## ISBN: 978-3-86644-405-8Probabilistic Framework for Sensor Management zur Erlangung des akademischen Grades eines

### Citations

1006 | Alignment by maximization of mutual information
- Viola, Wells
- 1997
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Citation Context ...ct, the bounds are universally valid and thus applicable in further information-theoretic tasks like capacity calculation of communication channels [45], parameter estimation [39], image registration =-=[182]-=-, and many others. Furthermore, providing a tight lower and upper bound of the entropy value allows deciding whether a direct approximation is meaningful or not, i.e., some kind of confidence interval... |

376 | Information-driven dynamic sensor collaboration
- Zhao, Shin, et al.
- 2002
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Citation Context ...2.6. Related Work 23 2.6.2 Myopic or Greedy Approaches A collection of different objective functions for myopic sensor management is described in detail and compared for a target tracking scenario in =-=[43, 199]-=-. In accordance with [57], it is shown that objective functions based on the expected posterior density function are merely a measure of the predicted density and thus of limited use. More appropriate... |

234 |
Der Merwe, “The unscented Kalman filter for nonlinear estimation
- Wan, Van
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Citation Context ...d, where the state estimates are represented by means of Gaussian mixture densities. In contrast to existing estimators employing statistical linearization like the well-known unscented Kalman filter =-=[91, 183]-=-, estimation quality of the novel Gaussian estimator can be adapted by adjusting the number of regression points used. Chapter 6 In nonlinear state estimation, it is generally inevitable to incorporat... |

105 |
Approximating posterior distributions by mixtures
- WEST
- 1993
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Citation Context ...the desired number of components. The first is Williams’ reduction algorithm [193], which can be considered as global reduction approach. The second is a local reduction algorithm proposed by M. West =-=[188]-=-, while the method of A. Runnalls [153] represents a compromise between local and global approaches. For a more detailed introduction to these algorithms and their classification into local and global... |

69 |
der Merwe. The Unscented Kalman Filter
- Wan, van
- 2001
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Citation Context ...the regressions points of the set ... |

53 |
Optimal Measurement Methods for Distributed Parameter System Identification
- Uciński
- 2005
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Citation Context ...g, that in optimum experimental design theory similar scalar objective functions are defined based on the Fisher information matrix (or its inverse) instead of the ones based on the covariance matrix =-=[11, 178]-=-. Minimizing such objective functions corresponds to minimizing a lower bound of the covariance matrix.20 Chapter 2. Considered Problem 2.5.2 Information Theoretic Objective Functions Shannon’s infor... |

36 | Analytic moment-based Gaussian process filtering - Deisenroth, Huber, et al. - 2009 |

34 | On Entropy Approximation for Gaussian Mixture Random Vectors,”
- Huber, Bailey, et al.
- 2008
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Citation Context ... Especially, the concept of the virtual measurements and pruning via the probabilistic branch-and-bound algorithm can be found here. The upper and lower bounds on the differential entropy are part of =-=[213]-=-. The combination of all these techniques to the information theoretic sensor manager and further improvements on the entropy bounds are the main contributions of this chapter. 4.1 Closed-loop Control... |

32 | Approximate dynamic programming for communication-constrained sensor network management.
- Williams, Fisher, et al.
- 2007
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Citation Context ... always tight [20], the resulting performance can divergence arbitrarily from the closed-loop performance. For target tracking applications with linear system dynamics and additive measurement noise, =-=[40, 190]-=- present open-loop control approaches, where the nonlinear sensor models are linearized multiple time steps ahead, based on the current system estimate. This facilitates the use of the Kalman filter w... |

28 | Information theoretic sensor management
- WILLIAMS
- 2007
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Citation Context ...mit their measurement values simultaneously. Furthermore,4 Chapter 1. Introduction often only those measurements are informative that are provided by sensors in close vicinity of the observed system =-=[189]-=-. To increase the operational lifetime of the sensor network, the measurement rate should be as low as possible, which on the other hand leads to a decrease in information gain and consequently in est... |

26 | Efficient derivative-free Kalman filters for online learning
- Merwe, Wan
- 2001
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Citation Context ...97]. For any nonlinear transformation, the propagated regression points capture the posterior mean and covariance matrix accurately up to the second order of the corresponding Taylor-series expansion =-=[180]-=-. For further improving the accuracy, the set of regression points used for the Gaussian estimator proposed in this chapter is not restricted to a fixed size. Increasing the number of regression point... |

