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, we present an algorithm for fast calculation of the normalized cross correlation and its application to the problem of template matching. Given a template t, whose position is to be determined in an image f, the basic idea of the algorithm is to represent the template, for which the normalized cross correlation is calculated, as a sum of rectangular basis functions. Then the correlation is calculated for each basis function instead of the whole template. The result of the correlation of the template t and the image f is obtained as the weighted sum of the correlation functions of the basis functions. Depending on the approximation, the algorithm can by far outperform Fourier-transform based implementations of the normalized cross correlation algorithm and it is especially suited to problems, where many different templates are to be found in the same image f.

Template Matching using Fast Normalized Cross Correlation

For many practical probability density representations such as for the widely used Gaussian mixture densities, an analytic evaluation of the differential entropy is not possible and thus, approximate calculations are inevitable. For this purpose, the first contribution of this paper deals with a novel entropy approximation method for Gaussian mixture random vectors, which is based on a component-wise Taylor-series expansion of the logarithm of a Gaussian mixture and on a splitting method of Gaussian mixture components. The employed order of the Taylor-series expansion and the number of components used for splitting allows balancing between accuracy and computational demand. The second contribution is the determination of meaningful and efficiently to calculate lower and upper bounds of the entropy, which can be also used for approximation purposes. In addition, a refinement method for the more important upper bound is proposed in order to approach the true entropy value.

/pdf/on-entropy-approximation-for-gaussian-mixture-random-vectors-4hi02sdaft.pdf

On entropy approximation for Gaussian mixture random vectors

Indoor positioning systems based on wireless LAN (WLAN) are being widely investigated in academia and industry. Meanwhile, the emerging low-cost MEMS sensors can also be used as another independent positioning source. In this paper, we propose a pedestrian tracking framework based on particle filters, which extends the typical WLAN-based indoor positioning systems by integrating low-cost MEMS accelerometer and map information. Our simulation and real world experiments indicate a remarkable performance improvement by using this fusion framework.

/pdf/wlan-based-pedestrian-tracking-using-particle-filters-and-3atf7d0i45.pdf

WLAN-Based Pedestrian Tracking Using Particle Filters and Low-Cost MEMS Sensors

This paper is about tracking an extended object or a group target, which gives rise to a varying number of measurements from different measurement sources. For this purpose, the shape of the target is tracked in addition to its kinematics. The target extent is modeled with a new approach called Random Hypersurface Model (RHM) that assumes varying measurement sources to lie on scaled versions of the shape boundaries. In this paper, a star-convex RHM is introduced for tracking star-convex shape approximations of targets. Bayesian inference for star-convex RHMs is performed by means of a Gaussian-assumed state estimator allowing for an efficient recursive closed-form measurement update. Simulations demonstrate the performance of this approach for typical extended object and group tracking scenarios.

/pdf/shape-tracking-of-extended-objects-and-group-targets-with-4dgsuic8qo.pdf

Shape tracking of extended objects and group targets with star-convex RHMs

Target tracking algorithms usually assume that the received measurements stem from a point source. However, in many scenarios this assumption is not feasible so that measurements may stem from different locations, named measurement sources, on the target surface. Then, it is necessary to incorporate the target extent into the estimation procedure in order to obtain robust and precise estimation results. This paper introduces the novel concept of Random Hypersurface Models for extended targets. A Random Hypersurface Model assumes that each measurement source is an element of a randomly generated hypersurface. The applicability of this approach is demonstrated by means of an elliptic target shape. In this case, a Random Hypersurface Model specifies the random (relative) Mahalanobis distance of a measurement source to the center of the target object. As a consequence, good estimation results can be obtained even if the true target shape significantly differs from the modeled shape. Additionally, Random Hypersurface Models are computationally tractable with standard nonlinear stochastic state estimators.

/pdf/random-hypersurface-models-for-extended-object-tracking-2d6l4jr8jw.pdf

Uwe D. Hanebeck

Papers

Template Matching using Fast Normalized Cross Correlation

On entropy approximation for Gaussian mixture random vectors

WLAN-Based Pedestrian Tracking Using Particle Filters and Low-Cost MEMS Sensors

Shape tracking of extended objects and group targets with star-convex RHMs

Random Hypersurface Models for extended object tracking