8,436 research outputs found
Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation
Volterra and polynomial regression models play a major role in nonlinear
system identification and inference tasks. Exciting applications ranging from
neuroscience to genome-wide association analysis build on these models with the
additional requirement of parsimony. This requirement has high interpretative
value, but unfortunately cannot be met by least-squares based or kernel
regression methods. To this end, compressed sampling (CS) approaches, already
successful in linear regression settings, can offer a viable alternative. The
viability of CS for sparse Volterra and polynomial models is the core theme of
this work. A common sparse regression task is initially posed for the two
models. Building on (weighted) Lasso-based schemes, an adaptive RLS-type
algorithm is developed for sparse polynomial regressions. The identifiability
of polynomial models is critically challenged by dimensionality. However,
following the CS principle, when these models are sparse, they could be
recovered by far fewer measurements. To quantify the sufficient number of
measurements for a given level of sparsity, restricted isometry properties
(RIP) are investigated in commonly met polynomial regression settings,
generalizing known results for their linear counterparts. The merits of the
novel (weighted) adaptive CS algorithms to sparse polynomial modeling are
verified through synthetic as well as real data tests for genotype-phenotype
analysis.Comment: 20 pages, to appear in IEEE Trans. on Signal Processin
Consistent parameter identification of partial differential equation models from noisy observations
This paper introduces a new residual-based recursive parameter estimation algorithm for linear partial differential equations. The main idea is to replace unmeasurable noise variables by noise estimates and to compute recursively both the model parameter and
noise estimates. It is proven that under some mild assumptions the estimated parameters converge to the true values with probability one. Numerical examples that demonstrate the effectiveness of the proposed approach are also provided
On the Stability and the Approximation of Branching Distribution Flows, with Applications to Nonlinear Multiple Target Filtering
We analyse the exponential stability properties of a class of measure-valued
equations arising in nonlinear multi-target filtering problems. We also prove
the uniform convergence properties w.r.t. the time parameter of a rather
general class of stochastic filtering algorithms, including sequential Monte
Carlo type models and mean eld particle interpretation models. We illustrate
these results in the context of the Bernoulli and the Probability Hypothesis
Density filter, yielding what seems to be the first results of this kind in
this subject
Aircraft adaptive learning control
The optimal control theory of stochastic linear systems is discussed in terms of the advantages of distributed-control systems, and the control of randomly-sampled systems. An optimal solution to longitudinal control is derived and applied to the F-8 DFBW aircraft. A randomly-sampled linear process model with additive process and noise is developed
Path sampling for particle filters with application to multi-target tracking
In recent work (arXiv:1006.3100v1), we have presented a novel approach for
improving particle filters for multi-target tracking. The suggested approach
was based on drift homotopy for stochastic differential equations. Drift
homotopy was used to design a Markov Chain Monte Carlo step which is appended
to the particle filter and aims to bring the particle filter samples closer to
the observations. In the current work, we present an alternative way to append
a Markov Chain Monte Carlo step to a particle filter to bring the particle
filter samples closer to the observations. Both current and previous approaches
stem from the general formulation of the filtering problem. We have used the
currently proposed approach on the problem of multi-target tracking for both
linear and nonlinear observation models. The numerical results show that the
suggested approach can improve significantly the performance of a particle
filter.Comment: Minor corrections, 23 pages, 8 figures. This is a companion paper to
arXiv:1006.3100v
Systematic experimental exploration of bifurcations with non-invasive control
We present a general method for systematically investigating the dynamics and
bifurcations of a physical nonlinear experiment. In particular, we show how the
odd-number limitation inherent in popular non-invasive control schemes, such as
(Pyragas) time-delayed or washout-filtered feedback control, can be overcome
for tracking equilibria or forced periodic orbits in experiments. To
demonstrate the use of our non-invasive control, we trace out experimentally
the resonance surface of a periodically forced mechanical nonlinear oscillator
near the onset of instability, around two saddle-node bifurcations (folds) and
a cusp bifurcation.Comment: revised and extended version (8 pages, 7 figures
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