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Series in Signal and Information Processing, Vol. 27
edited by Hans-Andrea Loeliger
Lukas Bruderer
Input Estimation and
Dynamical System Identification:
New Algorithms and
Results
1. Auflage/1st edition 2015. XIV, 172 Seiten/pages, € 64,00.
ISBN 978-3-86628-533-0
Recovery of signals from distorted or noisy observations has been a
longstanding research problem with a wide variety of practical applications. We
advocate to approach these types of problems by
interpreting them as input estimation in finite-order linear state-space
models. Among other applications the input signal may represent a physical
quantity and the state-space model a sensor yielding corrupted readings. In
this thesis, we provide new estimation algorithms and theoretical results for
different classes of input signals: continuous-time input signals and weakly
sparse input signals. The latter method is obtained by specializing
a more general framework for inference with sparse priors and sparse signal
recovery, which in contrast to standard methods, amounts to iterations of
Gaussian message passing. Applicability of input estimation is extended to
complex models, which generally are computationally more demanding and may be
prone to numerical instability, by introducing new numerically robust
computation methods expressed as Gaussian message passing in factor graphs.
In practical applications, a signal model may not necessarily be
available a-priori. As a consequence, in addition to input estimation,
estimation of the state-space model itself must also be adressed.
To this end, we introduce a variational statistical
framework to retrieve convenient statespace models
for input estimation and present a joint input and model estimation algorithm
for weakly sparse input signals.
The proposed methods are substantiated with two real world application
examples. First, we consider impaired mechanical sensor measurements in
machining processes and show that input estimation and suitable model
identification can result in more accurate measurements, when strong resonances
distort the sensor readings. Secondly, we show that our simultaneous weakly-sparse
input estimation and model estimation method is capable of identifying
individual heart beats from ballistocardiographic
measurements, a method used to measure non-invasively the cardiac output.
Keywords: Gaussian Message Passing; State-space models; Factor Graphs; Sparse
Estimation; System Identification.
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