Ellipsoidal estimation over observations with a vector impulse component
Michael Basin · 2002
An estimation problem over discrete-continuous observations is considered for an impulse component. A filtering procedure is suggested to design filtering equations over discrete-continuous observations (DCO) proceeding from the known filtering equations over continuous ones. This paper aims to obtain filtering equations over DCO with a vector impulse component. The ellipsoidal guaranteed estimation problem is selected as an example that illustrates the difference between filtering equations in scalar and vector distribution. Indeed, the obtained ellipsoidal estimation equations contain discontinuous regular functions in righthand sides. To define a solution uniquely and therefore to use a filtering procedure is possible if a transfer function in an observation equation is a symmetric matrix one. Then a right-hand side of each filtering equation satisfies the one-side solvability condition which is equivalent to the one-side Frobenius condition ensuring uniqueness. A vibrosolution, defined as a unique limit, to a system of ellipsoidal filtering equations is thus to be a pair of ellipsoid parameters optimal in the given sense. In case of scalar distribution the one-side solvability condition is always satisfied.>