ABSTRACT
Kalman Filtering is the signal processing tool of choice when an
application requires knowledge of the internal, non-observable,
state variables of a complex dynamical system. Given the observed
output of the system and its mathematical model, the Kalman
Filter estimates adaptively, optimally, or near-optimally depending
on the linearity of the system, the internal system state. While
one of the most important factors for the success of the Kalman
Filter is the adaptive estimation of the state-vector covariance
matrix, this estimation becomes computationally infeasible once
the dimensionality of the state-space becomes too large. The
Ensemble Kalman Filter is designed to circumvent this restriction
using a sample of estimations of the state variables, whose sample
covariance is a low-rank approximation to the underlying covariance
matrix. In this chapter, we describe the non-linear Ensemble
Kalman Filter and include some illustrative examples exploiting its
features.
