1,372 research outputs found
Compressive Estimation of a Stochastic Process with Unknown Autocorrelation Function
In this paper, we study the prediction of a circularly symmetric zero-mean
stationary Gaussian process from a window of observations consisting of
finitely many samples. This is a prevalent problem in a wide range of
applications in communication theory and signal processing. Due to
stationarity, when the autocorrelation function or equivalently the power
spectral density (PSD) of the process is available, the Minimum Mean Squared
Error (MMSE) predictor is readily obtained. In particular, it is given by a
linear operator that depends on autocorrelation of the process as well as the
noise power in the observed samples. The prediction becomes, however, quite
challenging when the PSD of the process is unknown. In this paper, we propose a
blind predictor that does not require the a priori knowledge of the PSD of the
process and compare its performance with that of an MMSE predictor that has a
full knowledge of the PSD. To design such a blind predictor, we use the random
spectral representation of a stationary Gaussian process. We apply the
well-known atomic-norm minimization technique to the observed samples to obtain
a discrete quantization of the underlying random spectrum, which we use to
predict the process. Our simulation results show that this estimator has a good
performance comparable with that of the MMSE estimator.Comment: 6 pages, 4 figures. Accepted for presentation in ISIT 2017, Aachen,
German
An autoregressive (AR) model based stochastic unknown input realization and filtering technique
This paper studies the state estimation problem of linear discrete-time
systems with stochastic unknown inputs. The unknown input is a wide-sense
stationary process while no other prior informaton needs to be known. We
propose an autoregressive (AR) model based unknown input realization technique
which allows us to recover the input statistics from the output data by solving
an appropriate least squares problem, then fit an AR model to the recovered
input statistics and construct an innovations model of the unknown inputs using
the eigensystem realization algorithm (ERA). An augmented state system is
constructed and the standard Kalman filter is applied for state estimation. A
reduced order model (ROM) filter is also introduced to reduce the computational
cost of the Kalman filter. Two numerical examples are given to illustrate the
procedure.Comment: 14 page
Polynomial-Chaos-based Kriging
Computer simulation has become the standard tool in many engineering fields
for designing and optimizing systems, as well as for assessing their
reliability. To cope with demanding analysis such as optimization and
reliability, surrogate models (a.k.a meta-models) have been increasingly
investigated in the last decade. Polynomial Chaos Expansions (PCE) and Kriging
are two popular non-intrusive meta-modelling techniques. PCE surrogates the
computational model with a series of orthonormal polynomials in the input
variables where polynomials are chosen in coherency with the probability
distributions of those input variables. On the other hand, Kriging assumes that
the computer model behaves as a realization of a Gaussian random process whose
parameters are estimated from the available computer runs, i.e. input vectors
and response values. These two techniques have been developed more or less in
parallel so far with little interaction between the researchers in the two
fields. In this paper, PC-Kriging is derived as a new non-intrusive
meta-modeling approach combining PCE and Kriging. A sparse set of orthonormal
polynomials (PCE) approximates the global behavior of the computational model
whereas Kriging manages the local variability of the model output. An adaptive
algorithm similar to the least angle regression algorithm determines the
optimal sparse set of polynomials. PC-Kriging is validated on various benchmark
analytical functions which are easy to sample for reference results. From the
numerical investigations it is concluded that PC-Kriging performs better than
or at least as good as the two distinct meta-modeling techniques. A larger gain
in accuracy is obtained when the experimental design has a limited size, which
is an asset when dealing with demanding computational models
Matched Filtering from Limited Frequency Samples
In this paper, we study a simple correlation-based strategy for estimating
the unknown delay and amplitude of a signal based on a small number of noisy,
randomly chosen frequency-domain samples. We model the output of this
"compressive matched filter" as a random process whose mean equals the scaled,
shifted autocorrelation function of the template signal. Using tools from the
theory of empirical processes, we prove that the expected maximum deviation of
this process from its mean decreases sharply as the number of measurements
increases, and we also derive a probabilistic tail bound on the maximum
deviation. Putting all of this together, we bound the minimum number of
measurements required to guarantee that the empirical maximum of this random
process occurs sufficiently close to the true peak of its mean function. We
conclude that for broad classes of signals, this compressive matched filter
will successfully estimate the unknown delay (with high probability, and within
a prescribed tolerance) using a number of random frequency-domain samples that
scales inversely with the signal-to-noise ratio and only logarithmically in the
in the observation bandwidth and the possible range of delays.Comment: Submitted to the IEEE Transactions on Information Theory on January
13, 201
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