  Studying the stability of the Kalman filter whose measurements are randomly
lost has been an active research topic for over a decade. In this paper we
extend the existing results to a far more general setting in which the
measurement equation, i.e., the measurement matrix and the measurement error
covariance, are random. Our result also generalizes existing ones in the sense
that it does not require the system matrix to be diagonalizable. For this
general setting, we state a necessary and a sufficient condition for stability,
and address its numerical computation. An important application of our
generalization is a networking setting with multiple sensors which transmit
their measurement to the estimator using a sensor scheduling protocol over a
lossy network. We demonstrate how our result is used for assessing the
stability of a Kalman filter in this multi-sensor setting.
