It is shown that the covariance intersection fusion rule, widely used in the context of distributed estimation, has a nice information-theoretic interpretation in terms of consensus on the Kullback-Leibler average of Gaussian probability density functions (PDFs). Based on this observation, a novel distributed state estimator based on the consensus among local posterior PDFs is proposed and its ...

The direct Fast Fourier Transform method is very attractive for its simplicity and speed in generating multidimensional random fields. This thesis describes an efficient FFT method for generating multivariate multidimensional random fields based on the alternative spectral representation. Generation of a multivariate random field is simplified by the use of the spectral factorization function. ...

We address the problem of estimation of covariance matrices expressible as a sum of Kronecker products (KPs). Our goal is to arrive at estimates of the KP component matrices within a maximum-likelihood (ML) framework. Since the exact solution of the ML cost function is non-tractable, we propose a covariance-matching (CM) approach, noting that the estimates obtained from covariance-matching coin...

The problem of constructing valid parametric cross-covariance functions is challenging. We propose a simple methodology, based on latent dimensions and existing covariance models for univariate random fields, to develop flexible, interpretable and computationally feasible classes of cross-covariance functions in closed form. We focus on spatio-temporal cross-covariance functions that can be non...

This paper deals with the fusion of random variables when cross covariances are unknown. This is a vital problem in nearly every real world application since cross covariances are often impossible to obtain but also cannot be ignored. We provide a rigorous derivation of the fusion equations which are also known as covariance intersection. This approach allows us to derive an iterative scheme fo...

We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W , i.e., an exogenous random function, a scalar response Y is modeled in dependence of an endogenous random function X. Assuming second order stationarity jointly for X and W a nonparametric estimator of the functional slope parameter and its derivative...

one-way analysis of covariance is a popular and common statisticalmethod, wherein the equality of the means of several random variables whichhave a linear relationship with a random mathematical variable, is tested. inthis study, a method is presented to improve the one-way analysis of covari-ance when there is an uncertainty in accepting the statistical hypotheses. themethod deals with a fuzzy...

In this mini-project, we have defined the problem of inferring a spatially varying function given a finite set of noisy sensor observations. The challenge lies in the nonuniform noise in the input space of the observed data. The assumption is that samples generated along a particular trajectory tend to experience similar levels of noise in their location information. Therefore, we design an inf...