Page 16 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

THE SCOPE OF THE BOOK 5

of equations is underdetermined then, but estimation is still possible if
enough prior knowledge exists, or if the parameters are related to each
other (possibly in a statistical sense). In either case, the engineer is
interested in the uncertainty of the estimate.

1.1.3 State estimation

In state estimation, one tries to do either of the following – either
assigning a class label, or deriving a parametric (real-valued) description –
but for processes which vary in time or space. There is a fundamental
difference between the problems of classification and parameter estima-
tion on the one hand, and state estimation on the other hand. This is the
ordering in time (or space) in state estimation, which is absent from
classification and parameter estimation. When no ordering in the data is
assumed, the data can be processed in any order. In time series, ordering
in time is essential for the process. This results in a fundamental differ-
ence in the treatment of the data.
In the discrete case, the states have discrete values (classes or labels)
that are usually drawn from a finite set. An example of such a set is the
alarm stages in a safety system (e.g. ‘safe’, ‘pre-alarm’, ‘red alert’, etc.).
Other examples of discrete state estimation are speech recognition,
printed or handwritten text recognition and the recognition of the
operating modes of a machine.
An example of real-valued state estimation is the water management
system of a region. Using a few level sensors, and an adequate dynamical
model of the water system, a state estimator is able to assess the water
levels even at locations without level sensors. Short-term prediction of
the levels is also possible. Figure 1.3 gives a view of a simple water
management system of a single canal consisting of three linearly con-
nected compartments. The compartments are filled by the precipitation
in the surroundings of the canal. This occurs randomly but with a
seasonal influence. The canal drains its water into a river. The measure-
ment of the level in one compartment enables the estimation of the levels
in all three compartments. For that, a dynamic model is used that
describes the relations between flows and levels. Figure 1.3 shows an
estimate of the level of the third compartment using measurements of the
level in the first compartment. Prediction of the level in the third com-
partment is possible due to the causality of the process and the delay
between the levels in the compartments.