Page 92 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

4

State Estimation

The theme of the previous two chapters will now be extended to the case
in which the variables of interest change over time. These variables can
be either real-valued vectors (as in Chapter 3), or discrete class variables
that only cover a finite number of symbols (as in Chapter 2). In both
cases, the variables of interest are called state variables.
The design of a state estimator is based on a state space model that
describes the underlying physical process of the application. For
instance, in a tracking application, the variables of interest are the
position and velocity of a moving object. The state space model gives
the connection between the velocity and the position (which, in this case,
is a kinematical relation). Variables, like position and velocity, are real
numbers. Such variables are called continuous states.
The design of a state estimator is also based on a measurement model
that describes how the data of a sensory system depend on the state
variables. For instance, in a radar tracking system, the measurements are
the azimuth and range of the object. Here, the measurements are directly
related to the two-dimensional position of the object if represented in
polar coordinates.
The estimation of a dynamic class variable, i.e. a discrete state variable
is sometimes called mode estimation or labelling. An example is in
speech recognition where – for the recognition of a word – a sequence
of phonetic classes must be estimated from a sequence of acoustic
features. Here too, the analysis is based on a state space model and a

Classification, Parameter Estimation and State Estimation: An Engineering Approach using MATLAB
F. van der Heijden, R.P.W. Duin, D. de Ridder and D.M.J. Tax
Ó 2004 John Wiley & Sons, Ltd ISBN: 0-470-09013-8