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Vesa Klumpp

	Dipl.-Inform. Research Assistant, Ph.D. Student
	Address:	Karlsruher Institut für Technologie Institut für Anthropomatik Gebäude 50.20 Raum 130 Adenauerring 2 D-76131 Karlsruhe
	Walk-in hours:	on arrangement
	Phone:	+49-721-608-5469
	E-mail:	Vesa.Klumpp@kit.edu

Academic Career

Research Interests

System and estimation theory, imprecise probability.

Publications

tm - Technisches Messen, Oldenbourg Verlag, 77(10):544-550, October, 2010.

URL

Author : Benjamin Noack, Vesa Klumpp, Daniel Lyons, Uwe D. Hanebeck
Title : Modellierung von Unsicherheiten und Zustandsschätzung mit Mengen von Wahrscheinlichkeitsdichten
In : tm - Technisches Messen, Oldenbourg Verlag
Date : October 2010

Abstract

Die systematische Behandlung von Unsicherheiten stellt eine wesentliche
Herausforderung in der Informationsfusion dar. Einerseits müssen
geeignete Darstellungsformen für die Unsicherheiten bestimmt
werden und andererseits darauf aufbauend effiziente Schätzverfahren
hergeleitet werden. Im Allgemeinen wird zwischen stochastischen und
mengenbasierten Unsicherheitsbeschreibungen unterschieden. Dieser
Beitrag stellt ein Verfahren zur Zustandsschätzung vor, welches
simultan stochastische und mengenbasierte Fehlergrößen berücksichtigen
kann, indem unsichere Größen nicht mehr durch eine einzelne
Wahrscheinlichkeitsdichte, sondern durch eine Menge von Dichten repräsentiert
werden. Besonderes Augenmerk liegt hier auf den Vorteilen und Anwendungsmöglichkeiten
dieser Unsicherheitsbeschreibung.

Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.

Author : Marcus Baum, Vesa Klumpp, Uwe D. Hanebeck
Title : A Novel Bayesian Method for Fitting a Circle to Noisy Points
In : Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)
Date : July 2010

Abstract

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.

Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.

Author : Henning Eberhardt, Vesa Klumpp, Uwe D. Hanebeck
Title : Density Trees for Efficient Nonlinear State Estimation
In : Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)
Date : July 2010

Abstract

In this paper, a new class of nonlinear Bayesian
estimators based on a special space partitioning structure, generalized
Octrees, is presented. This structure minimizes memory and calculation
overhead. It is used as a container framework for a set of node functions
that approximate a density piecewise. All necessary operations are derived
in a very general way in order to allow for a great variety of Bayesian
estimators. The presented estimators are especially well suited for
multi-modal nonlinear estimation problems. The running time performance
of the resulting estimators is first analyzed theoretically and then backed
by means of simulations. All operations have a linear running time in
the number of tree nodes.

Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.

Author : Vesa Klumpp, Frederik Beutler, Uwe D. Hanebeck, Dietrich Fränken
Title : The Sliced Gaussian Mixture Filter with Adaptive State Decomposition Depending on Linearization Error
In : Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)
Date : July 2010

Abstract

In this paper, a novel nonlinear/non-linear model
decomposition for the Sliced Gaussian Mixture Filter is presented.
Based on the level of nonlinearity of the model, the overall estimation
problem is decomposed into a severely nonlinear and a slightly
nonlinear part, which are processed by different estimation techniques.
To further improve the efficiency of the estimator, an adaptive state
decomposition algorithm is introduced that allows decomposition
according to the linearization error for nonlinear system and
measurement models. Simulations show that this approach has orders of
magnitude less complexity compared to other state of the art
estimators, while maintaining comparable estimation errors.

Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.

Author : Vesa Klumpp, Benjamin Noack, Marcus Baum, Uwe D. Hanebeck
Title : Combined Set-Theoretic and Stochastic Estimation: A Comparison of the SSI and the CS Filter
In : Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)
Date : July 2010

Abstract

In estimation theory, mainly set-theoretic or
stochastic uncertainty is considered. In some cases, especially when
some statistics of a distribution are not known or additional
stochastic information is used in a set-theoretic estimator, both
types of uncertainty have to be considered. In this paper, two
estimators that cope with combined stoachastic and set-theoretic
uncertainty are compared, namely the Set-theoretic and Statistical
Information filter, which represents the uncertainty by means of
random sets, and the Credal State filter, in which the state
information is given by sets of probability density functions.
The different uncertainty assessment in both estimators leads to
different estimation results, even when the prior information and
the measurement and system models are equal. This paper explains
these differences and states directions, when which estimator
should be applied to a given estimation problem.

Proceedings of the 13th International Conference on Information Fusion (Fusion 2010), Edinburgh, United Kingdom, July, 2010.

