Received: January 18, 2005 Revised: July 3, 2007 Communicated by Ulf Rehmann Abstract. We deal with a ertain observation mapping de ned by means of weighted measurments on a dynami al system and give ne essary and su ient onditions, under whi h this mapping is generially an inje tive immersion. 2000 Mathemati s Subje t Classi ation: 93B07, 37C20, 37C10, 94A20.