  This paper concerns state estimation problems in a mean field control
setting. In a finite population model, the goal is to estimate the joint
distribution of the population state and the state of a typical individual. The
observation equations are a noisy measurement of the population.
  The general results are applied to demand dispatch for regulation of the
power grid, based on randomized local control algorithms. In prior work by the
authors it has been shown that local control can be carefully designed so that
the aggregate of loads behaves as a controllable resource with accuracy
matching or exceeding traditional sources of frequency regulation. The
operational cost is nearly zero in many cases.
  The information exchange between grid and load is minimal, but it is assumed
in the overall control architecture that the aggregate power consumption of
loads is available to the grid operator. It is shown that the Kalman filter can
be constructed to reduce these communication requirements,
