14,154 research outputs found
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
Integrated adaptive filtering and design for control experiments of flexible structures
A novel method is presented of identifying a state space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relations between the state space model and the finite difference model for linear stochastic systems derived through projection filters. It is proven that least squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model. In estimating the corresponding state estimator gain, a z-domain method is used. First the deterministic component of the output is subtracted out, and then the state estimator gain is obtained by whitening the remaining signal. Experimental example is used to illustrate the feasibility of the method
A Nonparametric Adaptive Nonlinear Statistical Filter
We use statistical learning methods to construct an adaptive state estimator
for nonlinear stochastic systems. Optimal state estimation, in the form of a
Kalman filter, requires knowledge of the system's process and measurement
uncertainty. We propose that these uncertainties can be estimated from
(conditioned on) past observed data, and without making any assumptions of the
system's prior distribution. The system's prior distribution at each time step
is constructed from an ensemble of least-squares estimates on sub-sampled sets
of the data via jackknife sampling. As new data is acquired, the state
estimates, process uncertainty, and measurement uncertainty are updated
accordingly, as described in this manuscript.Comment: Accepted at the 2014 IEEE Conference on Decision and Contro
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms
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