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— 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… (More)

— 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… (More)

—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,… (More)

— 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… (More)

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… (More)

— Efficiently implementing nonlinear Bayesian esti-mators is still an unsolved problem, especially for the mul-tidimensional 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.… (More)

— Efficiently implementing nonlinear Bayesian esti-mators 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… (More)

— 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 programming 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… (More)

In this paper we attempt to lay the foundation for a novel filtering technique for the fusion of two random vectors with imprecisely known sto-chastic 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… (More)