Page 15 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

4 INTRODUCTION

fingerprint recognition or face recognition. A third problem that can be
solved by classification-like techniques is retrieval from a database, e.g.
finding an image in an image database by specifying image features.

1.1.2 Parameter estimation

In parameter estimation, one tries to derive a parametric description for
an object, a physical process, or an event. For example, in a beacon-
based position measurement system (Figure 1.2), the goal is to find the
position of an object, e.g. a ship or a mobile robot. In the two-
dimensional case, two beacons with known reference positions suffice.
The sensory system provides two measurements: the distances from the
beacons to the object, r 1 and r 2 . Since the position of the object involves
two parameters, the estimation seems to boil down to solving two
equations with two unknowns. However, the situation is more complex
because measurements always come with uncertainties. Usually, the
application not only requires an estimate of the parameters, but also
an assessment of the uncertainty of that estimate. The situation is even
more complicated because some prior knowledge about the position
must be used to resolve the ambiguity of the solution. The prior know-
ledge can also be used to reduce the uncertainty of the final estimate.
In order to improve the accuracy of the estimate the engineer can
increase the number of (independent) measurements to obtain an over-
determined system of equations. In order to reduce the cost of the
sensory system, the engineer can also decrease the number of measure-
ments leaving us with fewer measurements than parameters. The system

beacon 1

r r r 1
prior
knowledge
beacon 2

r r r 2
object

Figure 1.2 Position measurement: a parameter estimation problem handling uncer-
tainties