1,283 research outputs found
Robust Gaussian Filtering using a Pseudo Measurement
Many sensors, such as range, sonar, radar, GPS and visual devices, produce
measurements which are contaminated by outliers. This problem can be addressed
by using fat-tailed sensor models, which account for the possibility of
outliers. Unfortunately, all estimation algorithms belonging to the family of
Gaussian filters (such as the widely-used extended Kalman filter and unscented
Kalman filter) are inherently incompatible with such fat-tailed sensor models.
The contribution of this paper is to show that any Gaussian filter can be made
compatible with fat-tailed sensor models by applying one simple change: Instead
of filtering with the physical measurement, we propose to filter with a pseudo
measurement obtained by applying a feature function to the physical
measurement. We derive such a feature function which is optimal under some
conditions. Simulation results show that the proposed method can effectively
handle measurement outliers and allows for robust filtering in both linear and
nonlinear systems
Data Assimilation by Conditioning on Future Observations
Conventional recursive filtering approaches, designed for quantifying the
state of an evolving uncertain dynamical system with intermittent observations,
use a sequence of (i) an uncertainty propagation step followed by (ii) a step
where the associated data is assimilated using Bayes' rule. In this paper we
switch the order of the steps to: (i) one step ahead data assimilation followed
by (ii) uncertainty propagation. This route leads to a class of filtering
algorithms named \emph{smoothing filters}. For a system driven by random noise,
our proposed methods require the probability distribution of the driving noise
after the assimilation to be biased by a nonzero mean. The system noise,
conditioned on future observations, in turn pushes forward the filtering
solution in time closer to the true state and indeed helps to find a more
accurate approximate solution for the state estimation problem
Variational Bayesian Approximations Kalman Filter Based on Threshold Judgment
The estimation of non-Gaussian measurement noise models is a significant
challenge across various fields. In practical applications, it often faces
challenges due to the large number of parameters and high computational
complexity. This paper proposes a threshold-based Kalman filtering approach for
online estimation of noise parameters in non-Gaussian measurement noise models.
This method uses a certain amount of sample data to infer the variance
threshold of observation parameters and employs variational Bayesian estimation
to obtain corresponding noise variance estimates, enabling subsequent
iterations of the Kalman filtering algorithm. Finally, we evaluate the
performance of this algorithm through simulation experiments, demonstrating its
accurate and effective estimation of state and noise parameters.Comment: 5 pages, conferenc
Joint State Estimation and Noise Identification Based on Variational Optimization
In this article, the state estimation problems with unknown process noise and
measurement noise covariances for both linear and nonlinear systems are
considered. By formulating the joint estimation of system state and noise
parameters into an optimization problem, a novel adaptive Kalman filter method
based on conjugate-computation variational inference, referred to as CVIAKF, is
proposed to approximate the joint posterior probability density function of the
latent variables. Unlike the existing adaptive Kalman filter methods utilizing
variational inference in natural-parameter space, CVIAKF performs optimization
in expectation-parameter space, resulting in a faster and simpler solution.
Meanwhile, CVIAKF divides optimization objectives into conjugate and
non-conjugate parts of nonlinear dynamical models, whereas conjugate
computations and stochastic mirror-descent are applied, respectively.
Remarkably, the reparameterization trick is used to reduce the variance of
stochastic gradients of the non-conjugate parts. The effectiveness of CVIAKF is
validated through synthetic and real-world datasets of maneuvering target
tracking.Comment: 13 page
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