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 observability (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 arithmetic 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 estimator 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 ...