There is no way to discover the waking is an idea except through deeper self-search

The perfume and smelling which one has in a dream are only an idea. This helps to understand why similarly the five sense experiences which one has in waking experience are also ideas.all ideas are reality within the illusion.

There is no way to discover the waking is an idea except through deeper self-search.  Then only one becomes aware of the fact that, mind itself is the matter and the substance of the mind is spirit or consciousness. Thus one realizes the fact that matter is spirit in its essence.

Three state analyses cannot be used for this: it is only an illustration in this connection. Three state analyses is not needed to prove idealism: Scientific, analyses of feeling the only real proof. Three state analyses can merely illustrate idealism, although it is the only proof when you step beyond idealism. Scientific analysis of feeling is quite enough to prove idealism. When world is known to be idea, Three state analysis is only proof of world being in Atman the true self , and only way to understand  and assimilate the nature of Atman.

People make the mistake of viewing and judging the worldview on the base of ego, not on the base of Ataman the true self. They are good at reasoning on the base of ego, not on the base of Ataman, which gives the truth. Proof of non duality can only be got from inquiry, analysis and reasoning on the true base. Then only can one sees the world and yet know it to be nothing more than illusion, and illusion as Atman. 

Where was the world before prior to waking experience? It must have been in the Atman the true self, similarly when one awake into non dual wisdom he knows waking is illusion, and illusion(universe or mind)  is Atman finally.

It will be a great error to write that the world is unreal. It is not.  The world is reality within the waking. The correct statement is: "The waking is like a dream." This is because both dream and waking worlds are mental.  Illusion is only momentary although one minute may look like 1000 years in dream.

Atman is that which sees, the Witness and it cannot be described. It is not a state, cannot be. The three states merge in the Atman which is beyond.  Sleep is always present in all the three states.