Explicit expressions for the second order statistics of cepstral components representing clean and noisy signal waveforms are derived. The noise is assumed additive to the signal, and the spectral components of each process are assumed statistically independent complex Gaussian random variables. The key result developed here is an explicit expression for the cross-covariance between the log-spe...

In this letter, the concept of stochastic degree of freedom (SDF) is introduced as the dual concept of normalized mean square covariance (NMSV) for general L2 stochastic processes. We consider the discrete-time representations of bandwidth and time limited WSSUS channels and show how the normalized mean square covariances can be computed for the equivalent discrete-time channels. Then, we use t...

Most estimates of sea spray aerosol source functions have used indirect means to infer the rate of production as a function of wind speed. Only recently has the technology become available to make high frequency measurements of aerosol spectra suitable for direct eddy correlation determination of the sea spray particle flux. This was accomplished in this study by combining a newly developed fas...

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero i...

In this paper, a multi-sensor information fusion steady-state Kalman estimator for discrete time stochastic linear systems with system errors and sensor errors is presented. Gevers-Wouters(G-W) algorithm is used in this paper. Steady-state Kalman estimator is presented in this paper avoids the complex Diophantine equation, and it is based on the ARMA model to compute the steady-state Kalman est...

The authors derived a best linear unbiased estimate (BLUE) for the estimation of noise covariance matrix, where matrix residuals regression equation is required. In previous paper, sample was given, but consistency not analyzed. this theoretical analysis shows that proposed consistent in certain sense.

We introduce new definitions of states and of representations of covariance systems. The GNS-construction is generalized to this context. It associates a representation with each state of the covariance system. Next, states are extended to states of an appropriate covariance algebra. Two applications are given. We describe a nonrelativistic quantum particle, and we give a simple description of ...

NANNY WERMUTH , D.R . COX and GIOVANNI M. MARCHETTI 3 Mathematical Statistics, Chalmers/Gothenburg University, Chalmers tvärgata 3, 41296 Göteborg, Sweden. E-mail: [email protected] Nuffield College, Oxford OX1 1NF, UK. E-mail: [email protected] Dipartimento di Statistica, Università degli Studi di Firenze ‘Giuseppe Parenti’, Viale Morgagni 59, Italy. E-mail: Giovanni.marchetti@u...

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form a covariance operator field. We show that, in most circumstances, covariance...