1,499 research outputs found
Adaptive Kalman Filtering with Multivariate Generalized Laplace System Noise
An adaptive Kalman filter is proposed to estimate the stats of a system where the system noise is assumed to be a multivariate generalized Laplace random vector. In the presence of outliers in the system noise, it is shown that improved state estimates can be obtained by using an adaptive factor to estimate the dispersion matrix of the system noise term. For the implementation of the filter, an algorithm which includes both single and multiple adaptive factors is proposed. A Monte-Carlo investigation is also carried out to access the performance of the proposed filters in comparison with other robust filters. The results show that, in the sense of minimum mean squared state error, the proposed filter is superior to other filters when the magnitude of a system change is moderate or large
Generalized Multi-kernel Maximum Correntropy Kalman Filter for Disturbance Estimation
Disturbance observers have been attracting continuing research efforts and
are widely used in many applications. Among them, the Kalman filter-based
disturbance observer is an attractive one since it estimates both the state and
the disturbance simultaneously, and is optimal for a linear system with
Gaussian noises. Unfortunately, The noise in the disturbance channel typically
exhibits a heavy-tailed distribution because the nominal disturbance dynamics
usually do not align with the practical ones. To handle this issue, we propose
a generalized multi-kernel maximum correntropy Kalman filter for disturbance
estimation, which is less conservative by adopting different kernel bandwidths
for different channels and exhibits excellent performance both with and without
external disturbance. The convergence of the fixed point iteration and the
complexity of the proposed algorithm are given. Simulations on a robotic
manipulator reveal that the proposed algorithm is very efficient in disturbance
estimation with moderate algorithm complexity.Comment: in IEEE Transactions on Automatic Control (2023
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
Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models
We propose a new class of filtering and smoothing methods for inference in
high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models.
The main idea is to combine the ensemble Kalman filter and smoother, developed
in the geophysics literature, with state-space algorithms from the statistics
literature. Our algorithms address a variety of estimation scenarios, including
on-line and off-line state and parameter estimation. We take a Bayesian
perspective, for which the goal is to generate samples from the joint posterior
distribution of states and parameters. The key benefit of our approach is the
use of ensemble Kalman methods for dimension reduction, which allows inference
for high-dimensional state vectors. We compare our methods to existing ones,
including ensemble Kalman filters, particle filters, and particle MCMC. Using a
real data example of cloud motion and data simulated under a number of
nonlinear and non-Gaussian scenarios, we show that our approaches outperform
these existing methods
A Multivariate Non-Gaussian Bayesian Filter Using Power Moments
In this paper, which is a very preliminary version, we extend our results on
the univariate non-Gaussian Bayesian filter using power moments to the
multivariate systems, which can be either linear or nonlinear. Doing this
introduces several challenging problems, for example a positive parametrization
of the density surrogate, which is not only a problem of filter design, but
also one of the multiple dimensional Hamburger moment problem. We propose a
parametrization of the density surrogate with the proofs to its existence,
Positivstellensatze and uniqueness. Based on it, we analyze the error of
moments of the density estimates through the filtering process with the
proposed density surrogate. An error upper bound in the sense of total
variation distance is also given. A discussion on continuous and discrete
treatments to the non-Gaussian Bayesian filtering problem is proposed to
explain why our proposed filter shall also be a mainstream of the non-Gaussian
Bayesian filtering research and motivate the research on continuous
parametrization of the system state. Last but not the least, simulation results
on estimating different types of multivariate density functions are given to
validate our proposed filter. To the best of our knowledge, the proposed filter
is the first one implementing the multivariate Bayesian filter with the system
state parameterized as a continuous function, which only requires the true
states being Lebesgue integrable.Comment: 16 pages, 2 figures. arXiv admin note: text overlap with
arXiv:2207.0851
Robust recursive estimation in the presence of heavy-tailed observation noise
Includes bibliographical references (p. 33-41).Supported by the U.S. Army Research Office fellowship. ARO-DAAL03-86-G-0017 Supported by the U.S. Air Force Office of Scientific Research. AFOSR-85-0227 AFOSR-89-0276Irvin C. Schick and Sanjoy K. Mitter
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