4,673 research outputs found
Kalman Filter Track Fits and Track Breakpoint Analysis
We give an overview of track fitting using the Kalman filter method in the
NOMAD detector at CERN, and emphasize how the wealth of by-product information
can be used to analyze track breakpoints (discontinuities in track parameters
caused by scattering, decay, etc.). After reviewing how this information has
been previously exploited by others, we describe extensions which add power to
breakpoint detection and characterization. We show how complete fits to the
entire track, with breakpoint parameters added, can be easily obtained from the
information from unbroken fits. Tests inspired by the Fisher F-test can then be
used to judge breakpoints. Signed quantities (such as change in momentum at the
breakpoint) can supplement unsigned quantities such as the various chisquares.
We illustrate the method with electrons from real data, and with Monte Carlo
simulations of pion decays.Comment: 27 pages including 10 figures. To appear in NI
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
Nudging the particle filter
We investigate a new sampling scheme aimed at improving the performance of
particle filters whenever (a) there is a significant mismatch between the
assumed model dynamics and the actual system, or (b) the posterior probability
tends to concentrate in relatively small regions of the state space. The
proposed scheme pushes some particles towards specific regions where the
likelihood is expected to be high, an operation known as nudging in the
geophysics literature. We re-interpret nudging in a form applicable to any
particle filtering scheme, as it does not involve any changes in the rest of
the algorithm. Since the particles are modified, but the importance weights do
not account for this modification, the use of nudging leads to additional bias
in the resulting estimators. However, we prove analytically that nudged
particle filters can still attain asymptotic convergence with the same error
rates as conventional particle methods. Simple analysis also yields an
alternative interpretation of the nudging operation that explains its
robustness to model errors. Finally, we show numerical results that illustrate
the improvements that can be attained using the proposed scheme. In particular,
we present nonlinear tracking examples with synthetic data and a model
inference example using real-world financial data
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