13,082 research outputs found
Maximum entropy properties of discrete-time first-order stable spline kernel
The first order stable spline (SS-1) kernel is used extensively in
regularized system identification. In particular, the stable spline estimator
models the impulse response as a zero-mean Gaussian process whose covariance is
given by the SS-1 kernel. In this paper, we discuss the maximum entropy
properties of this prior. In particular, we formulate the exact maximum entropy
problem solved by the SS-1 kernel without Gaussian and uniform sampling
assumptions. Under general sampling schemes, we also explicitly derive the
special structure underlying the SS-1 kernel (e.g. characterizing the
tridiagonal nature of its inverse), also giving to it a maximum entropy
covariance completion interpretation. Along the way similar maximum entropy
properties of the Wiener kernel are also given
Identification of Stochastic Wiener Systems using Indirect Inference
We study identification of stochastic Wiener dynamic systems using so-called
indirect inference. The main idea is to first fit an auxiliary model to the
observed data and then in a second step, often by simulation, fit a more
structured model to the estimated auxiliary model. This two-step procedure can
be used when the direct maximum-likelihood estimate is difficult or intractable
to compute. One such example is the identification of stochastic Wiener
systems, i.e.,~linear dynamic systems with process noise where the output is
measured using a non-linear sensor with additive measurement noise. It is in
principle possible to evaluate the log-likelihood cost function using numerical
integration, but the corresponding optimization problem can be quite intricate.
This motivates studying consistent, but sub-optimal, identification methods for
stochastic Wiener systems. We will consider indirect inference using the best
linear approximation as an auxiliary model. We show that the key to obtain a
reliable estimate is to use uncertainty weighting when fitting the stochastic
Wiener model to the auxiliary model estimate. The main technical contribution
of this paper is the corresponding asymptotic variance analysis. A numerical
evaluation is presented based on a first-order finite impulse response system
with a cubic non-linearity, for which certain illustrative analytic properties
are derived.Comment: The 17th IFAC Symposium on System Identification, SYSID 2015,
Beijing, China, October 19-21, 201
Regularized Nonparametric Volterra Kernel Estimation
In this paper, the regularization approach introduced recently for
nonparametric estimation of linear systems is extended to the estimation of
nonlinear systems modelled as Volterra series. The kernels of order higher than
one, representing higher dimensional impulse responses in the series, are
considered to be realizations of multidimensional Gaussian processes. Based on
this, prior information about the structure of the Volterra kernel is
introduced via an appropriate penalization term in the least squares cost
function. It is shown that the proposed method is able to deliver accurate
estimates of the Volterra kernels even in the case of a small amount of data
points
Stochastic Behavior Analysis of the Gaussian Kernel Least-Mean-Square Algorithm
The kernel least-mean-square (KLMS) algorithm is a popular algorithm in nonlinear adaptive filtering due to its
simplicity and robustness. In kernel adaptive filters, the statistics of the input to the linear filter depends on the parameters of the kernel employed. Moreover, practical implementations require a finite nonlinearity model order. A Gaussian KLMS has two design parameters, the step size and the Gaussian kernel bandwidth. Thus, its design requires analytical models for the algorithm behavior as a function of these two parameters. This paper studies the steady-state behavior and the transient behavior of the
Gaussian KLMS algorithm for Gaussian inputs and a finite order nonlinearity model. In particular, we derive recursive expressions for the mean-weight-error vector and the mean-square-error. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady state. This allows the explicit analytical determination of stability limits, and gives opportunity
to choose the algorithm parameters a priori in order to achieve prescribed convergence speed and quality of the estimate. Design examples are presented which validate the theoretical analysis and illustrates its application
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