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Dietrich Brunn

	Dipl.-Ing. Research Assistant, Ph.D. Student
	Address:	Institut für Anthropomatik Universität Karlsruhe (TH) Gebäude 20.20 Raum 252 Zirkel 2 D-76131 Karlsruhe
	Walk-in hours:	on arrangement
	Phone:	+49-721-608-4354
	E-mail:	brunn@ira.uka.de

Academic Career

Research Interests

Measurement engineering, signal processing, modelling, robotics

Publications

Proceedings of the 17th IFAC World Congress (IFAC 2008), 17, Seoul, Republic of Korea, July, 2008.

Author : Florian Weissel, Marco F. Huber, Dietrich Brunn, Uwe D. Hanebeck
Title : Stochastic Optimal Control based on Value-Function Approximation using Sinc Interpolation
In : Proceedings of the 17th IFAC World Congress (IFAC 2008)
Date : July 2008

Abstract

An effcient approach for solving stochastic optimal control problems is to employ
dynamic programming (DP). For continuous-valued nonlinear systems, the corresponding
DP recursion generally cannot be solved in closed form. Thus, a typical approach is to
discretize the DP value functions in order to be able to carry out the calculation. Especially
for multidimensional systems, either a large number of discretization points is necessary or
the quality of approximation degrades. This problem can be alleviated by interpolating the
discretized value function. In this paper, we present an approach based on optimal low-pass
interpolation employing sinc functions (sine cardinal). For the important case of systems with
Gaussian mixture noise (including the special case of Gaussian noise), we show how the
calculations required for this approach, especially the nontrivial calculation of an expected
value of a Gaussian mixture random variable transformed by a sinc function, can be carried out
analytically. We illustrate the effectiveness of the proposed interpolation scheme by an example
from the field of Stochastic Nonlinear Model Predictive Control (SNMPC).

Proceedings of the 11th International Conference on Information Fusion (Fusion 2008), pp. 1-8, Cologne, Germany, July, 2008.

Author : Benjamin Noack, Vesa Klumpp, Dietrich Brunn, Uwe D. Hanebeck
Title : Nonlinear Bayesian Estimation with Convex Sets of Probability Densities
In : Proceedings of the 11th International Conference on Information Fusion (Fusion 2008)
Date : July 2008

Abstract

This paper presents a theoretical framework for
Bayesian estimation in the case of imprecisely known probability
density functions. The lack of knowledge about the true density
functions is represented by sets of densities. A formal Bayesian
estimator for these sets is introduced, which is intractable for
infinite sets. To obtain a tractable filter, properties of convex
sets in form of convex polytopes of densities are investigated.
It is shown that pathwise connected sets and their convex hulls
describe the same ignorance. Thus, an exact algorithm is derived,
which only needs to process the hull, delivering tractable results
in the case of a proper parametrization. Since the estimator
delivers a convex hull of densities as output, the theoretical
grounds are laid for deriving efficient Bayesian estimators for
sets of densities. The derived filter is illustrated by means of an
example.

Proceedings of the 11th International Conference on Information Fusion (Fusion 2008), pp. 1-7, Cologne, Germany, July, 2008.

Author : Hui Wang, Andrei Szabo, Joachim Bamberger, Dietrich Brunn, Uwe D. Hanebeck
Title : Performances Comparison of Nonlinear Filters for Indoor WLAN Positioning
In : Proceedings of the 11th International Conference on Information Fusion (Fusion 2008)
Date : July 2008

Abstract

Indoor WLAN positioning should be modeled as a nonlinear
and non-Gaussian dynamic system due to the complex indoor environment,
radio propagation and motion behaviour. The aim of this paper is to
analyze different filtering strategies for real life indoor WLAN
positioning systems. The performance criteria for the comparison are
the mean of localization errors and computational complexity.
Three nonlinear filters are analyzed: Fourier density approximation (FF),
particle filter (PF) and grid-based filter (GF), which are representatives for
deterministic and random density approximation approaches.
Our experimental results help to choose the appropriate filtering
techniques under different resource limitations.