23 | Cost-Function-Based Gaussian Mixture Reduction for Target Tracking
- Williams, Maybeck
- 2003
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Citation Context ...r divergence (2.30) can also be used, especially as it is the ideal deviation measure for mixture7.1. Gaussian Mixture Reduction via Homotopy Continuation 113 reduction in a maximum likelihood sense =-=[153, 193]-=-. Due to the fact that it is impossible to evaluate this measure in closed form for Gaussian mixtures, numerical integration schemes have to be employed, which leads to increased computational costs. ... |

22 |
Optimal sensor location for parameter estimation of distributed processes,”
- Ucinski
- 2000
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Citation Context ...trix. As the PCRLB depends on the future system state, the PCRLB is calculated approximately in a predictive manner based on particle filtering [41, 80], a priori and constant estimation of the state =-=[143, 179]-=-, or adaptive discretization [79]. As the PCRLB is merely a lower bound, which is above all not always tight [20], the resulting performance can divergence arbitrarily from the closed-loop performance... |

16 | Information-theoretic approaches for sensor selection and placement in sensor networks for target localization and tracking.
- Wang, Yao, et al.
- 2005
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Citation Context ...er’s number. Mutual Information R ... |

16 | On the minimum volume covering ellipsoid of ellipsoids,” Dept
- Yildirim
- 2005
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Citation Context ...etermination of the covering ellipsoid that contains the ellipsoids of all sensor information matrices. This problem is similar to the so-called covariance union or Löwner ellipsoid problem (see e.g. =-=[23, 198]-=-). Thanks to the fact that all sensor information ellipsoids have the same center, the covariance union problem can be significantly simplified. At first, it is sufficient to consider the determinatio... |

15 | Closed-Form Prediction of Nonlinear Dynamic Systems by Means of Gaussian Mixture Approximation of the Transition Density - Huber, Brunn, et al. - 2006 |

14 |
Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation
- Huber, Hanebeck
- 2008
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Citation Context ...ty. The complete Gaussian estimator and an extension to Gaussian mixtures is presented in Section 5.4 and Section 5.5, respectively. The Gaussian estimator introduced in this section was published in =-=[217]-=- and its applicability on the real-world localization problem of tracking a human in a telepresence environment was demonstrated in experiments in [209]. Extensions to these publications are the grid ... |

13 | Decentralized Sigma-Point Information Filters for Target Tracking in Collaborative Sensor Networks
- Vercauteren, Wang
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Citation Context ... ˆ... |

11 | Performance guarantees for information theoretic active inference
- Williams, Fisher, et al.
- 2007
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Citation Context ...en applied to the problems of sensor subset selection [103], sensor scheduling [104], or sensor placement selection [105]. Extensions to sensor management problems for dynamic systems can be found in =-=[191, 192]-=-. 2.6.3 Non-myopic Sensor Management For discrete state spaces, solutions to the closed-loop control sensor management problem based on dynamic programming can be found for example in [33, 112]. Espec... |

11 |
Unscented Kalman filtering for additive noise case: augmented vs.
- Wu, Hu, et al.
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Citation Context ...the regressions points of the set ... |

10 | Gaussian Mixture Reduction via Clustering - Schieferdecker, Huber - 2009 |

8 | The hybrid density filter for nonlinear estimation based on hybrid conditional density approximation
- Huber, Hanebeck
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Citation Context ...mponents of the Bayesian estimator, while all other components contain the approximations that are necessary for performing estimations by means of the HDF. The HDF for scalar states was published in =-=[215, 216]-=-, while the extension to the multivariate case represents unpublished material. The proposed estimator was applied to stochastic model predictive control problems [226, 230] and parameter identificati... |

8 | Progressive Gaussian Mixture Reduction
- Huber, Hanebeck
- 2008
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Citation Context ...of the proposed reduction method, closed-form solutions for all necessary calculations are derived. The fundamentals of the proposed progressive Gaussian mixture reduction algorithm were published in =-=[219]-=- for univariate Gaussian mixtures. This chapter extends the results of this paper to the multivariate case. 1 For an introduction to homotopy continuation see for example [3].110 Chapter 7. Progressi... |

6 |
Target tracking with glint noise
- Wu
- 1993
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Citation Context ...e the performance of the estimators for stronger and more heavily tailored noise. For the given simulation setup the following four estimators are considered: 2 For tracking with glint noise see e.g. =-=[195]-=-.6.3. Extension to Multivariate States 105 HDF A HDF exploiting that merely the position [... |

6 | Efficient nonlinear measurement updating based on Gaussian mixture approximation of conditional densities
- Huber, Brunn, et al.
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Citation Context ... Cramér-von Mises distance [24] ... |

