The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory is treated here as an H∞-optimal control one under phase constraints with the objective to minimize a given 'weak' performance index under 'worst' possible disturbances. Existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimally are derived on the basis of constructing a sequence of suboptimal solutions associated, in turn, with a sequence of finite-dimensional maximum principles