Felix Sawo

Nonlinear Multidimensional Bayesian Estimation with Fourier Densities

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

Sensor node localization methods based on local observations of distributed natural phenomena

This paper addresses the model-based localization of sensor networks based on local observations of a distributed phenomenon. For the localization process, we propose the rigorous exploitation of strong mathematical models of distributed phenomena. By unobtrusively exploiting background phenomena, the individual sensor nodes can be localized by only observing its local surrounding without the necessity of heavy infrastructure. In this paper, we introduce two novel approaches: (a) the polynomial system localization method (PSL-method) and (b) the simultaneous reconstruction and localization method (SRL-method). The first approach (PSL-method) is based on restating the mathematical model of the distributed phenomenon in terms of a polynomial system. These equations depend on both the state of the phenomenon and the node locations. Solving the system of polynomials for each individual sensor node directly leads to the desired locations. The second approach (SRL-method) basically regards the localization problem as a simultaneous state and parameter estimation problem with the node locations as parameters. By this means, the distributed phenomenon is reconstructed and the individual nodes are localized in a simultaneous fashion. In addition, within this framework the uncertainties in the mathematical model and the measurements are considered. The performance of the two different localization approaches is demonstrated by means of simulation results.

Parameter identification and reconstruction for distributed phenomena based on hybrid density filter

This paper addresses the problem of model-based reconstruction and parameter identification of distributed phenomena characterized by partial differential equations. The novelty of the proposed method is the systematic approach and the integrated treatment of uncertainties, which naturally occur in the physical system and arise from noisy measurements. The main challenge of accurate reconstruction is that model parameters, i.e., diffusion coefficients, of the physical model are not known in advance and usually need to be identified. Generally, the problem of parameter identification leads to a nonlinear estimation problem. Hence, a novel efficient recursive procedure is employed. Unlike other estimators, the so-called Hybrid Density Filter not only assures accurate estimation results for nonlinear systems, but also offers an efficient processing. By this means it is possible to reconstruct and identify distributed phenomena monitored by autonomous wireless sensor networks. The performance of the proposed estimation method is demonstrated by means of simulations.

Efficient Nonlinear Bayesian Estimation based on Fourier Densities

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

Parameterized Joint Densities with Gaussian and Gaussian Mixture Marginals

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 coefficient, this parameter is a sufficient 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

Passivity-based dynamic visual feedback control of manipulators with kinematic redundancy

In this paper a passivity-based dynamic visual feedback control system, based on extended task space formulation, is addressed to control the kinematically redundant manipulator. Specifically, we consider the target tracking problem of dynamic visual feedback systems in the 3D-workspace. Firstly the brief summary of the visual feedback system is given with the fundamental representation of a relative rigid body motion. Secondly we derive the passivity of the dynamic visual feedback system by combining the manipulator dynamics (expressed in extended task space) and the visual feedback system. Using the proposed dynamic visual feedback control, one can optimize a performance index while tracking a moving target object. Finally we present simulation results to confirm the effectiveness of the proposed visual feedback control method and to verify the stability of both the end-effector motion and the null-space motion

Parameterized joint densities with Gaussian mixture marginals and their potential use in nonlinear robust estimation

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 ξ̱. 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 ξ̱. 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.

Model-based approaches for sensor data monitoring for smart bridges

At present, bridge maintenance management typically consists of regular visual building inspections. Structural damage frequently remains undiscovered until it becomes clearly visible, a situation which makes little economic sense. However, it is often the case that damage and critical reactions to a bridges internal structure occur in inaccessible and concealed places, and are caused by existing but often unknown effects on the construction. Existing as well as newly-constructed bridges should therefore be able to provide information about their condition and its development at an early stage in addition to the building inspections. To achieve this, flexible and adaptable modular systems are required in and on the bridge structures to provide measurement-technology support, together with differentiated evaluation procedures and a correspondingly enlarged maintenance management program. The instrumentation required must consist of capable and durable sensor technology to register effects on the structures and the reactions of individual structural elements; on the other hand smart measurement data processing must also be in place to ensure the plausibility, fusion, interpolation and reduction of sensor data streams in situ. This article summarises the approaches and prospects of implementing a high-performance sensor data analysis and monitoring concept which has been examined in the context of current research with a focus on practical aspects of monitoring bridge structures. The discussion in this contribution focuses on model-based analysis techniques with regard to areas of application and input-to-benefit-ratios. The findings of this research are of general interest and therefore transferable to other areas of infrastructure maintenance management.

Decentralized State Estimation of Distributed Phenomena based on Covariance Bounds

Abstract This paper addresses the problem of decentralized state estimation of distributed physical phenomena observed by a sensor network. The centralized approaches are not scalable for large sensor networks, because all information has to be transmitted to a powerful central processing node requiring an extensive amount of communication bandwidth and a lot of processing power. Thus, for a decentralized reconstruction of distributed phenomena, we propose a novel methodology consisting of three steps: (a) conversion of the distributed phenomenon into a lumped-parameter system description, (b) decomposition of the resulting system in order to map the description to the actual sensor network, and (c) decomposition of the density representation leading to a decentralized estimation approach. The main problem of a decentralized approach is that due to the propagation of local information through the network, unknown correlations are caused. This fact needs to be considered during the reconstruction process in order to get correct and consistent estimation results. For that reason, we employ a robust estimator (based on Covariance Bounds) for the local reconstruction update on each sensor node. By this means, the individual sensor nodes are able to estimate the local state of the distributed phenomenon using local estimates obtained and communicated by adjacent nodes only. The information about their correlations is not stored in the sensor network.

Modellbasierte Quellenverfolgung in räumlich ausgedehnten Phänomenen mittels Sensoreinsatzplanung

Zusammenfassung Bewegte Quellen können durch Emission räumlich ausgedehnte Phänomene wie beispielsweise Schadstoff- oder Temperaturverteilungen erzeugen. Zur Lokalisierung von Quellen mit unbekannter Position stehen in vielen Aufgabenstellungen Informationen nur indirekt durch die verteilte Vermessung des induzierten Phänomens zur Verfügung — etwa unter Verwendung stationärer oder mobiler Sensoren. Dieser Beitrag stellt modellbasierte Verfahren für eine echtzeitfähige Lokalisierung und Verfolgung von bewegten Quellen vor. Zur gezielten Maximierung des Informationsgehalts der Messungen wird dabei eine vorausschauende Sensoreinsatzplanung genutzt, welche eine hohe Lokalisierungsgüte bei geringem Aufwand ermöglicht. Abstract Space-time continuous phenomena such as pollution loads or temperature distributions often originate from unknown and possibly movable sources. In many real-world scenarios, however, information about the location of such sources can only be gained indirectly by monitoring the induced physical phenomena using distributed sensing systems, e. g., stationary or mobile sensors. In this article, a model-based approach for real-time source localization and target tracking is introduced. To maximize specific information gained from the measurements, this approach strongly relies on a non-myopic sensor management methodology, which allows for tracking moving sources in an efficient and accurate manner.