Analysis of Set-theoretic and Stochastic Models for Fusion under Unknown Correlations

In data fusion theory, multiple estimates are combined to yield an optimal result. In this paper, the set of all possible results is investigated, when two random variables with unknown correlations are fused. As a first step, recursive processing of the set of estimates is examined. Besides set-theoretic considerations, the lack of knowledge about the unknown correlation coefficient is modeled as a stochastic quantity. Especially, a uniform model is analyzed, which provides a new optimization criterion for the covariance intersection algorithm in scalar state spaces. This approach is also generalized to multi-dimensional state spaces in an approximative, but fast and scalable way, so that consistent estimates are obtained

One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks

This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive quantization, coding, and field reconstruction scheme is developed and an upper-bound to the associated mean squared error (MSE) at any point and any snapshot is derived in terms of the local spatio-temporal smoothness properties of the underlying field. It is shown that when the noise, sensor placement pattern, and the sensor schedule satisfy certain weak technical requirements, it is possible to drive the MSE to zero with increasing sensor density at points of field continuity while ensuring that the per-sensor bitrate and sensing-related network overhead rate simultaneously go to zero. The proposed scheme achieves the order-optimal MSE versus sensor density scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review format), 4 figures. Submitted to IEEE Transactions on Signal Processing. Current version is updated for journal submission: revised author list, modified formulation and framework. Previous version appeared in Proceedings of Allerton Conference On Communication, Control, and Computing 200

Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets

We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the “big N" problem for big data and the curse of dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high-dimensional stochastic dynamical systems, simultaneously accounting for multifidelity in physical models as well as multifidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to 10⁵ input dimensions and 10⁵ training points on a standard desktop computer

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed

Noise suppressing sensor encoding and neural signal orthonormalization

In this paper we regard first the situation where parallel channels are disturbed by noise. With the goal of maximal information conservation we deduce the conditions for a transform which "immunizes" the channels against noise influence before the signals are used in later operations. It shows up that the signals have to be decorrelated and normalized by the filter which corresponds for the case of one channel to the classical result of Shannon. Additional simulations for image encoding and decoding show that this constitutes an efficient approach for noise suppression. Furthermore, by a corresponding objective function we deduce the stochastic and deterministic learning rules for a neural network that implements the data orthonormalization. In comparison with other already existing normalization networks our network shows approximately the same in the stochastic case but, by its generic deduction ensures the convergence and enables the use as independent building block in other contexts, e.g. whitening for independent component analysis. Keywords: information conservation, whitening filter, data orthonormalization network, image encoding, noise suppression

Linear Estimation in Interconnected Sensor Systems with Information Constraints

A ubiquitous challenge in many technical applications is to estimate an unknown state by means of data that stems from several, often heterogeneous sensor sources. In this book, information is interpreted stochastically, and techniques for the distributed processing of data are derived that minimize the error of estimates about the unknown state. Methods for the reconstruction of dependencies are proposed and novel approaches for the distributed processing of noisy data are developed