A Comparison Of Estimation Accuracy By The Use
Of KF, EKF & UKF Filters
Author(s)
S. Konatowski & A. T. Pieniężny
Abstract
This paper considers the problem of applying the Kalman filters to nonlinear
systems. The Kalman filter (KF) is an optimal linear estimator when the process
noise and the measurement noise can be modeled by white Gaussian noise. The
KF only utilizes the first two moments of the state (mean and covariance) in its
update rule. In situations when the problems are nonlinear or the noise that
distorts the signals is non-Gaussian, the Kalman filters provide a solution that
may be far from optimal. Nonlinear problems can be solved with the extended
Kalman filter (EKF). This filter is based upon the principle of linearization of the
state transition matrix and the observation matrix with Taylor series expansions.
Exploiting the assumption that all transformations are quasi-linear, the EKF
simply makes linear all nonlinear transformations and substitutes Jacobian
matrices for the linear transformations in the KF equations. The linearization can
lead to poor performance and divergence of the filter for highly non-linear
problems. An improvement to the extended Kalman filter is the unscented
Kalman filter (UKF). The UKF approximates the probability density resulting
from the nonlinear transformation of a random variable. It is done by evaluating
the nonlinear function with a minimal set of carefully chosen sample points.
The posterior mean and covariance estimated from the sample points are
accurate to the second order for any nonlinearity. The paper presents
a comparison of the estimation quality for two nonlinear measurement models of
the following Kalman filters: covariance filter (KF), extended filter (EKF) and
unscented filter (UKF).
Keywords: nonlinear model, discrete Kalman filter, extended Kalman filter,
unscented Kalman filter, integrated navigation system.
Keywords
nonlinear model, discrete Kalman filter, extended Kalman filter,
unscented Kalman filter, integrated navigation system.
Related Book
Other papers in this volume
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