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 work, we present a novel scheme for nonlinear hyperspherical estimation using the von Mises–Fisher distribution. Deterministic sample sets with an isotropic layout are exploited for the efficient and informative representation of the underlying distribution in a geometrically adaptive manner. The proposed deterministic sampling approach allows manually configurable sample sizes, considerably enhancing the filtering performance under strong nonlinearity. Furthermore, the progressive paradigm is applied to the fusing of measurements of non-identity models in conjunction with the isotropic sample sets. We evaluate the proposed filtering scheme in a nonlinear spherical tracking scenario based on simulations. Numerical results show the evidently superior performance of the proposed scheme over state-of-the-art von Mises–Fisher filters and the particle filter.

/pdf/progressive-von-mises-fisher-filtering-using-isotropic-38kjjl8i8a.pdf

Progressive von Mises-Fisher Filtering Using Isotropic Sample Sets for Nonlinear Hyperspherical Estimation.

Sensoreinsatzplanung zur Verfolgung von Quellen räumlich ausgedehnter Phänomene

An amendment to this paper has been published and can be accessed via the original article. Following publication of the original article [1], two concerns were brought to the attention of EURASIP Journal on Wireless Communications and Networking.

/pdf/correction-to-commentary-to-tdoa-versus-atdoa-for-wide-area-3nid41k0gn.pdf

Correction to: Commentary to: TDOA versus ATDOA for wide area multilateration system

This study takes into consideration remote state estimation, where the state of a system is to be shared with a number of authorized users for any purpose (e.g., tracking, control), in the presence of eavesdroppers. We propose a novel control-theoretic secrecy mechanism to securely transmit the state estimate among the authorized users in the system. Moreover, as there isn’t any cryptographic mechanism applied to the shared information in the conventional sense, it is not possible for the eavesdroppers to understand that the state estimate is hidden. A use-case of the proposed secrecy mechanism for a target tracking example is also demonstrated.

State Estimation with Model-Mismatch-Based Secrecy against Eavesdroppers

This work was partially supported by the German Research Founda­ tion (DFG) within the Research Training Group GRK 1194 "Self-organizing Sensor-Actuator-Networks". . densities are a popular representation of non-Gaussian densi­ ties. They are a universal function approximator in that, given a sufficient number of components, they can approximate any smooth function to arbitrary accuracy [6]. They also tend to be a useful representation in practice for multivariate densities. However, there is no known closed-form solution to dif­ ferential entropy for Gaussian mixtures. There exist several approximations in the literature, including loose upper and lower bounds, but the only existent approximation that can be demonstrated to converge to the true entropy relies on expensive random sampling methods. Other approximations offer either very loose bounds or can be shown to deviate from the true entropy in an arbitrary fashion and hence, are of limited usefulness. In this paper, we present a novel approximation to differen­ tial entropy for Gaussian mixture random vectors based on Taylor-series expansions. For each Gaussian mixture com­ ponent, a Taylor-series expansion of the logarithm of the Gaussian mixture is determined as described in Section IV, which facilitates an analytical evaluation of the entropy measure. Additionally, a splitting technique for Gaussian densities is employed in Section IV-B in order to avoid Gaus­ sian components with high variance, which would require computationally expensive higher order expansion terms. Through the use of higher-order terms or component splitting it is possible to obtain an entropy approximation, which is of practical usefulness and versatile applicability as it • permits a tradeoff between computational demand and accuracy

http://ieeexplore.ieee.org/iel5/4634656/4648003/04648062.pdf

Uwe D. Hanebeck

Papers

Progressive von Mises-Fisher Filtering Using Isotropic Sample Sets for Nonlinear Hyperspherical Estimation.

Sensoreinsatzplanung zur Verfolgung von Quellen räumlich ausgedehnter Phänomene

Correction to: Commentary to: TDOA versus ATDOA for wide area multilateration system

State Estimation with Model-Mismatch-Based Secrecy against Eavesdroppers

On Entropy Approxilllation for Gaussian Mixture Randolll Vectors