13,167 research outputs found
A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating
An important part of system modeling is determining parameter values,
particularly for biomolecular systems, where direct measurements of individual
parameters are typically hard. While Extended Kalman Filters have been used for
this purpose, the choice of the process noise covariance is generally unclear.
In this chapter, we address this issue for biomolecular systems using a
combination of Monte Carlo simulations and experimental data, exploiting the
dependence of the process noise covariance on the states and parameters, as
given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering
technique by updating the process noise covariance at each time step based on
estimates. We compare the performance of this framework with different fixed
values of process noise covariance in biomolecular system models, including an
oscillator model, as well as in experimentally measured data for a negative
transcriptional feedback circuit. We find that the Extended Kalman Filter with
such process noise covariance update is closer to the optimality condition in
the sense that the innovation sequence becomes white and in achieving a balance
between the mean square estimation error and parameter convergence time. The
results of this chapter may help in the use of Extended Kalman Filters for
systems where process noise covariance depends on states and/or parameters.Comment: 23 pages, 9 figure
Adaptive detection with bounded steering vectors mismatch angle
We address the problem of detecting a signal of interest (SOI), using multiple observations in the primary data, in a background of noise with unknown covariance matrix. We consider a situation where the signal signature is not known perfectly, but its angle with a nominal and known signature is bounded. Furthermore, we consider a possible scaling
inhomogeneity between the primary and the secondary noise covariance matrix. First, assuming that the noise covariance matrix is known, we derive the generalized-likelihood ratio test (GLRT), which involves solving a semidefinite programming problem. Next, we substitute the unknown
noise covariance matrix for its estimate obtained from secondary data, to yield the final detector. The latter is compared with a detector that assumes a known signal signature
DOA Estimation in Partially Correlated Noise Using Low-Rank/Sparse Matrix Decomposition
We consider the problem of direction-of-arrival (DOA) estimation in unknown
partially correlated noise environments where the noise covariance matrix is
sparse. A sparse noise covariance matrix is a common model for a sparse array
of sensors consisted of several widely separated subarrays. Since interelement
spacing among sensors in a subarray is small, the noise in the subarray is in
general spatially correlated, while, due to large distances between subarrays,
the noise between them is uncorrelated. Consequently, the noise covariance
matrix of such an array has a block diagonal structure which is indeed sparse.
Moreover, in an ordinary nonsparse array, because of small distance between
adjacent sensors, there is noise coupling between neighboring sensors, whereas
one can assume that nonadjacent sensors have spatially uncorrelated noise which
makes again the array noise covariance matrix sparse. Utilizing some recently
available tools in low-rank/sparse matrix decomposition, matrix completion, and
sparse representation, we propose a novel method which can resolve possibly
correlated or even coherent sources in the aforementioned partly correlated
noise. In particular, when the sources are uncorrelated, our approach involves
solving a second-order cone programming (SOCP), and if they are correlated or
coherent, one needs to solve a computationally harder convex program. We
demonstrate the effectiveness of the proposed algorithm by numerical
simulations and comparison to the Cramer-Rao bound (CRB).Comment: in IEEE Sensor Array and Multichannel signal processing workshop
(SAM), 201
Continuous time systems identification with unknown noise covariance = SystĂšmes d'identification de temps continu avec co-variation de bruit (ou bruits) inconnus = Identifikation zeitkontinuierlicher systeme mit unbekannter rauschkovarianz
In identifying parameters of a continuous-time dynamical system, a difficulty arises when the observation noise covariance is unknown. The present paper solves this problem in the case of a linear time-invariant system with white noise affecting additively both the state and the observation. The problem is that the likelihood functional cannot be obtained when the observation noise covariance is unknown. A related procedure is suggested, however, and the estimates are obtained by finding roots of an appropriate functional. It is shown that the estimates obtained are consistent
Generalization of the noise model for time-distance helioseismology
In time-distance helioseismology, information about the solar interior is
encoded in measurements of travel times between pairs of points on the solar
surface. Travel times are deduced from the cross-covariance of the random wave
field. Here we consider travel times and also products of travel times as
observables. They contain information about e.g. the statistical properties of
convection in the Sun. The basic assumption of the model is that noise is the
result of the stochastic excitation of solar waves, a random process which is
stationary and Gaussian. We generalize the existing noise model (Gizon and
Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using
a recurrence relation, we calculate the noise covariance matrices for the
moments of order 4, 6, and 8 of the observed wave field, for the moments of
order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and
4 of the travel times. All noise covariance matrices depend only on the
expectation value of the cross-covariance of the observed wave field. For
