The goal in this section is to explain the fundamentals of Kalman filter theory
by a few illustrative examples.
The Kalman filter requires a state space model for describing the signal
dynamics. To describe its role, we need a concrete example, so let us return to
the target tracking example from Chapter 1. Assume that we want a model
with the states z1 = X , x2 = Y, x3 = X och x4 = Y . This is the simplest
possible case of state vector used in practice. Before we derive a model in the
next section, a few remarks will be given on what role...