Page 20 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

ENGINEERING 9

All three subjects are mature research areas, and many overview
books have been written. Naturally, by combining the three subjects
into one book, it cannot be avoided that some details are left out.
However, the discussion above shows that the three subjects are close
enough to justify one integrated book, covering these areas.
The combination of the three topics into one book also introduces
some additional challenges if only because of the differences in termin-
ology used in the three fields. This is, for instance, reflected in the
difference in the term used for ‘measurements’. In classification theory,
the term ‘features’ is frequently used as a replacement for ‘measure-
ments’. The number of measurements is called the ‘dimension’, but in
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classification theory the term ‘dimensionality’ is often used. The same
remark holds true for notations. For instance, in classification theory the
measurements are often denoted by x. In state estimation, two notations
are in vogue: either y or z (MATLAB uses y, but we chose z). In all cases
we tried to be as consistent as possible.

1.2 ENGINEERING

The top-down design of an instrument always starts with some primary
need. Before starting with the design, the engineer has only a global view of
the system of interest. The actual need is known only at a high and abstract
level. The design process then proceeds through a number of stages during
which progressively more detailed knowledge becomes available, and the
system parts of the instrument are described at lower and more concrete
levels. At each stage, the engineer has to make design decisions. Such
decisions must be based on explicitly defined evaluation criteria. The
procedure, the elementary design step, is shown in Figure 1.5. It is used
iteratively at the different levels and for the different system parts.
An elementary design step typically consists of collecting and organiz-
ing knowledge about the design issue of that stage, followed by an
explicit formulation of the involved task. The next step is to associate

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Our definition complies with the mathematical definition of ‘dimension’, i.e. the maximal
number of independent vectors in a vector space. In MATLAB the term ‘dimension’ refers to an
index of a multidimensional array as in phrases like: ‘the first dimension of a matrix is the row
index’, and ‘the number of dimensions of a matrix is two’. The number of elements along a row
is the ‘row dimension’ or ‘row length’. In MATLAB the term ‘dimensionality’ is the same as the
‘number of dimensions’.