| dc.description.abstract | Whenever the state of a system is estimated from information that is character
ized with errors, a state estimator is employed to fuse the data with the model to
produce an accurate estimate of the state. When the system dynamics and obser
vation models are linear, the Kalman Filter, which is optimal, is used. However, in
most applications of interest the system dynamics and observations equations are
not-linear and suitable extensions of the Kalman Filter have been developed; for
example, the Extended Kalman Filter(EKF). The Extended Kalman Filter is based
on linearization by the Taylor series expansion about the mean of the state. This
filtering process is however computationally expensive especially in high dimensional
data. The cause for this is the high cost of integrating the equation of evolution of
covariances. Due to this complexity in integration, new methods were sought known
as the particle filters. They replace linearisation of non-linearities with Monte Carlo
methods. They also formed a basis for Ensemble Kalman Filter (EnKF) an exten
sion of Kalman filter to non-linear models. The EnKF reduced the computational
cost but its innovation process did not capture information sufficiently hence there is
need to improve its performance. This study has developed a new filter, Second order
Extended Ensemble Filter (SoEEF). We derived it from stochastic state models by
expansion of expected values to the second order by use of Taylor series together with
Monte Carlo method. We used Lorenz 63 system of ordinary differential equations
to test the performance of the new filter using the MATLAB. Then we compared
its performance with four other filters like Bootstrap Particle Filter (BPF), First
order Kalman Bucy Filter (FoEKBF), Second order Kalman Bucy Filter (SoKBF)
and First order Extended Ensemble Filter (FoEEF). The performance of SoEEKF
improves with the increase in ensemble size. | en_US |
