The study on upper bound of measurement error with constraint of stochastic passage characteristics

Due to the restrictions of technology and cost, the sensors with measurement precision as lower as possible are in good graces in actual engineering on the premise of guaranteed system performance. For a class of estimation problem that the target future position is a plane (or spatial) area (target area) in some electro-optical tracking systems, the admissible maximum measurement error variance is studied. Firstly, the consistency between the constraint indices of regional pole, prediction error variance and stochastic passage characteristics (opportunity awaiting index) of such kind tracking system is analyzed. Secondly, the multi indices are converted into a set of bi-linear matrix inequalities (BMIs). Then, the admissible maximum measurement error variance is given by iteratively solving linear matrix inequalities (LMIs) to approximate BMIs. Finally, the obtained results are demonstrated by a numerical example.