In deriving all our state estimators we worked with our basic state-variable model. In many practical applications we begin with a model that differs from the basic state-variable model. The purpose of this lesson is to explain how to use or modify our previous state estimators when there are:
1. Either nonzero-mean noise processes or known bias functions or both in the state or measurement equations; or
2. Correlated noise processes in the state and measurement equations; or
3. Colored disturbances or measurement noises; or
4. Some perfect measurements.
No new concepts are needed to handle items 1 and 2. A state augmentation procedure is needed to handle item 3. Colored ...