Is it possible to reset the ECU on 03 Impreza's as you can on older models?

 

No

You need a SECS Unit or similar to reset the ECU

 

what about disconecting the battery?

 

unlikely, it'll be stored on an eeprom (or something similar) that doesn't need power to retain its data.

edit: response to battery question.

 

disconnect the battery for a while, then run the car to 1 bar and hold it through most of the rev range (where possible) to learn it...(thats how i was told to do it)

 

As Ninnybobs mentioned disconnecting the battery will not "reset" the ECU as maps / faults are on EPROM.

Disconnecting the battery will remove any "learning" the ECU has done and it will learn again from scratch.

Midlife.....