products of travel times, the noise covariance matrix consists of three terms
proportional to , , and , where is the duration of the
observations. For typical observation times of a few hours, the term
proportional to dominates and , where the are arbitrary travel times. This
result is confirmed for travel times by Monte Carlo simulations and
comparisons with SDO/HMI observations. General and accurate formulae have been
derived to model the noise covariance matrix of helioseismic travel times and
products of travel times. These results could easily be generalized to other
methods of local helioseismology, such as helioseismic holography and ring
diagram analysis
A generalized spatiotemporal covariance model for stationary background in analysis of MEG data
Using a noise covariance model based on a single Kronecker product of spatial
and temporal covariance in the spatiotemporal analysis of MEG data was
demonstrated to provide improvement in the results over that of the commonly
used diagonal noise covariance model. In this paper we present a model that is
a generalization of all of the above models. It describes models based on a
single Kronecker product of spatial and temporal covariance as well as more
complicated multi-pair models together with any intermediate form expressed as
a sum of Kronecker products of spatial component matrices of reduced rank and
their corresponding temporal covariance matrices. The model provides a
framework for controlling the tradeoff between the described complexity of the
background and computational demand for the analysis using this model. Ways to
estimate the value of the parameter controlling this tradeoff are also
discussedComment: 4 pages, EMBS 2006 conferenc
Optimized Large-Scale CMB Likelihood And Quadratic Maximum Likelihood Power Spectrum Estimation
We revisit the problem of exact CMB likelihood and power spectrum estimation
with the goal of minimizing computational cost through linear compression. This
idea was originally proposed for CMB purposes by Tegmark et al.\ (1997), and
here we develop it into a fully working computational framework for large-scale
polarization analysis, adopting \WMAP\ as a worked example. We compare five
different linear bases (pixel space, harmonic space, noise covariance
eigenvectors, signal-to-noise covariance eigenvectors and signal-plus-noise
covariance eigenvectors) in terms of compression efficiency, and find that the
computationally most efficient basis is the signal-to-noise eigenvector basis,
which is closely related to the Karhunen-Loeve and Principal Component
transforms, in agreement with previous suggestions. For this basis, the
information in 6836 unmasked \WMAP\ sky map pixels can be compressed into a
smaller set of 3102 modes, with a maximum error increase of any single
multipole of 3.8\% at , and a maximum shift in the mean values of a
joint distribution of an amplitude--tilt model of 0.006. This
compression reduces the computational cost of a single likelihood evaluation by
a factor of 5, from 38 to 7.5 CPU seconds, and it also results in a more robust
likelihood by implicitly regularizing nearly degenerate modes. Finally, we use
the same compression framework to formulate a numerically stable and
computationally efficient variation of the Quadratic Maximum Likelihood
implementation that requires less than 3 GB of memory and 2 CPU minutes per
iteration for , rendering low- QML CMB power spectrum
analysis fully tractable on a standard laptop.Comment: 13 pages, 13 figures, accepted by ApJ
The impact of beam deconvolution on noise properties in CMB measurements: Application to Planck LFI
We present an analysis of the effects of beam deconvolution on noise
properties in CMB measurements. The analysis is built around the artDeco beam
deconvolver code. We derive a low-resolution noise covariance matrix that
describes the residual noise in deconvolution products, both in harmonic and
pixel space. The matrix models the residual correlated noise that remains in
time-ordered data after destriping, and the effect of deconvolution on it. To
validate the results, we generate noise simulations that mimic the data from
the Planck LFI instrument. A test for the full 70 GHz covariance in
multipole range yields a mean reduced of 1.0037. We
compare two destriping options, full and independent destriping, when
deconvolving subsets of available data. Full destriping leaves substantially
less residual noise, but leaves data sets intercorrelated. We derive also a
white noise covariance matrix that provides an approximation of the full noise
at high multipoles, and study the properties on high-resolution noise in pixel
space through simulations.Comment: 22 pages, 25 figure
Adaptive detection of a signal known only to lie on a line in a known subspace, when primary and secondary data are partially homogeneous
This paper deals with the problem of detecting a signal, known only to lie on a line in a subspace, in the presence
of unknown noise, using multiple snapshots in the primary data. To account for uncertainties about a signal's signature, we assume that the steering vector belongs to a known linear subspace. Furthermore, we consider the partially homogeneous case, for which the covariance matrix of the primary and the secondary data have the same structure but possibly different levels. This provides an extension to the framework considered by Bose and Steinhardt. The natural invariances of the detection problem are studied, which leads to the derivation of the maximal invariant. Then, a detector is proposed that proceeds in two steps. First, assuming that the noise covariance matrix is known, the generalized-likelihood ratio test (GLRT) is formulated. Then, the noise covariance matrix is replaced by its sample estimate based on the secondary data to yield the final detector. The latter is compared with a similar detector that assumes the steering vector to be known
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