Authors:
Vikram Krishnamurthy,
Robert J. Elliott,
Volume: 1, Page 286 Paper number 2034
Abstract:
We consider the problem of fixed-interval smoothing of a continuous-time
partially observed nonlinear stochastic dynamical system. Existing
results for such smoothers require the use of two sided stochastic
calculus. The main contribution of this paper is to present a robust
formulation of the smoothing equations. Under this robust formulation,
the smoothing equations are non-stochastic parabolic partial differential
equations (with random coefficients -- and hence the technical machinery
associated with two sided stochastic calculus is not required. Furthermore,
the robust smoothed state estimates are locally Lipschitz in the observations
-- which is useful for numerical simulation. As an example, finite
dimensional robust versions of the Hidden Markov Model smoothers
are derived.
Authors:
Stephen S.T. Yau,
Volume: 1, Page 292 Paper number 1304
Abstract:
The Kalman-Bucy filter is widely used in modern industry. Despite
its usefulness, however, the Kalman-Bucy filter is not perfect. One
of the weakness is that it needs a Gaussian assumption for the initial
data. The other weakness is that it requires the drift term f(x) be
a linear function. Brockett [Br], Brockett and Clark [Br-Cl], and
Mitter [Mi] proposed independently using a Lie algebraic method to
solve Duncan-Mortensen-Zakai equation for nonlinear filtering. This
method requires only n sufficient statistics, where n is the state
space dimension, and it allows the initial condition be modeled by
an arbitrary distribution. The idea was worked out in detail by Tam-Wong-Yau
[TWY] and Yau [Ya 1] [Ya 2]. However, in the Lie algebraic method,
one has to know explicitly the structure of the estimation algebra.
In 1983, Brockett proposed to classify all finite dimensional filters.
In this paper, we report the recent results on classification of finite
dimensional maximal rank estimation algebras with arbitrary state space
dimension.
Authors:
Angelo Alessandri,
Marcello Sanguineti,
Volume: 1, Page 298 Paper number 1900
Abstract:
Estimation problems are addressed for continuous-time, nonlinear dynamic
systems in a general (cal) L_p framework. In this setting, the
connection between the observation and the filtering problems is investigated.
Under some regularity assumptions for the nonlinearities and suitable
bounds on the (cal) L_p norm of the noises, it is proved that the
same hypotheses sufficient to design an exponential observer for a
system without noises enable one to design a filter which is (cal)
L -stable with respect to system and measurement noises. An illustrative
example is finally presented.
Authors:
Alessandro Chiuso,
Stefano Soatto,
Volume: 1, Page 304 Paper number 1407
Abstract:
We propose a nonlinear filter for estimating the trajectory of a
random walk on a matrix Lie group with constant computational complexity.
It is based on a finite-dimensional approximation of the conditional
distribution of the state - given past measurements - via a set of
fair samples, which are updated at each step and proven to be consistent
with the updated conditional distribution. The algorithm proposed,
like other Monte Carlo methods, can in principle track arbitrary
distributions evolving on arbitrarily large state spaces. However,
several issues concerning sample impoverishment need to be taken
into account when designing practical working systems.
Authors:
Jae-Won Lee,
Sukhan Lee,
Dongmok Shin,
Volume: 1, Page 310 Paper number 2057
Abstract:
In this paper, we propose a geometric data fusion(GDF) method using
Perception-Net which can provide error reducing, uncertainty management,
and maintaining consistency. We propose a Perception-Net to design
a new state estimator for dynamic systems and apply the proposed geometric
data fusion method to obtain the optimal estimate, propagate uncertainties
and utilize the system knowledge. We present comparisons between the
proposed estimator and the conventional estimators. It is also shown
that the additional priori information on the system can be easily
utilized in the proposed estimator to improve the performance. Through
illustrative examples, it is verified that the proposed estimator presents
better performances than the existing filters and improves performances
via utilizing system knowledge.
Authors:
Yi Xiong,
Mehrdad Saif,
Volume: 1, Page 316 Paper number 1221
Abstract:
A new sliding mode observer for linear uncertain systems is proposed.
The advantage of the proposed observer is that it works under much
less conservative conditions than Wallcot and Zak's observer. In addition,
we address the issue of estimating a function of the state as well
as unknown inputs or structural uncertainties. Further, the idea is
extended to a general class of nonlinear uncertain systems. Numerical
examples are used to illustrate the validity of the proposed observer
design strategy.
Authors:
Yi Xiong,
Mehrdad Saif,
Volume: 1, Page 322 Paper number 1222
Abstract:
A new sliding mode observer based on Wallcot and Zak's observer for
linear uncertain systems was proposed in Part I of this article. The
proposed observer works under much less conservative conditions than
the ones previously proposed. In this article, the observer design
methodology that was proposed for linear systems in the first part
of this paper is extended to a general class of nonlinear uncertain
systems. Numerical examples are used to illustrate the validity of
the proposed observer design strategy.
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