Author : Benjamin Noack, Vesa Klumpp, Nikolay Petkov, Uwe D. Hanebeck
Title : Bounding Linearization Errors with Sets of Densities in Approximate Kalman Filtering
In : Proceedings of the 13th International Conference on Information Fusion (Fusion 2010)
Date : July 2010

Abstract

Applying the Kalman filtering scheme to linearized system dynamics and observation models does in general not yield optimal state estimates.
More precisely, inconsistent state estimates and covariance matrices are caused by neglected linearization errors.
This paper introduces a concept for systematically predicting and updating bounds for the linearization errors within the Kalman filtering framework.
To achieve this, an uncertain quantity is not characterized by a single probability density anymore, but rather by a set of densities and accordingly,
the linear estimation framework is generalized in order to process sets of probability densities. By means of this generalization,
the Kalman filter may then not only be applied to stochastic quantities, but also to unknown but bounded quantities.
In order to improve the reliability of Kalman filtering results, the last-mentioned quantities are utilized to bound the typically neglected nonlinear parts of a linearized mapping.

Proceedings of the 2010 American Control Conference (ACC 2010), Baltimore, Maryland, USA, June, 2010.

Author : Henning Eberhardt, Vesa Klumpp, Uwe D. Hanebeck
Title : Optimal Dirac Approximation by Exploiting Independencies
In : Proceedings of the 2010 American Control Conference (ACC 2010)
Date : June 2010

Abstract

The sample-based recursive prediction of discrete-time nonlinear
stochastic dynamic systems requires a regular reapproximation of the Dirac mixture
densities characterizing the state estimate with an exponentially increasing number
of components. For that purpose, a systematic approximation method is proposed that
is deterministic and guaranteed to minimize a new type distance measure, the so
called modified Cramér-von Mises distance. A huge increase in approximation
performance is achieved by exploiting structural independencies usually occurring
between the random variables used as input to the system. The corresponding prediction
step achieves optimal performance when no further assumptions can be made about the
system function. In addition, the proposed approach shows a much better convergence
compared to the prediction step of the particle filter and by far fewer Dirac components
are required for achieving a given approximation quality. As a result, the new
approximation method opens the way for the development of new fully deterministic and
optimal stochastic state estimators for nonlinear dynamic systems.

Verteilte Messsysteme, pp. 167-178, KIT Scientific Publishing, March, 2010.

URL

Author : Benjamin Noack, Vesa Klumpp, Daniel Lyons, Uwe D. Hanebeck
Title : Systematische Beschreibung von Unsicherheiten in der Informationsfusion mit Mengen von Wahrscheinlichkeitsdichten
In : Verteilte Messsysteme
Date : March 2010

Abstract

Die systematische Behandlung von Unsicherheiten stellt eine wesentliche
Herausforderung in der Informationsfusion dar. Einerseits müssen geeignete Darstellungsformen
für die Unsicherheiten bestimmt werden und andererseits darauf aufbauend effiziente
Schätzverfahren hergeleitet werden. Im Allgemeinen wird zwischen stochastischen und
mengenbasierten Unsicherheitsbeschreibungen unterschieden. Dieser Beitrag stellt ein Verfahren
zur Zustandsschätzung vor, welches simultan stochastische und mengenbasierte Fehlergrößen
berücksichtigen kann, indem unsichere Größen nicht mehr durch eine einzelne
Wahrscheinlichkeitsdichte, sondern durch eine Menge von Dichten repräsentiert werden.
Besonderes Augenmerk liegt hier auf den Vorteilen und Anwendungsmöglichkeiten dieser
Unsicherheitsbeschreibung.

Proceedings of the 2009 IEEE Conference on Decision and Control (CDC 2009), Shanghai, China, December, 2009.

Author : Uwe D. Hanebeck, Marco F. Huber, Vesa Klumpp
Title : Dirac Mixture Approximation of Multivariate Gaussian Densities
In : Proceedings of the 2009 IEEE Conference on Decision and Control (CDC 2009)
Date : December 2009

Abstract

For the optimal approximation of multivariate
Gaussian densities by means of Dirac mixtures, i.e., by means of
a sum of weighted Dirac distributions on a continuous domain,
a novel systematic method is introduced. The parameters of
this approximate density are calculated by minimizing a global
distance measure, a generalization of the well–known Cramér–
von Mises distance to the multivariate case. This generalization
is obtained by defining an alternative to the classical cumulative
distribution, the Localized Cumulative Distribution (LCD). In
contrast to the cumulative distribution, the LCD is unique
and symmetric even in the multivariate case. The resulting
deterministic approximation of Gaussian densities by means of
discrete samples provides the basis for new types of Gaussian
filters for estimating the state of nonlinear dynamic systems
from noisy measurements.

