REAL-TIME TARGET TRACKING - OPTIMAL DETERMINATION OF THE CHARACTERISTICS, USING MARTINGALE TOOLS

We study the problem of real-time target tracking: How do we use all t he previous observations in order to get, at a given time, the best kn owledge of the position of the target? A realistic approach is to take into account the processing time for each observation, and if the pre cision an the position is low, the processing will take longer. As was shown by C. Olivier (Real-time observability of targets with constrai ned processing power, to appear), the tracking is efficient when some affine random walk (characterizing the precision of the tracking) is a lmost surely bounded. Using martingale techniques, we show that this i s the case under proper (and realistic) conditions on the parameters. (C) 1996 Academic Press, Inc.