Proceedings of the 2007 American Control Conference (ACC 2007), pp. 4425-4430, New York, New York, USA, July, 2007.

Author : Marco F. Huber, Dietrich Brunn, Uwe D. Hanebeck
Title : Efficient Nonlinear Measurement Updating based on Gaussian Mixture Approximation of Conditional Densities
In : Proceedings of the 2007 American Control Conference (ACC 2007)
Date : July 2007

Abstract

Filtering or measurement updating for nonlinear stochastic dynamic
systems requires approximate calculations, since an exact solution
is impossible to obtain in general. We propose a Gaussian mixture
approximation of the conditional density, which allows performing
measurement updating in closed form. The conditional density is a
probabilistic representation of the nonlinear system and depends
on the random variable of the measurement given the system state.
Unlike the likelihood, the conditional density is independent of
actual measurements, which permits determining its approximation
off-line. By treating the approximation task as an optimization problem,
we use progressive processing to achieve high quality results. Once
having calculated the conditional density, the likelihood can be
determined on-line, which, in turn, offers an efficient approximate
filter step. As result, a Gaussian mixture representation of the
posterior density is obtained. The exponential growth of Gaussian
mixture components resulting from repeated filtering is avoided implicitly
by the prediction step using the proposed techniques.

tm - Technisches Messen, Oldenbourg Verlag, 3:75-90, March, 2007.

Author : Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
Title : Modellbasierte Vermessung verteilter Phänomene und Generierung optimaler Messsequenzen
In : tm - Technisches Messen, Oldenbourg Verlag
Date : March 2007

Abstract

Dieser Beitrag befasst sich mit modellbasierten Methoden zur Vermessung
verteilter physikalischer Phänomene. Diese Methoden zeichnen
sich durch eine systematische Behandlung von Unsicherheiten aus,
so dass neben der Rekonstruktion der vollständigen Wahrscheinlichkeitsdichte
der relevanten Größen aus einer geringen Anzahl von zeit-,
orts- und wertdiskreten Messungen auch die Generierung optimaler
Messsequenzen möglich ist. Es wird dargestellt, wie eine Beschreibung
für ein verteilt-parametrisches System in Form einer partiellen
Differentialgleichung, welche einen unendlich-dimensionalen Zustandsraum
beschreibt, in eine konzentriert-parametrische Form konvertiert wird.
Diese kann als Grundlage für den Entwurf klassischer Schätzer,
wie z. B. des Kalman-Filters, dienen. Ferner wird eine Methode zur
Sensoreinsatzplanung vorgestellt, mit der eine optimale Sequenz von
Messparametern bestimmt werden kann, um mit einem minimalen Messaufwand
die Unsicherheit auf ein gewünschtes Maß zu reduzieren. Die
Anwendung dieser Methoden wird an zwei Beispielen, einer Temperaturverteilung
und der Verformung einer Führungsschiene, demonstriert. Zusätzlich
werden die Herausforderungen bei der Behandlung nichtlinearer Systeme
und die Probleme bei der dezentralen Verarbeitung, wie sie typischerweise
beim Einsatz von Sensornetzwerken auftreten, diskutiert.

Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006), pp. 1303-1308, San Diego, California, USA, December, 2006.

Author : Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
Title : Nonlinear Multidimensional Bayesian Estimation with Fourier Densities
In : Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006)
Date : December 2006

Abstract

Efficiently implementing nonlinear Bayesian estimators is still an
unsolved problem, especially for the multidimensional case. A trade-off
between estimation quality and demand on computational resources
has to be found. Using multidimensional Fourier series as representation
for probability density functions, so called Fourier densities, is
proposed. To ensure non-negativity, the approximation is performed
indirectly via Psi-densities, of which the absolute square represent
the Fourier density. It is shown that PSI-densities can be determined
using the efficient fast Fourier transform algorithm and their coefficients
have an ordering with respect to the Hellinger metric. Furthermore,
the multidimensional Bayesian estimator based on Fourier Densities
is derived in closed form. That allows an efficient realization of
the Bayesian estimator where the demands on computational resources
are adjustable.

Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006), San Diego, California, USA, December, 2006.

Author : Oliver C. Schrempf, Dietrich Brunn, Uwe D. Hanebeck
Title : Density Approximation Based on Dirac Mixtures with Regard to Nonlinear Estimation and Filtering
In : Proceedings of the 2006 IEEE Conference on Decision and Control (CDC 2006)
Date : December 2006

Abstract

A deterministic procedure for optimal approximation of arbitrary probability
density functions by means of Dirac mixtures with equal weights is
proposed. The optimality of this approximation is guaranteed by minimizing
the distance of the approximation from the true density. For this
purpose a distance measure is required, which is in general not well
defined for Dirac mixtures. Hence, a key contribution is to compare
the corresponding cumulative distribution functions. This paper concentrates
on the simple and intuitive integral quadratic distance measure.
For the special case of a Dirac mixture with equally weighted components,
closed-form solutions for special types of densities like uniform
and Gaussian densities are obtained. Closed-form solution of the
given optimization problem is not possible in general. Hence, another
key contribution is an efficient solution procedure for arbitrary
true densities based on a homotopy continuation approach. In contrast
to standard Monte Carlo techniques like particle filters that are
based on random sampling, the proposed approach is deterministic
and ensures an optimal approximation with respect to a given distance
measure. In addition, the number of required components (particles)
can easily be deduced by application of the proposed distance measure.
The resulting approximations can be used as basis for recursive nonlinear
filtering mechanism alternative to Monte Carlo methods.

Proceedings of the 2006 IEEE International Conference on Control Applications (CCA 2006), Munich, Germany, October, 2006.

Author : Felix Sawo, Dietrich Brunn, Uwe D. Hanebeck
Title : Parameterized Joint Densities with Gaussian Mixture Marginals and their Potential Use in Nonlinear Robust Estimation
In : Proceedings of the 2006 IEEE International Conference on Control Applications (CCA 2006)
Date : October 2006

Abstract

This paper addresses the challenges of the fusion of two random vectors
with imprecisely known stochastic dependency. This problem mainly
occurs in decentralized estimation, e.g. of a distributed phenomenon,
where the stochastic dependencies between the individual states are
not stored. To cope with such problems we propose to exploit parameterized
joint densities with both Gaussian marginals and Gaussian mixture
marginals. Under structural assumptions these parameterized joint
densities contain all information about the stochastic dependencies
between their marginal densities in terms of a generalized correlation
parameter vector xi. The parameterized joint densities are applied
to the prediction step and the measurement step under imprecisely
known correlation leading to a whole family of possible estimation
results. The resulting density functions are characterized by the
generalized correlation parameter vector xi. Once this structure
and the bounds of these parameters are known, it is possible to find
bounding densities containing all possible density functions, i.e.,
conservative estimation results.

Informationsfusion in der Mess- und Sensortechnik, pp. 75-90, Universitätsverlag Karlsruhe, September, 2006.

Author : Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
Title : Informationsfusion für verteilte Systeme
In : Informationsfusion in der Mess- und Sensortechnik
Date : September 2006

Abstract

Dieser Beitrag befasst sich mit modellbasierten Methoden zur Vermessung
verteilter physikalischer Phänomene. Diese Methoden zeichnen
sich durch eine systematische Behandlung stochastischer Unsicherheiten
aus, so dass neben der Rekonstruktion der vollständigen Wahrscheinlichkeitsdichte
der relevanten Größen aus einer geringen Anzahl von zeit-,
orts- und wertdiskreten Messungen auch die Generierung optimaler
Messsequenzen möglich ist. Es wird dargestellt, wie eine Beschreibung
für ein verteilt-parametrisches System in Form einer partiellen
Differentialgleichung, welche einen unendlich-dimensionalen Zustandsraum
beschreibt, in eine konzentriert-parametrische Form konvertiert
wird. Diese kann als Grundlage für den Entwurf klassischer Schätzer,
wie z.B. des Kalman Filters, dienen. Ferner wird eine Methode zur
Sensoreinsatzplanung vorgestellt, mit der eine optimale Sequenz von
Messparametern bestimmt werden kann, um mit einem minimalen Messaufwand
die Unsicherheit auf ein gewünschtes Maß zu reduzieren. Die
Anwendung dieser Methoden wird an zwei Beispielen, einer Temperaturverteilung
und der Verformung einer Führungsschiene, demonstriert. Zusätzlich
werden die Herausforderungen bei der Behandlung nichtlinearer Systeme
und die Probleme bei der dezentralen Verarbeitung, wie sie typischerweise
beim Einsatz von Sensornetzwerken auftreten, diskutiert.

Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), pp. 312-322, Heidelberg, Germany, September, 2006.

Author : Dietrich Brunn, Felix Sawo, Uwe D. Hanebeck
Title : Efficient Nonlinear Bayesian Estimation based on Fourier Densities
In : Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006)
Date : September 2006

Abstract

Efficiently implementing nonlinear Bayesian estimators is still not
a fully solved problem. For practical applications, a trade-off between
estimation quality and demand on computational resources has to be
found. In this paper, the use of nonnegative Fourier series, so-called
Fourier densities, for Bayesian estimation is proposed. By using
the absolute square of Fourier series for the density representation,
it is ensured that the density stays nonnegative. Nonetheless, approximation
of arbitrary probability density functions can be made by using the
Fourier integral formula. An efficient Bayesian estimator algorithm
with constant complexity for nonnegative Fourier series is derived
and demonstrated by means of an example.

Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), pp. 371-376, Heidelberg, Germany, September, 2006.

Author : Marc P. Deisenroth, Toshiyuki Ohtsuka, Florian Weissel, Dietrich Brunn, Uwe D. Hanebeck
Title : Finite-Horizon Optimal State-Feedback Control of Nonlinear Stochastic Systems Based on a Minimum Principle
In : Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006)
Date : September 2006

Abstract

In this paper, an approach to the finite-horizon
optimal state-feedback control problem of nonlinear, stochastic,
discrete-time systems is presented. Starting from the dynamic
equation, the value function will be approximated
by means of Taylor series expansion up to second-order
derivatives. Moreover, the problem will be reformulated, such
that a minimum principle can be applied to the stochastic
problem. Employing this minimum principle, the optimal control
problem can be rewritten as a two-point boundary-value
problem to be solved at each time step of a shrinking horizon.
To avoid numerical problems, the two-point boundary-value
problem will be solved by means of a continuation method.
Thus, the curse of dimensionality of dynamic programming
is avoided, and good candidates for the optimal state-feedback
controls are obtained. The proposed approach will be evaluated
by means of a scalar example system.

Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), pp. 98-103, Heidelberg, Germany, September, 2006.

Author : Marco Huber, Dietrich Brunn, Uwe D. Hanebeck
Title : Closed-Form Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density
In : Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006)
Date : September 2006

Abstract

Recursive prediction of the state of a nonlinear stochastic dynamic
system cannot be efficiently performed in general, since the complexity
of the probability density function characterizing the system state
increases with every prediction step. Thus, representing the density
in an exact closed-form manner is too complex or even impossible.
So, an appropriate approximation of the density is required. Instead
of directly approximating the predicted density, we propose the approximation
of the transition density by means of Gaussian mixtures. We treat
the approximation task as an optimization problem that is solved
offline via progressive processing to bypass initialization problems
and to achieve high quality approximations. Once having calculated
the transition density approximation offline, prediction can be performed
efficiently resulting in a closed-form density representation with
constant complexity.

Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006), pp. 512-517, Heidelberg, Germany, September, 2006.

