Applied optimal estimation by Gelb A.

By Gelb A.

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The variables that affect the system are its input, and these are described with a set X . The variables by which the system affects its environment are its output, and these are described with a set Y . The variables that constitute the system are its state, and these are described with a set S. The dynamic behavior of the system is described by functions from time to the sets of input, output, and states. The set of times used by the system is called its time base; for discrete-time systems this is the set N of natural numbers.

Mathematically, unlocked = (locked, x[0, 1)) where x(0) = k. If we can turn the key again, we expect the lock to close: locked = (unlocked, x[0, 1)). If the lock is closed and we turn the key twice, we expect it to be closed when we are done: locked = (locked, x • x). To summarize, we expect locked = (locked, x • x) = ( (locked, x), x). It is also significant that is a function and not some weaker construct. Suppose that we make a copy, call it k2 , of the original key k1 . These keys are indistinguishable, so k1 = k2 .

It has methods to insert and remove objects, iterate through the contained objects, and determine the number of objects in the container. The EventListener can be registered with the Simulator, which will notify the listener when the model produces output and changes its state. The EventListener has two abstract methods: stateChange and outputEvent. The stateChange method is called by the Simulator when the model changes its state. The outputEvent method is called when the model produces an output.

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