"At" is a preposition used before the noun and after the verb requiring direction. But we do not need a preposition with home when it is used with any verb referring to direction, as below:
Note that most verbs expressing direction require the preposition to before the noun, but not home. Compare the following:
- I shall be arriving / going / coming / leaving home late this evening.
Some more examples requiring no direction, so preposition 'at' is used before 'Home'
- I made my way to the mosque before sunrise.
- I ran all the way to the theatre so that I wouldn't be late.
- Once you arrive home, you are then at home. (With the second "home" no more direction is suggested, so at is then the appropriate preposition to use with home:)
Will you be at home tonight or are you going out? ~ No, I'll be at home.