Proceedings of the 12th International Conference on Information Fusion (Fusion 2009), Seattle, Washington, USA, July, 2009.

Author : Julian Hörst, Felix Sawo, Vesa Klumpp, Uwe D. Hanebeck, Dietrich Fränken
Title : Extension of the Sliced Gaussian Mixture Filter with Application to Cooperative Passive Target Tracking
In : Proceedings of the 12th International Conference on Information Fusion (Fusion 2009)
Date : July 2009

Abstract

This paper copes with the problem of nonlinear Bayesian state estimation.
A nonlinear filter, the Sliced Gaussian Mixture Filter (SGMF), employs linear
substructures in the nonlinear measurement and prediction model in order to
simplify the estimation process.
Here, a special density representation, the sliced Gaussian mixture
density, is used to derive an exact solution of the Chapman-Kolmogorov equation.
The sliced Gaussian mixture density is obtained by a systematic and deterministic
approximation of a continuous density minimizing a certain distance measure.
In contrast to previous work, improvements of the SGMF presented here include an
extended system model and the processing of multi-dimensional nonlinear
subspaces. As an application for the SGMF, cooperative passive target tracking,
where sensors take angular measurements from a target, is considered in this paper.
Finally, the performance of the proposed estimator is compared to the
marginalized particle filter (MPF) in simulations.

Proceedings of the 12th International Conference on Information Fusion (Fusion 2009), Seattle, Washington, USA, July, 2009.

Author : Vesa Klumpp, Uwe D. Hanebeck
Title : Nonlinear Fusion of Multi-Dimensional Densities in Joint State Space
In : Proceedings of the 12th International Conference on Information Fusion (Fusion 2009)
Date : July 2009

Abstract

Nonlinear fusion of multi-dimensional densities
is an important application in Bayesian state estimation.
In the approach proposed here, a joint density over all
considered densities is build, which is then approximated
by means of a Dirac mixture density by partitioning the
joint state space into regions that are represented by single
Dirac components. This approximation procedure depends
on the nonlinear fusion model and only areas relevant to this
model are considered. The processing in joint state space
has advantages, especially when fusing Dirac mixture densities.
Within this approach, degeneration can be avoided
and even densities without mutual support can be combined.
Thus, this approach gives an alternative to multiplication of
Dirac mixtures with a likelihood, as used in the particle filter.
Furthermore, a nonlinear Bayesian estimator with filter
and prediction step can be formulated, which is able to cope
with both discrete and continuous densities.

Proceedings of the 12th International Conference on Information Fusion (Fusion 2009), Seattle, Washington, USA, July, 2009.

Author : Vesa Klumpp, Uwe D. Hanebeck
Title : Bayesian Estimation with Uncertain Parameters of Probability Density Functions
In : Proceedings of the 12th International Conference on Information Fusion (Fusion 2009)
Date : July 2009

Abstract

In this paper, we address the problem of
processing imprecisely known probability density func-
tions by means of Bayesian estimation. The imprecise
knowledge about probability density functions is given
as stochastic uncertainty about their parameters. The
proposed processing of this special density in a Bayesian
estimator is accomplished by reinterpretation of the Fil-
ter and prediction equations. Here, the parameters are
treated as a higher order state, which can be processed
by Bayesian estimation techniques. For state estima-
tion, this avoids the need to select specific values for
unknown parameters and, thus, allows the processing of
all potential parameters at once. The proposed approach
further allows the use of imprecisely known model equa-
tions for measurement and state prediction by the same
principle.

Proceedings of the 12th International Conference on Information Fusion (Fusion 2009), Seattle, Washington, USA, July, 2009.

Author : Benjamin Noack, Vesa Klumpp, Uwe D. Hanebeck
Title : State Estimation with Sets of Densities considering Stochastic and Systematic Errors
In : Proceedings of the 12th International Conference on Information Fusion (Fusion 2009)
Date : July 2009

Abstract

In practical applications, state estimation requires the consideration of
stochastic and systematic errors. If both error types are present, an exact
probabilistic description of the state estimate is not possible, so that
common Bayesian estimators have to be questioned. This paper introduces a
theoretical concept, which allows for incorporating unknown but bounded errors
into a Bayesian inference scheme by utilizing sets of densities. In order to
derive a tractable estimator, the Kalman filter is applied to ellipsoidal sets
of means, which are used to bound additive systematic errors. Also, an
extension to nonlinear system and observation models with ellipsoidal error
bounds is presented. The derived estimator is motivated by means of two
example applications.

Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), pp. 33-39, Seoul, Republic of Korea, August, 2008.