Author : Oliver C. Schrempf, Dietrich Brunn, Uwe D. Hanebeck
Title : Dirac Mixture Density Approximation Based on Minimization of the Weighted Cramér-von Mises Distance
In : Proceedings of the 2006 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2006)
Date : September 2006

Abstract

This paper proposes a systematic procedure for approximating arbitrary
probability density functions by means of Dirac mixtures. For that
purpose, a distance measure is required, which is in general not
well defined for Dirac mixture densities. Hence, a distance measure
comparing the corresponding cumulative distribution functions is
employed. Here, we focus on the weighted Cramer-von Mises distance,
a weighted integral quadratic distance measure, which is simple and
intuitive. Since a closed-form solution of the given optimization
problem is not possible in general, an efficient solution procedure
based on a homotopy continuation approach is proposed. Compared to
a standard particle approximation, the proposed procedure ensures
an optimal approximation with respect to a given distance measure.
Although useful in their own respect, the results also provide the
basis for a recursive nonlinear filtering mechanism as an alternative
to the popular particle filters.

Proceedings of the 9th International Conference on Information Fusion (Fusion 2006), Florence, Italy, July, 2006.

Author : Vesa Klumpp, Dietrich Brunn, Uwe D. Hanebeck
Title : Approximate Nonlinear Bayesian Estimation Based on Lower and Upper Densities
In : Proceedings of the 9th International Conference on Information Fusion (Fusion 2006)
Date : July 2006

Abstract

Recursive calculation of the probability density function characterizing
the state estimate of a nonlinear stochastic dynamic system in general
cannot be performed exactly, since the type of the density changes
with every processing step and the complexity increases. Hence, an
approximation of the true density is required. Instead of using a
single complicated approximating density, this paper is concerned
with bounding the true density from below and from above by means
of two simple densities. This provides a kind of guaranteed estimator
with respect to the underlying true density, which requires a mechanism
for ordering densities. Here, a partial ordering with respect to
the cumulative distributions is employed. Based on this partial ordering,
a modified Bayesian filter step is proposed, which recursively propagates
lower and upper density bounds. A specific implementation for piecewise
linear densities with finite support is used for demonstrating the
performance of the new approach in simulations.

Proceedings of the 9th International Conference on Information Fusion (Fusion 2006), Florence, Italy, July, 2006.

Author : Felix Sawo, Dietrich Brunn, Uwe D. Hanebeck
Title : Parameterized Joint Densities with Gaussian and Gaussian Mixture Marginals
In : Proceedings of the 9th International Conference on Information Fusion (Fusion 2006)
Date : July 2006

Abstract

In this paper we attempt to lay the foundation for a novel filtering
technique for the fusion of two random vectors with imprecisely known
stochastic dependency. This problem mainly occurs in decentralized
estimation, e.g., of a distributed phenomenon, where the stochastic
dependencies between the individual states are not stored. Thus,
we derive parameterized joint densities with both Gaussian marginals
and Gaussian mixture marginals. These parameterized joint densities
contain all information about the stochastic dependencies between
their marginal densities in terms of a parameter vector xi, which
can be regarded as a generalized correlation parameter. Unlike the
classical correlation coeffcient, this parameter is a suffcient measure
for the stochastic dependency even characterized by more complex
density functions such as Gaussian mixtures. Once this structure
and the bounds of these parameters are known, bounding densities
containing all possible density functions could be found.

Proceedings of the 2005 IEEE International Conference on Robotics and Automation (ICRA 2005), Barcelona, Spain, April, 2005.

Author : Dietrich Brunn, Uwe D. Hanebeck
Title : A Model-Based Framework for Optimal Measurements in Machine Tool Calibration
In : Proceedings of the 2005 IEEE International Conference on Robotics and Automation (ICRA 2005)
Date : April 2005

Abstract

Calibration is the procedure of quantifying mechanical depciencies
of machines and compensating them by appropriate adjustment. This
paper introduces a model- based measurement framework for improving
calibration procedures of machine tools. The goal is to precisely
estimate the mechanical depciencies based on a minimal number of
measurements. For that purpose, the mechanical depciencies of linear
and rotary joints are modeled using splines. Uncertainties of the
depciency model are formulated stochastically, which allows incorporation
of imprecise measurement data and prediction of optimal measurement
parameters. We derive a method for optimally estimating a set of
splines, i.e., joint errors, based on a set of measurements and for
predicting the optimal joint configuration for new measurements.