Marco F. Huber

On entropy approximation for Gaussian mixture random vectors

For many practical probability density representations such as for the widely used Gaussian mixture densities, an analytic evaluation of the differential entropy is not possible and thus, approximate calculations are inevitable. For this purpose, the first contribution of this paper deals with a novel entropy approximation method for Gaussian mixture random vectors, which is based on a component-wise Taylor-series expansion of the logarithm of a Gaussian mixture and on a splitting method of Gaussian mixture components. The employed order of the Taylor-series expansion and the number of components used for splitting allows balancing between accuracy and computational demand. The second contribution is the determination of meaningful and efficiently to calculate lower and upper bounds of the entropy, which can be also used for approximation purposes. In addition, a refinement method for the more important upper bound is proposed in order to approach the true entropy value.

Analytic moment-based Gaussian process filtering

We propose an analytic moment-based filter for nonlinear stochastic dynamic systems modeled by Gaussian processes. Exact expressions for the expected value and the covariance matrix are provided for both the prediction step and the filter step, where an additional Gaussian assumption is exploited in the latter case. Our filter does not require further approximations. In particular, it avoids finite-sample approximations. We compare the filter to a variety of Gaussian filters, that is, the EKF, the UKF, and the recent GP-UKF proposed by Ko et al. (2007).

Gaussian Filter based on Deterministic Sampling for High Quality Nonlinear Estimation

In this paper, a Gaussian filter for nonlinear Bayesian estimation is introduced that is based on a deterministic sample selection scheme. For an effective sample selection, a parametric density function representation of the sample points is employed, which allows approximating the cumulative distribution function of the prior Gaussian density. The computationally demanding parts of the optimization problem formulated for approximation are carried out off-line for obtaining an efficient filter, whose estimation quality can be altered by adjusting the number of used sample points. The improved performance of the proposed Gaussian filter compared to the well-known unscented Kalman filter is demonstrated by means of two examples.

Robust Filtering and Smoothing with Gaussian Processes

We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP) models. GPs are gaining increasing importance in signal processing, machine learning, robotics, and control for representing unknown system functions by posterior probability distributions. This modern way of system identification is more robust than finding point estimates of a parametric function representation. Our principled filtering/smoothing approach for GP dynamic systems is based on analytic moment matching in the context of the forward-backward algorithm. Our numerical evaluations demonstrate the robustness of the proposed approach in situations where other state-of-the-art Gaussian filters and smoothers can fail.

Dirac mixture approximation of multivariate Gaussian densities

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 Cramérvon 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.

A survey of technologies for the internet of things

The number of smart things is growing exponentially. By 2020, tens of billions of things will be deployed worldwide, collecting a wealth of diverse data. Traditional computing models collect in-field data and then transmit it to a central data center where analytics are applied to it, but this is no longer a sustainable model. New approaches and new technologies are required to transform enormous amounts of collected data into meaningful information. Technology also will enable the interconnection around things in the IoT ecosystem but further research is required in the development, convergence and interoperability of the different IoT elements. In this paper, we provide a picture of the main technological components needed to enable the interconnection among things in order to realize IoT concepts and applications.

Recursive Gaussian process: On-line regression and learning

Abstract Two approaches for on-line Gaussian process regression with low computational and memory demands are proposed. The first approach assumes known hyperparameters and performs regression on a set of basis vectors that stores mean and covariance estimates of the latent function. The second approach additionally learns the hyperparameters on-line. For this purpose, techniques from nonlinear Gaussian state estimation are exploited. The proposed approaches are compared to state-of-the-art sparse Gaussian process algorithms.

Optimal Pruning for Multi-Step Sensor Scheduling

In the considered linear Gaussian sensor scheduling problem, only one sensor out of a set of sensors performs a measurement. To minimize the estimation error over multiple time steps in a computationally tractable fashion, the so-called information-based pruning algorithm is proposed. It utilizes the information matrices of the sensors and the monotonicity of the Riccati equation. This allows ordering sensors according to their information contribution and excluding many of them from scheduling. Additionally, a tight lower is calculated for branch-and-bound search, which further improves the pruning performance.

Low Resolution Person Detection with a Moving Thermal Infrared Camera by Hot Spot Classification

In many visual surveillance applications the task of person detection and localization can be solved easier by using thermal long-wave infrared (LWIR) cameras which are less affected by changing illumination or background texture than visual-optical cameras. Especially in outdoor scenes where usually only few hot spots appear in thermal infrared imagery, humans can be detected more reliably due to their prominent infrared signature. We propose a two-stage person recognition approach for LWIR images: (1) the application of Maximally Stable Extremal Regions (MSER) to detect hot spots instead of background subtraction or sliding window and (2) the verification of the detected hot spots using a Discrete Cosine Transform (DCT) based descriptor and a modified Random Naïve Bayes (RNB) classifier. The main contributions are the novel modified RNB classifier and the generality of our method. We achieve high detection rates for several different LWIR datasets with low resolution videos in real-time. While many papers in this topic are dealing with strong constraints such as considering only one dataset, assuming a stationary camera, or detecting only moving persons, we aim at avoiding such constraints to make our approach applicable with moving platforms such as Unmanned Ground Vehicles (UGV).

Probabilistic Framework for Sensor Management

A probabilistic sensor management framework is introduced, which maximizes the utility of sensor systems with many different sensing modalities by dynamically configuring the sensor system in the most beneficial way. For this purpose, techniques from stochastic control and Bayesian estimation are combined such that long-term effects of possible sensor configurations and stochastic uncertainties resulting from noisy measurements can be incorporated into the sensor management decisions.