5 | Distributed greedy sensor scheduling for model-based reconstruction of space-time continuous physical phenomena.
- Huber, Kuwertz, et al.
- 2009
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Citation Context ...ensor management could be to employ submodular objective functions [104, 192], which provide a tight bound on the estimation performance in case of greedy/myopic sensor management. As demonstrated in =-=[220]-=-, myopic sensor management in turn simplifies a distributed implementation as only local knowledge is necessary. Constrained Sensor Management The objective functions employed in this thesis, namely c... |

5 | A Closed–Form Model Predictive Control Framework for Nonlinear Noise–Corrupted Systems - Weissel, Huber, et al. - 2007 |

4 | Optimal control of stochastic systems with costly observations - the general markovian model and the LQG problem
- Wu, Arapostathis
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Citation Context ...nt policy from the measurement values. The separation principle still holds for the additional consideration of running measurement costs, which are associated with the requested level of information =-=[194]-=-. Works toward pure sensor management strategies neglecting the control of the dynamic system and employing more adequate objective functions can be found in [37, 88, 119, 138, 148]. In [119], mutual ... |

4 | Hybrid transition density approximation for efficient recursive prediction of nonlinear dynamic systems
- Huber, Hanebeck
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Citation Context ...mponents of the Bayesian estimator, while all other components contain the approximations that are necessary for performing estimations by means of the HDF. The HDF for scalar states was published in =-=[215, 216]-=-, while the extension to the multivariate case represents unpublished material. The proposed estimator was applied to stochastic model predictive control problems [226, 230] and parameter identificati... |

4 | Priority List Sensor Scheduling using Optimal Pruning
- Huber, Hanebeck
- 2008
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Citation Context ... depending on the concrete application and required accuracy. The novel open-loop model predictive sensor management approach named quasi-linear sensor management proposed in this section is based on =-=[218, 221]-=-. Extensions to these publications are in particular the linearization procedure as well as the derivation of the bounding sensor for pruning.26 Chapter 3. Quasi-linear Sensor Management 3.1 Linear G... |

4 |
Parameter Identification and Reconstruction Based on Hybrid Density Filter for Distributed Phenomena
- Sawo, Huber, et al.
- 2007
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Citation Context ...extension to the multivariate case represents unpublished material. The proposed estimator was applied to stochastic model predictive control problems [226, 230] and parameter identification problems =-=[222]-=-. 6.1 Conditional Density Approximation In this section, only scalar states are considered for brevity and clarity. The extension to multivariate states is content of Section 6.3. Furthermore, it is a... |

4 | A nonlinear model predictive control framework approximating noise corrupted systems with hybrid transition densities
- Weissel, Huber, et al.
- 2007
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Citation Context ...ar states was published in [215, 216], while the extension to the multivariate case represents unpublished material. The proposed estimator was applied to stochastic model predictive control problems =-=[226, 230]-=- and parameter identification problems [222]. 6.1 Conditional Density Approximation In this section, only scalar states are considered for brevity and clarity. The extension to multivariate states is ... |

4 | Test-Environment based on a Team of Miniature Walking Robots for Evaluation of Collaborative Control Methods - Weissel, Huber, et al. - 2007 |

3 |
A novel gaussian sum filter method for accurate solution to nonlinear filtering problem.
- Terejanu, Singla, et al.
- 2008
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Citation Context ... steps have to be performed consecutively without a measurement update in-between or when the measurement noise is strong. For the Gaussian sum filter, a simultaneous weight calculation is derived in =-=[177]-=-, which can be adapted for the proposed Gaussian mixture estimator in a straightforward manner. 5.5.2 Measurement Update Step Analogously to the prediction step, state and noise Gaussian mixtures are ... |

3 | Stochastic Model Predictive Control of Time-Variant Nonlinear Systems with Imperfect State Information
- Weissel, Schreiter, et al.
- 2008
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Citation Context ... a computationally tractable determination of the configuration sequence, their application is not restrict to the proposed sensor management approach. The foundation of this chapter was published in =-=[230]-=- in the context of closed-loop model predictive control of stochastic nonlinear systems. Especially, the concept of the virtual measurements and pruning via the probabilistic branch-and-bound algorith... |

2 |
Entropy based Sensor Selection Heuristic for Target Localization
- Wang, Yao, et al.
- 2004
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Citation Context ...nd thus of limited use. More appropriate are objective functions that evaluate the expected information gain as for example mutual information or the expected entropy do. This finding is exploited in =-=[52, 186]-=-. For a reduced computational burden, entropy differences defined over the measurement space are used in [186] for approximating mutual information instead of considering the joint state and measureme... |

