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A relaxation of the general infinite horizon sensor scheduling problem for state estimation in linear time-invariant systems is presented. The optimal schedule is assumed to be periodic, and the relaxation allows the full problem, a nonlinear combinatorial optimization problem, to be converted to a mixed integer quadratic programming problem which can be easily solved. The relaxation is based on the system being driven by low-intensity process noise. To find the solution the integer constraint is first relaxed to find an initial unconstrained solution using a standard quadratic programming solver. The integer constraint is then satisfied by using established integer- constrained quadratic least-squares techniques and the Hessian of the cost function. Examples illustrate the performance of the algorithm versus the truth solution found by an exhaustive search.