ON THE PROBLEM OF APPROXIMATING THE INTERSECTION OF ELLIPSOIDS

Considers the problem of constructing an ellipsoid of minimal volume containing the intersection of two given ellipsoids. A solution of this problem is obtained for the case of similar ellipsoids, when the matrices defining these ellipsoids differ only by a scalar factor. This result serves as a basis for a new method of constructing an ellipsoid, quasioptimal with respect to the volume, which approximates the intersection of two arbitrary ellipsoids. This method provides better results than known ones, and can be used for construction of minimax filters in dynamic systems.