What is the relationship between the narrator and his victim in "The Tell-tale Heart"?

As in other stories of his, Poe does not establish a precise relationship of the narrator/killer and his victim.  This ambiguity serves to heighten the gothic suspense as the horrified reader wonders why the killer commits his action.  In "Tell-Tale Heart," for instance, the narrator declares,

It is impossible to say how the idea first entered my brain....Passion there was none.  I loved the old man. He had never wronged me.  He had never given me insult. For his gold I had no desire.  I think it was he eye! Yes! it was this!

Obviously, the narrator is well-acquainted with the old man.  However, there are none of the "normal" motives here for murder.  The motive seems to be generated by the obsessive "nervous" insanity of the narrator:  He focuses on the "pale blue eye, with a film over it."  As in the poem "The Raven" in which the narrator imagines that the bird itself has a sinister reason for persisting in the repetition of "Nevermore!" so the narrator here imagines that the eye itself is evil.  Thus, the narrator himself creates the deadly, grotesque relationship:

He had the eye of a vulture....Whenever it fell upon me my blood ran cold; and so by degrees, very gradually, [as he becomes more obsessed] I made up my mind to take the life of the old man, and thus rid myself of the eye forever.