2,403 research outputs found
Adaptive parallel-cascade truncated volterra filters
Journal ArticleAbstract-This paper studies adaptive truncated Volterra filters employing parallel-cascade structures. Parallel-cascade realizations implement higher order Volterra systems a s a parallel connection of multiplicative combinations of lower order truncated Volterra systems. A normalized LMS adaptive filter is developed, and its performance capabilities are evaluated using a series of simulation experiments. The experimental results indicate that the normalized LMS adaptive parallel-cascade Volterra filter has superior convergence properties over several competing structures. This paper also includes an experiment that demonstrates the capability of the parallel-cascade adaptive system to reduce its implementation complexity by using fewer than the maximum number of branches required for the most general realization of the system
Inference for Differential Equation Models using Relaxation via Dynamical Systems
Statistical regression models whose mean functions are represented by
ordinary differential equations (ODEs) can be used to describe phenomenons
dynamical in nature, which are abundant in areas such as biology, climatology
and genetics. The estimation of parameters of ODE based models is essential for
understanding its dynamics, but the lack of an analytical solution of the ODE
makes the parameter estimation challenging. The aim of this paper is to propose
a general and fast framework of statistical inference for ODE based models by
relaxation of the underlying ODE system. Relaxation is achieved by a properly
chosen numerical procedure, such as the Runge-Kutta, and by introducing
additive Gaussian noises with small variances. Consequently, filtering methods
can be applied to obtain the posterior distribution of the parameters in the
Bayesian framework. The main advantage of the proposed method is computation
speed. In a simulation study, the proposed method was at least 14 times faster
than the other methods. Theoretical results which guarantee the convergence of
the posterior of the approximated dynamical system to the posterior of true
model are presented. Explicit expressions are given that relate the order and
the mesh size of the Runge-Kutta procedure to the rate of convergence of the
approximated posterior as a function of sample size
Tensor Network alternating linear scheme for MIMO Volterra system identification
This article introduces two Tensor Network-based iterative algorithms for the
identification of high-order discrete-time nonlinear multiple-input
multiple-output (MIMO) Volterra systems. The system identification problem is
rewritten in terms of a Volterra tensor, which is never explicitly constructed,
thus avoiding the curse of dimensionality. It is shown how each iteration of
the two identification algorithms involves solving a linear system of low
computational complexity. The proposed algorithms are guaranteed to
monotonically converge and numerical stability is ensured through the use of
orthogonal matrix factorizations. The performance and accuracy of the two
identification algorithms are illustrated by numerical experiments, where
accurate degree-10 MIMO Volterra models are identified in about 1 second in
Matlab on a standard desktop pc
Sequential Bayesian inference for implicit hidden Markov models and current limitations
Hidden Markov models can describe time series arising in various fields of
science, by treating the data as noisy measurements of an arbitrarily complex
Markov process. Sequential Monte Carlo (SMC) methods have become standard tools
to estimate the hidden Markov process given the observations and a fixed
parameter value. We review some of the recent developments allowing the
inclusion of parameter uncertainty as well as model uncertainty. The
shortcomings of the currently available methodology are emphasised from an
algorithmic complexity perspective. The statistical objects of interest for
time series analysis are illustrated on a toy "Lotka-Volterra" model used in
population ecology. Some open challenges are discussed regarding the
scalability of the reviewed methodology to longer time series,
higher-dimensional state spaces and more flexible models.Comment: Review article written for ESAIM: proceedings and surveys. 25 pages,
10 figure
Sparse Nonlinear MIMO Filtering and Identification
In this chapter system identification algorithms for sparse nonlinear multi input multi output (MIMO) systems are developed. These algorithms are potentially useful in a variety of application areas including digital transmission systems incorporating power amplifier(s) along with multiple antennas, cognitive processing, adaptive control of nonlinear multivariable systems, and multivariable biological systems. Sparsity is a key constraint imposed on the model. The presence of sparsity is often dictated by physical considerations as in wireless fading channel-estimation. In other cases it appears as a pragmatic modelling approach that seeks to cope with the curse of dimensionality, particularly acute in nonlinear systems like Volterra type series. Three dentification approaches are discussed: conventional identification based on both input and output samples, semi–blind identification placing emphasis on minimal input resources and blind identification whereby only output samples are available plus a–priori information on input characteristics. Based on this taxonomy a variety of algorithms, existing and new, are studied and evaluated by simulation
Lattice algorithms for recursive least squares adaptive second-order volterra filtering
Journal ArticleThis paper presents two computationally efficient recursive least-square (RLS) lattice algorithms for adaptive nonlinear filtering based on a truncated second-order Volterra system model. The lattice formulation transforms the nonlinear filtering problem into an equivalent multichannel, linear filtering problem and then generalizes the lattice solution to the nonlinear filtering problem. One of the algorithms is a direct extension of the conventional RLS lattice adaptive linear filtering algorithm to the nonlinear case. The other algorithms is based on the QR decomposition of the prediction error covariance matrices using orthogonal transformations. Several experiments demonstrating and comparing the properties of the two algorithms in finite and "infinite" precision environments are included in the paper. The results indicate that both the algorithms retain the fast convergence behavior of the RLS Volterra filters and are numerically stable
- …