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In some object tracking systems, the moving object future position is an area (i.e., target area). It is a successful estimation strategy if the predicted points fall in the target area. If the object makes a sudden maneuvering, the prediction may get out of the target area easily which may make the tracking system lose the object. The aim is to investigate the admissible maximum object maneuvering intensity, which is characterized as model noise variance, for such kind of tracking system. Firstly, the concept of stochastic passage characteristics over the boundary of target area and their relationship with prediction error variance are described. Secondly, the consistency among the indices of regional pole, prediction error variance and stochastic passage characteristics is analyzed. Thirdly, the multi-indices constraints are characterized by a set of bi-linear matrix inequalities (BMls). Then, the admissible maximum model noise variance and the satisfactory estimation strategy are presented by iteratively solving linear matrix inequalities (LMls) to approximate BMls. Finally, a numerical example is proposed to demonstrate the obtained results.