Authors:
Babak Azimi-Sadjadi,
Perinkulam S. Krishnaprasad,
Volume: 1, Page 1579 Paper number 2096
Abstract:
In this paper we address the problem of nonlinear filtering in the
presence of integer uncertainty. This setup is specially important
for the case of differential GPS with carrier phase measurements. In
simulation results we show that Particle Filtering is capable of resolving
integer ambiguity in the given nonlinear setup. Motivated by these
results we introduce a new Particle Filtering algorithm that can reduce
the computational complexity for a certain class of problems. In this
class, it is assumed that the conditional density of the state of the
system given the observations is close to a known exponential family
of densities.
Authors:
François LeGland,
Nadia Oudjane,
Volume: 1, Page 1585 Paper number 1833
Abstract:
In this paper, the stability of the optimal filter w.r.t. its initial
condition and w.r.t. the model, is studied in a general HMM using the
Hilbert projective metric. These stability results are then used to
prove the uniform convergence of the interacting particle filter to
the optimal filter, as the number of particles goes to infinity.
Authors:
Ola Markusson,
Haakan Hjalmarsson,
Volume: 1, Page 1591 Paper number 1338
Abstract:
Prediction error and maximum likelihood estimation of nonlinear stochastic
models requires inversion of the model, a step which may require substantial
efforts, either in terms of manual calculations or through the use
of software capable of symbolic computations. In this paper we show
that model inversion can be easily implemented in numerical software
such as, e.g., Simulink and MatrixX, by means of a feedback connection
based on the model. We derive sufficient conditions for the existence
of a stable causal inverse as well as sufficient conditions for the
initial transient to decay. These conditions are given in terms of
properties for a linear time-varying system associated with the nonlinear
model. The method is illustrated on a numerical example.
Authors:
Peng Shi,
Mehmet Karan,
C. Yalcin Kaya,
Volume: 1, Page 1597 Paper number 1792
Abstract:
This paper considers the filtering problem for a class of linear
hybrid systems with nonlinear uncertainties and Markovian jump parameters.
The unknown nonlinearities in the system are time-varying and norm-bounded.
First, we show the equivalence of the norm bounded linear and nonlinear
uncertainty sets. Then, instead of the original hybrid linear system
with nonlinear uncertainties, we consider the same system with linear
uncertainties. By using a Riccati equation approach for this new
system, a robust filter is designed using two sets of coupled Riccati-like
equations such that the estimation error is guaranteed to have an
upper bound.
Authors:
Paula Milheiro-Oliveira,
Jean Picard,
Volume: 1, Page 1599 Paper number 1130
Abstract:
The asymptotic behaviour of a nonlinear continuous time approximate
filter when the variance of the observation noise tends to 0 is investigated.
We consider a particular class of signals modeled by a two-dimensional
quasi-linear diffusion from which only one of the components is noisy,
and we assume that a one-dimensional linear function of the signal,
depending only of the unnoisy component, is observed in a low noise
channel. Under some detectability assumptions the unobserved signal
can be restored by means of an approximate nonlinear filter. We establish
that the filtering error converges to 0 and we give an upper bound
for the convergence rate. The efficiency of the approximate filter
is compared with the efficiency of the optimal filter and the order
of magnitude of the error between the two filters, as the observation
noise vanishes, is obtained. A more general case is briefly presented.
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