2 | Performance guarantees for information theoretic sensor resource management
- Williams, Fisher, et al.
- 2007
(Show Context)
Citation Context ...en applied to the problems of sensor subset selection [103], sensor scheduling [104], or sensor placement selection [105]. Extensions to sensor management problems for dynamic systems can be found in =-=[191, 192]-=-. 2.6.3 Non-myopic Sensor Management For discrete state spaces, solutions to the closed-loop control sensor management problem based on dynamic programming can be found for example in [33, 112]. Espec... |

2 |
An Improvement to Unscented Transformation
- Wu, Wu, et al.
- 2004
(Show Context)
Citation Context ...nding weights that exactly captures the mean ˆ... |

2 | Nichtlineare Sensoreinsatzplanung zur modellbasierten Quellenverfolgung bei räumlich ausgedehnten Phänomenen (Nonlinear Sensor Management for Model-based Source Detection - Kuwertz - 2009 |

2 | Prädiktions- und Einsatzplanungsverfahren zur effizienten Zustandsschätzung von Prozessketten (Prediction and Scheduling Methods for Efficient State Estimation of Supply Chains - Stiegeler |

2 | Instantaneous Pose Estimation using Rotation Vectors
- Beutler, Huber, et al.
- 2009
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Citation Context ...tor introduced in this section was published in [217] and its applicability on the real-world localization problem of tracking a human in a telepresence environment was demonstrated in experiments in =-=[209]-=-. Extensions to these publications are the grid approach for the extension to multivariate densities and the extension to Gaussian mixtures. 5.1 Problem Formulation In order to derive a Gaussian estim... |

2 | Probabilistic instantaneous modelbased signal processing applied to localization and tracking, Robotics and Autonomous Systems 57 (3 - Beutler, Huber, et al. - 2009 |

1 |
Stochastische modell-prädiktive Regelung nichtlinearer System (Stochastic Model Predictive Control of nonlinear Systems
- Weissel
- 2009
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Citation Context ...rithm is used, which ensures even in this particular case that the optimal solutions is always found. In the following, a brief review of PBAB is given. A detailed description of PBAB can be found in =-=[187]-=- and [230]. Since PBAB operates on negative objective function values for maximization, the step objectives are converted according to ¯... |

1 | Mehrschrittige nichtlineare Sensoreinsatzplanung zur Lokalisierung mobiler Roboter (Non-myopic Nonlinear Sensor Management for Mobile Robot Localization). Student research project, Intelligent Sensor-Actuator-Systems - Chlebek - 2009 |

1 | Erweiterung eines progressiven Verfahrens zur Reduktion multivariater Gaußmischdichten (Extension of a Progressive Gaussian Mixture Reduction Method to the Multivariate Case). Student research project, Intelligent Sensor-Actuator-Systems - Ding - 2008 |

1 | Mehrstufiges Clustering-Verfahren zur Komponentenreduktion von Gaußmischdichten (Multi-stage Clustering-based Approach to Gaussian Mixture Reduction). Student research project, Intelligent Sensor-Actuator-Systems - Itte - 2009 |

1 |
Nichtlineare Sensoreinsatzplanung für Sensor-Aktor-Netzwerke (Nonlinear Sensor Scheduling for Sensor-Actuator-Networks
- Meyer
- 2007
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Citation Context ...(... |

1 | Sensoreinsatzplanung in unzuverlässigen Kommunikationsnetzwerken (Sensor Scheduling in Unreliable Communication Networks). Student research project - Stiegeler |

1 |
Gaussian Filtering using State Decomposition Methods
- Beutler, Huber, et al.
- 2009
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Citation Context ...see next section), where the noise dimensions can be considered as less relevant. Furthermore, the techniques proposed in Section 6.3.2 for decomposing the state vector can also be employed here (see =-=[208]-=-). By this means, only parts of the state vector needs to be represented by a set of regression points, which facilitates the application of the grid approach even for many high-dimensional problems.... |

1 | On Sensor Scheduling in Case of Unreliable Communication
- Huber, Stiegeler, et al.
- 2007
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Citation Context ... depending on the concrete application and required accuracy. The novel open-loop model predictive sensor management approach named quasi-linear sensor management proposed in this section is based on =-=[218, 221]-=-. Extensions to these publications are in particular the linearization procedure as well as the derivation of the bounding sensor for pruning.26 Chapter 3. Quasi-linear Sensor Management 3.1 Linear G... |

1 | Stochastic Optimal Control based on Value-Function Approximation using Sinc Interpolation - Weissel, Huber, et al. - 2008 |

1 | Efficient Control of Nonlinear Noise– Corrupted Systems Using a Novel Model Predictive Control Framework - Weissel, Huber, et al. - 2007 |

1 | Stochastic Nonlinear Model Predictive Control based on Gaussian Mixture Approximations - Weissel, Huber, et al. |