Page 264 - Classification Parameter Estimation & State Estimation An Engg Approach Using MATLAB

8

State Estimation in Practice

Chapter 4 discussed the theory needed for the design of a state estimator.
The current chapter addresses the practical issues related to the design.
Usually, the engineer cycles through a number of design stages of which
some are depicted in Figure 8.1.
One of the first steps in the design process is system identification. The
purpose is to formulate a mathematical model of the system of interest.
As stated in Chapter 4, the model is composed of two parts: the state
space model of the physical process and the measurement model of the
sensory system. Using these models, the theory from Chapter 4 provides
us with the mathematical expressions of the optimal estimator.
The next questions in the design process are the issues of observa-
bility (can all states of the process be estimated from the given set of
measurements?) and stability. If the system is not observable or not
stable, either the model must be revised or the sensory system must be
redesigned.
If the design passes the observability and the stability tests, the
attention is focussed at the computational issues. Due to finite arith-
metic precision, there might be some pitfalls. Since in state estimation
the measurements are processed sequentially, the effects of round-off
errors may accumulate and may cause inaccurate results. The estima-
tor may even completely fail to work due to numerical instabilities.
Although the optimal solution of an estimation problem is often
unique, there are a number of different implementations which are

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