13,264 research outputs found
Exact Spectral Analysis of Single-h and Multi-h CPM Signals through PAM decomposition and Matrix Series Evaluation
In this paper we address the problem of closed-form spectral evaluation of
CPM. We show that the multi-h CPM signal can be conveniently generated by a PTI
SM. The output is governed by a Markov chain with the unusual peculiarity of
being cyclostationary and reducible; this holds also in the single-h context.
Judicious reinterpretation of the result leads to a formalization through a
stationary and irreducible Markov chain, whose spectral evaluation is known in
closed-form from the literature. Two are the major outcomes of this paper.
First, unlike the literature, we obtain a PSD in true closed-form. Second, we
give novel insights into the CPM format.Comment: 31 pages, 10 figure
Individual risk in mean-field control models for decentralized control, with application to automated demand response
Flexibility of energy consumption can be harnessed for the purposes of
ancillary services in a large power grid. In prior work by the authors a
randomized control architecture is introduced for individual loads for this
purpose. In examples it is shown that the control architecture can be designed
so that control of the loads is easy at the grid level: Tracking of a balancing
authority reference signal is possible, while ensuring that the quality of
service (QoS) for each load is acceptable on average. The analysis was based on
a mean field limit (as the number of loads approaches infinity), combined with
an LTI-system approximation of the aggregate nonlinear model. This paper
examines in depth the issue of individual risk in these systems. The main
contributions of the paper are of two kinds:
Risk is modeled and quantified:
(i) The average performance is not an adequate measure of success. It is
found empirically that a histogram of QoS is approximately Gaussian, and
consequently each load will eventually receive poor service.
(ii) The variance can be estimated from a refinement of the LTI model that
includes a white-noise disturbance; variance is a function of the randomized
policy, as well as the power spectral density of the reference signal.
Additional local control can eliminate risk:
(iii) The histogram of QoS is truncated through this local control, so that
strict bounds on service quality are guaranteed.
(iv) This has insignificant impact on the grid-level performance, beyond a
modest reduction in capacity of ancillary service.Comment: Publication without appendix to appear in the 53rd IEEE Conf. on
Decision and Control, December, 201
Markov analysis of stochastic resonance in a periodically driven integrate-fire neuron
We model the dynamics of the leaky integrate-fire neuron under periodic
stimulation as a Markov process with respect to the stimulus phase. This avoids
the unrealistic assumption of a stimulus reset after each spike made in earlier
work and thus solves the long-standing reset problem. The neuron exhibits
stochastic resonance, both with respect to input noise intensity and stimulus
frequency. The latter resonance arises by matching the stimulus frequency to
the refractory time of the neuron. The Markov approach can be generalized to
other periodically driven stochastic processes containing a reset mechanism.Comment: 23 pages, 10 figure
Using Markov chain Monte Carlo methods for estimating parameters with gravitational radiation data
We present a Bayesian approach to the problem of determining parameters for
coalescing binary systems observed with laser interferometric detectors. By
applying a Markov Chain Monte Carlo (MCMC) algorithm, specifically the Gibbs
sampler, we demonstrate the potential that MCMC techniques may hold for the
computation of posterior distributions of parameters of the binary system that
created the gravity radiation signal. We describe the use of the Gibbs sampler
method, and present examples whereby signals are detected and analyzed from
within noisy data.Comment: 21 pages, 10 figure
A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy
The analysis of data from gravitational wave detectors can be divided into
three phases: search, characterization, and evaluation. The evaluation of the
detection - determining whether a candidate event is astrophysical in origin or
some artifact created by instrument noise - is a crucial step in the analysis.
The on-going analyses of data from ground based detectors employ a frequentist
approach to the detection problem. A detection statistic is chosen, for which
background levels and detection efficiencies are estimated from Monte Carlo
studies. This approach frames the detection problem in terms of an infinite
collection of trials, with the actual measurement corresponding to some
realization of this hypothetical set. Here we explore an alternative, Bayesian
approach to the detection problem, that considers prior information and the
actual data in hand. Our particular focus is on the computational techniques
used to implement the Bayesian analysis. We find that the Parallel Tempered
Markov Chain Monte Carlo (PTMCMC) algorithm is able to address all three phases
of the anaylsis in a coherent framework. The signals are found by locating the
posterior modes, the model parameters are characterized by mapping out the
joint posterior distribution, and finally, the model evidence is computed by
thermodynamic integration. As a demonstration, we consider the detection
problem of selecting between models describing the data as instrument noise, or
instrument noise plus the signal from a single compact galactic binary. The
evidence ratios, or Bayes factors, computed by the PTMCMC algorithm are found
to be in close agreement with those computed using a Reversible Jump Markov
Chain Monte Carlo algorithm.Comment: 19 pages, 12 figures, revised to address referee's comment
Data series subtraction with unknown and unmodeled background noise
LISA Pathfinder (LPF), ESA's precursor mission to a gravitational wave
observatory, will measure the degree to which two test-masses can be put into
free-fall, aiming to demonstrate a residual relative acceleration with a power
spectral density (PSD) below 30 fm/s/Hz around 1 mHz. In LPF data
analysis, the measured relative acceleration data series must be fit to other
various measured time series data. This fitting is required in different
experiments, from system identification of the test mass and satellite dynamics
to the subtraction of noise contributions from measured known disturbances. In
all cases, the background noise, described by the PSD of the fit residuals, is
expected to be coloured, requiring that we perform such fits in the frequency
domain. This PSD is unknown {\it a priori}, and a high accuracy estimate of
this residual acceleration noise is an essential output of our analysis. In
this paper we present a fitting method based on Bayesian parameter estimation
with an unknown frequency-dependent background noise. The method uses noise
marginalisation in connection with averaged Welch's periodograms to achieve
unbiased parameter estimation, together with a consistent, non-parametric
estimate of the residual PSD. Additionally, we find that the method is
equivalent to some implementations of iteratively re-weighted least-squares
fitting. We have tested the method both on simulated data of known PSD, and to
analyze differential acceleration from several experiments with the LISA
Pathfinder end-to-end mission simulator.Comment: To appear Phys. Rev. D90 August 201
Characterization of Model-Based Detectors for CPS Sensor Faults/Attacks
A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for
identifying faulty/falsified sensor measurements. First, given the system
dynamics, we derive tools for tuning the CUSUM procedure in the fault/attack
free case to fulfill a desired detection performance (in terms of false alarm
rate). We use the widely-used chi-squared fault/attack detection procedure as a
benchmark to compare the performance of the CUSUM. In particular, we
characterize the state degradation that a class of attacks can induce to the
system while enforcing that the detectors (CUSUM and chi-squared) do not raise
alarms. In doing so, we find the upper bound of state degradation that is
possible by an undetected attacker. We quantify the advantage of using a
dynamic detector (CUSUM), which leverages the history of the state, over a
static detector (chi-squared) which uses a single measurement at a time.
Simulations of a chemical reactor with heat exchanger are presented to
illustrate the performance of our tools.Comment: Submitted to IEEE Transactions on Control Systems Technolog
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