These are two quite different words. And their meaning also differs whether the object is a person or an object.
Etwas erkennen means to recognize something, i.e. used to describe the fact of recognizing a far away or very small object.
Etwas anerkennen is a term to describe acceptance of a fact or a treaty. Not very often used expression. A government for instance may accept a treaty as valid. That would be
Die Regierung erkennt den Friedensvertrag an. (Duden, Fall 2, case 1a is similar but more general)
Similar here: akzeptieren.
Jemanden anerkennen (more common: jemandem Anerkennung entgegenbringen) means bringing recognition towards somebody, i.e. by complimenting his work.
Matthias anerkannte Leo, der Bemühungen um eine friedliche Beilegung des Konfliktes unternahm. (Duden, Fall 1b)
Jemanden erkennen is an old term (used i.e. in the bible) to describe having sex with somebody. Sounds silly if you use it nowadays. It can be used in the first case though, meaning to recognize somebody from a distance or by remembering their face. Compare:
Als Josef seine Brüder sah, erkannte er sie. (Gen 42,7)
Adam erkannte Eva, seine Frau; sie wurde schwanger und gebar Kain. (Gen 4,1)