Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation

The scientific objectives of the Lisa Technology Package (LTP) experiment, on board of the LISA Pathfinder mission, demand for an accurate calibration and validation of the data analysis tools in advance of the mission launch. The levels of confidence required on the mission outcomes can be reached only with an intense activity on synthetically generated data. A flexible procedure allowing the generation of cross-correlated stationary noise time series was set-up. Multi-channel time series with the desired cross correlation behavior can be generated once a model for a multichannel cross-spectral matrix is provided. The core of the procedure is the synthesis of a noise coloring multichannel filter through a frequency-by-frequency eigendecomposition of the model cross-spectral matrix and a Z-domain fit. The common problem of initial transients in noise time series is solved with a proper initialization of the filter recursive equations. The noise generator performances were tested in a two dimensional case study of the LTP dynamics along the two principal channels of the sensing interferometer.Comment: Accepted for publication in Physical Review D (http://prd.aps.org/

Multichannel high resolution NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modeling time-frequency (TF) representations of audio signals such as spectrograms, notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high-resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. The new model can represent a variety of stationary and non-stationary signals, including autoregressive moving average (ARMA) processes and mixtures of damped sinusoids. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to piano signals, and proves capable of accurately modeling reverberation, restoring missing observations, and separating pure tones with close frequencies

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Rational approximations of spectral densities based on the Alpha divergence

We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by minimizing a suitable distance from the given spectrum and under the constraints corresponding to imposing the given second-order statistics. Here, we consider the Alpha divergence family as a distance measure. We show that the corresponding approximation problem leads to a family of rational solutions. Secondly, such a family contains the solution which generalizes the Kullback-Leibler solution proposed by Georgiou and Lindquist in 2003. Finally, numerical simulations suggest that this family contains solutions close to the non-rational solution given by the principle of minimum discrimination information.Comment: to appear in the Mathematics of Control, Signals, and System

Modeling of Traffic Excitation for System Identification of Bridge Structures

In long-term health monitoring of bridge structures, system identification is often performed based only on the system output (bridge vibration responses) because the system input (traffic excitation) is difficult to measure. To facilitate the identification of the bridge properties, traffic excitation is commonly modeled as spatially uncorrelated white noise. A physical model of a stationary stream of vehicles (moving loads) arriving in accordance with a Poisson process, traversing an elastic beam, shows that the traffic excitation is spatially correlated. Employing the dynamic nodal loading approach, this spatial correlation results in a frequency-dependent excitation spectrum density matrix, and shifts the response spectra obtained from those excited by spatially uncorrelated white noise. It is shown that the application of system identification techniques based on the conventional excitation model may result in misleading structural properties. Hence, this study further proposes an output-only gray-box identification technique for bridge structures, in which knowledge about the nature of the traffic excitation, such as its spatial correlation, is implanted into an autoregressive-moving-average (ARMA) model. The identifiability of the ARMA model so constructed is assured and the feasibility of the proposed identification technique is demonstrated by a numerical example

Modeling of Traffic Excitation for System Identification of Bridge Structures

In long-term health monitoring of bridge structures, system identification is often performed based only on the system output (bridge vibration responses) because the system input (traffic excitation) is difficult to measure. To facilitate the identification of the bridge properties, traffic excitation is commonly modeled as spatially uncorrelated white noise. A physical model of a stationary stream of vehicles (moving loads) arriving in accordance with a Poisson process, traversing an elastic beam, shows that the traffic excitation is spatially correlated. Employing the dynamic nodal loading approach, this spatial correlation results in a frequency-dependent excitation spectrum density matrix, and shifts the response spectra obtained from those excited by spatially uncorrelated white noise. It is shown that the application of system identification techniques based on the conventional excitation model may result in misleading structural properties. Hence, this study further proposes an output-only gray-box identification technique for bridge structures, in which knowledge about the nature of the traffic excitation, such as its spatial correlation, is implanted into an autoregressive-moving-average (ARMA) model. The identifiability of the ARMA model so constructed is assured and the feasibility of the proposed identification technique is demonstrated by a numerical example

Time and spectral domain relative entropy: A new approach to multivariate spectral estimation

The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy rates. This naturally leads to a new spectral estimation technique where a multivariate version of the Itakura-Saito distance is employed}. It may be viewed as an extension of the approach, called THREE, introduced by Byrnes, Georgiou and Lindquist in 2000 which, in turn, followed in the footsteps of the Burg-Jaynes Maximum Entropy Method. Spectral estimation is here recast in the form of a constrained spectrum approximation problem where the distance is equal to the processes relative entropy rate. The corresponding solution entails a complexity upper bound which improves on the one so far available in the multichannel framework. Indeed, it is equal to the one featured by THREE in the scalar case. The solution is computed via a globally convergent matricial Newton-type algorithm. Simulations suggest the effectiveness of the new technique in tackling multivariate spectral estimation tasks, especially in the case of short data records.Comment: 32 pages, submitted for publicatio