Jai Jai ShriGokulesh,
The term "khyati" actually mean knowledge has been fixed for "bhraanti" or error (perceptual, auditory etc) in Indian philosophy. Various prefixes like "Anya" "Anyatha" "Abhinavanyatha" "Viparita" "Anirvachaniya" "A" "Sat" etc differentiate one Khyati from other types of Khyatis. Out of these Khyatis,Anya-khyati is advocated by Sri Vallabhacharya
Anyatha-khyati by Nyaay School
Abhinavanyatha-khyati by Madhvacharya
Viparita by Kumarilbhatta
Anirvachaniya by Shankaracharya
A-khyati by Prabhakaracharya
Sat-khyati by Ramanujacharya and so on.
It will become an essay if each and every above school is elaborated. Therefore, we shall briefly deal Anyathakhyati, Satkhyati, Akhyati and Anyakhyati.
To explain Khyati, example of shell-silver and rope-snake illusion is universally given by al most all the philosophical systems.
Anyatha-khyati:
Nyaya-Vaisheshika school believes that the cause for shell appearing as silver is due to former experience. According to them, real object is mistaken as another real object, which exist elsewhere. The word "Anyatha" means else-wise and elsewhere. The presented object (Shell) is perceived "else-wise" and the represented object (Silver) exist elsewhere. The shell and silver are both, separately real, only their synthesis their relation as "shell-silver" is unreal. The shell is misperceived as silver, which exists elsewhere, i.e. in the jeweler"s shop.
Satkhyati:
Ramanujvedant advocates Satkhyati. According to them every objected of this world is Bhautika, that is made of five Bhutas. Therefore, every object contains in greater of smaller amount all five elements in it. In such case, when we see shell on silver, according to R. Vedant, we do not see anything unreal, we see silver particles only which is normally not seen.
Akhyati:
This theory, attributed to the Prabhakara school of mimaamsaa, analyses perceptual error as a "failure in discrimination": the perceiver fails to discriminate between the perceived object and something remembered which is significantly similar to it.
Anyakhyati:
Suddhadvaita theory of error is known as "Anyakhyati". Anyakhyati means: knowledge of an altogether different object (like silver) then which is in contact with sense organ i.e. shell. This is known as "Anyakhyati".
The process of error:
When the Lord"s power Maya deludes Buddhi with predominance of Tamoguna after the rise of indeterminate ordinary knowledge, due to sense object (eye shell) contact. Thus when Buddhi (intellect) is deluded the right knowledge, "this is shell"" does not arise, because ignorance is product of Tamoguna. Similarly, Buddhi deluded by Maya does not grasp the true nature of the object. Due to the predominance of impressions of silver, Buddhi grasps the resemblance of shining-ness, whiteness etc. and creates silver on the shell. Then, Buddhi grasps this silver, which already exists in the Buddhi. At the time of Samanya-jnana i.e., at the time of sense object contact, silver is not created in the Samanya-jnana, since, silver is absent at that moment and silver is created by Buddhi only after indeterminate knowledge. Therefore, the conclusion can be drawn that the object of Samanya-jnana is shell only. After Samanya-jnana the special kind of knowledge is produced by Buddhi and silver existing in the Buddhi is the object of error.
It is said in the Subodhini "silver is produced by intellect after indeterminate knowledge and intellect only is the cause. This creation which is seen between sense and object is false or illusory"".
Sri Purushottamaji says, since there are two different types of perceivers one like ours and another Sarvajna, we have to classify perception in two types. He says, those who are realized persons, for them everything is Pratyaksha. Their knowledge is always true. In their case it is Akhyati, i.e. wrong knowledge is not possible. (Here, it must be remembered that the term "Akhyati" is not used with reference to Akhyativada of Prabhakara) Regarding ordinary people, Anyakhyati has to be accepted. Because of predominance of impressions, Buddhi only projects illusory object influenced by Maya. Therefore, characteristics of silver only are grasped.