Author : Uwe D. Hanebeck, Vesa Klumpp
Title : Localized Cumulative Distributions and a Multivariate Generalization of the Cramér-von Mises Distance
In : Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008)
Date : August 2008

Abstract

This paper is concerned with distances for comparing
multivariate random vectors with a special focus on the case
that at least one of the random vectors is of discrete type, i.e.,
assumes values from a discrete set only. The first contribution
is a new type of characterization of multivariate random
quantities, the so called Localized Cumulative Distribution
(LCD) that, in contrast to the conventional definition of a
cumulative distribution, is unique and symmetric. Based on the
LCDs of the random vectors under consideration, the second
contribution is the definition of generalized distance measures
that are suitable for the multivariate case. These distances
are used for both analysis and synthesis purposes. Analysis
is concerned with assessing whether a given sample stems from
a given continuous distribution. Synthesis is concerned with
both density estimation, i.e., calculating a suitable continuous
approximation of a given sample, and density discretization,
i.e., approximation of a given continuous random vector by a
discrete one.

Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), pp. 168-174, Seoul, Republic of Korea, August, 2008.

Author : Vesa Klumpp, Uwe D. Hanebeck
Title : Direct Fusion of Dirac Mixture Densities using an Efficient Approximation in Joint State Space
In : Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008)
Date : August 2008

Abstract

In this paper, we present a direct fusion algorithm
for processing the combination of two Dirac mixture densities.
The proposed approach allows the multiplication of two Dirac
mixture densities without requiring identical support and thus
enables the fusion of two independently generated sample sets.
The resulting posterior Dirac mixture density is an approximation
of the true continuous density that would result from the
processing of the underlying true continuous density functions.
This procedure is based on a suboptimal greedy approximation
of the joint state space by means of a Dirac mixture that
iteratively increases the resolution of the fusion result while
considering only the relevant regions in the joint state space,
where the fusion constraint holds.

Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008), pp. 593-600, Seoul, Republic of Korea, August, 2008.

Author : Vesa Klumpp, Uwe D. Hanebeck
Title : Dirac Mixture Trees for Fast Suboptimal Multi-Dimensional Density Approximation
In : Proceedings of the 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI 2008)
Date : August 2008

Abstract

We consider the problem of approximating an
arbitrary multi–dimensional probability density function by
means of a Dirac mixture density. Instead of an optimal
solution based on minimizing a global distance measure between
the true density and its approximation, a fast suboptimal
anytime procedure is proposed, which is based on sequentially
partitioning the state space and component placement by local
optimization. The proposed procedure adaptively covers the
entire state space with a gradually increasing resolution. It
can be efficiently implemented by means of a pre–allocated
tree structure in a straightforward manner. The resulting computational
complexity is linear in the number of components
and linear in the number of dimensions. This allows a large
number of components to be handled, which is especially useful
in high–dimensional state spaces.

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

Author : Vesa Klumpp, Felix Sawo, Uwe D. Hanebeck, Dietrich Fränken
Title : The Sliced Gaussian Mixture Filter for Efficient Nonlinear Estimation
In : Proceedings of the 11th International Conference on Information Fusion (Fusion 2008)
Date : July 2008

Abstract

This paper addresses the efficient state estimation
for mixed linear/nonlinear dynamic systems with noisy measurements.
Based on a novel density representation – sliced Gaussian
mixture density – the decomposition into a (conditionally) linear
and nonlinear estimation problem is derived. The systematic
approximation procedure minimizing a certain distance measure
allows the derivation of (close to) optimal and deterministic
estimation results. This leads to high-quality representations of
the measurement-conditioned density of the states and, hence, to
an overall more efficient estimation process. The performance of
the proposed estimator is compared to state-of-the-art estimators,
like the well-known marginalized particle filter.

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. 1-8, Cologne, Germany, July, 2008.

Author : Felix Sawo, Vesa Klumpp, Uwe D. Hanebeck
Title : Simultaneous State and Parameter Estimation of Distributed-Parameter Physical Systems based on Sliced Gaussian Mixture Filter
In : Proceedings of the 11th International Conference on Information Fusion (Fusion 2008)
Date : July 2008

Abstract

This paper presents a method for the simultaneous
state and parameter estimation of finite-dimensional models of
distributed systems monitored by a sensor network. In the
first step, the distributed system is spatially and temporally
decomposed leading to a linear finite-dimensional model in state
space form. The main challenge is that the simultaneous state and
parameter estimation of such systems leads to a high-dimensional
nonlinear problem. Thanks to the linear substructure contained
in the resulting finite-dimensional model, the development of an
overall more efficient estimation process is possible. Therefore,
in the second step, we propose the application of a novel density
representation – sliced Gaussian mixture density – in order to
decompose the estimation problem into a (conditionally) linear
and a nonlinear problem. The systematic approximation procedure
minimizing a certain distance measure allows the derivation
of (close to) optimal and deterministic results. The proposed
estimation process provides novel prospects in sensor network
applications. The performance is demonstrated by means of
simulation results.

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.