prediction step and the filtering step based on existing ideas known as covariance intersection. Solutions are given for the most general case of updating an N-dimensional state vector estimate based on M-dimensional observations. Furthermore, computationally efficient solutions for obtaining minimum covariance estimates are derived to avoid numerical optimization otherwise required.

New results for stochastic prediction and filtering with unknown correlations

First person games are computer games, in which the user experiences the virtual game world from an avatar's view. This avatar is the user's alter ego in the game. In this paper, we present a telepresence interface for the first person game Quake III Arena, which gives the user the impression of presence in the game and thus leads to identification with his avatar. This is achieved by tracking the user's motion and using this motion data as control input for the avatar. As the user is wearing a head-mounted display and he perceives his actions affecting the virtual environment, he fully immerses into the target environment. Without further processing of the user's motion data, the virtual environment would be limited to the size of the user's real environment, which is not desirable. The use of Motion Compression, however, allows exploring an arbitrarily large virtual environment while the user is actually moving in an environment of limited size.

/pdf/telepresence-techniques-for-controlling-avatar-motion-in-1sqzthb0av.pdf

Uwe D. Hanebeck

Papers

A new probability distribution for simultaneous representation of uncertain position and orientation

Optimal sequence-based LQG control over TCP-like networks subject to random transmission delays and packet losses

Unscented von Mises–Fisher Filtering

New results for stochastic prediction and filtering with unknown correlations

Telepresence techniques for controlling avatar motion in first person games