| dc.description.abstract | The Kalman flter is a recursive algorithm that estimates the state of a linear dynamical system
from a sequence of noisy sensor measurements. Due to its relative simplicity, numerical efficiency
and optimality, the Kalman flter and its variants have been applied to a wide range of problems
in technology, notably in the areas of guidance, navigation, and control. The traditional
definition of the Kalman flter is based on the assumption that at any given time, the errors
associated with the predicted state estimate and the observation are statistically independent.
However, in many practical problems, this assumption is not satisfied, and as such the Kalman
filter may provide overconfident state estimates and diverge. This can have serious consequences
in the context of safety-critical systems.
Although there are modifications of the Kalman filter that accommodate various types of
correlation in the process and observation noises, these are not suitable in the situation where
the correlation between the errors associated with the predicted state estimate and the observation
is caused by the presence of common past information between the state estimate and
the observation, which is characteristic of distributed sensor networks. On the contrary, existing
methods that deal with the common past information problem either provide overly conservative
estimates, or have too strict assumptions on the structure of the problem, such as the
communication topology of the sensor network.
This thesis presents two new filters to address various correlated estimation problems that
are based on the Ensemble Kalman filter, a Monte Carlo variant of the Kalman filter, which
represents the state estimates and observations using sets of random samples instead of the
conventional mean vectors and covariance matrices. Specifically, both of these filters provide a
new generalised update rule that computes consistent state estimates even in the presence of
correlation between the errors associated with the state estimate and the observation. This is
only possible due to the fact that in the context of the Ensemble Kalman filter, the magnitude
of such a correlation can be estimated from the random samples The new filters retain all of the important features of the Ensemble Kalman filter, such as
scaling linearly with the number of state-space dimensions, and supporting non-linear process
and observation models. An analysis of the numerical properties of the filters is provided, including
a comparison with state-of-the-art methods in several benchmark scenarios. Furthermore, in
order to demonstrate their practical utility, the new filters have been applied to three different
real-world problems in the larger field of robot localisation: cooperative vehicle localisation,
simultaneous localisation and mapping, and global satellite-based positioning. | en |
