1,031 research outputs found
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation
Dual optimal filters for parameter estimation of a multivariate autoregressive process from noisy observations
This study deals with the estimation of a vector process disturbed by an additive white noise. When this process is
modelled by a multivariate autoregressive (M-AR) process, optimal filters such as Kalman or H1 filter can be used for
prediction or estimation from noisy observations. However, the estimation of the M-AR parameters from noisy observations is
a key issue to be addressed. Off-line or iterative approaches have been proposed recently, but their computational costs can be
a drawback. Using on-line methods such as extended Kalman filter and sigma-point Kalman filter are of interest, but the size
of the state vector to be estimated is quite high. In order to reduce this size and the resulting computational cost, the authors
suggest using dual optimal filters. In this study, the authors propose to extend to the multi-channel case the so-called dual
Kalman or H1 filters-based scheme initially proposed for single-channel applications. The proposed methods are first tested
with a synthetic M-AR process and then with an M-AR process corresponding to a mobile fading channel. The comparative
simulation study the authors carried out with existing techniques confirms the effectiveness of the proposed methods
Bayesian spectral modeling for multiple time series
We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series. The log-periodogram distribution for each series is modeled as a mixture of Gaussian distributions with frequency-dependent weights and mean functions. The implied model for the log-spectral density is a mixture of linear mean functions with frequency-dependent weights. The mixture weights are built through successive differences of a logit-normal distribution function with frequency-dependent parameters. Building from the construction for a single spectral density, we develop a hierarchical extension for multiple time series. Specifically, we set the mean functions to be common to all spectral densities and make the weights specific to the time series through the parameters of the logit-normal distribution. In addition to accommodating flexible spectral density shapes, a practically important feature of the proposed formulation is that it allows for ready posterior simulation through a Gibbs sampler with closed form full conditional distributions for all model parameters. The modeling approach is illustrated with simulated datasets, and used for spectral analysis of multichannel electroencephalographic recordings (EEGs), which provides a key motivating application for the proposed methodology
A new Kalman filter-based algorithm for adaptive coherence analysis of non-stationary multichannel time series
IEEE International Symposium on Circuits and Systems, Island of Kos, Greece, 21-24 May 2006This paper proposes a new Kalman filter-based algorithm for multichannel autoregressive (AR) spectrum estimation and adaptive coherence analysis with variable number of measurements. A stochastically perturbed k -order difference equation constraint model is used to describe the dynamics of the AR coefficients and the intersection of confidence intervals (ICI) rule is employed to determine the number of measurements adaptively to improve the timefrequency resolution of the AR spectrum and coherence function. Simulation results show that the proposed algorithm achieves a better time-frequency resolution than conventional algorithms for non-stationary signals. © 2006 IEEE.published_or_final_versio
Measuring information-transfer delays
In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics
Structured Sparsity Models for Multiparty Speech Recovery from Reverberant Recordings
We tackle the multi-party speech recovery problem through modeling the
acoustic of the reverberant chambers. Our approach exploits structured sparsity
models to perform room modeling and speech recovery. We propose a scheme for
characterizing the room acoustic from the unknown competing speech sources
relying on localization of the early images of the speakers by sparse
approximation of the spatial spectra of the virtual sources in a free-space
model. The images are then clustered exploiting the low-rank structure of the
spectro-temporal components belonging to each source. This enables us to
identify the early support of the room impulse response function and its unique
map to the room geometry. To further tackle the ambiguity of the reflection
ratios, we propose a novel formulation of the reverberation model and estimate
the absorption coefficients through a convex optimization exploiting joint
sparsity model formulated upon spatio-spectral sparsity of concurrent speech
representation. The acoustic parameters are then incorporated for separating
individual speech signals through either structured sparse recovery or inverse
filtering the acoustic channels. The experiments conducted on real data
recordings demonstrate the effectiveness of the proposed approach for
multi-party speech recovery and recognition.Comment: 31 page
- …