  In [1], Sinopoli et al. analyze the problem of optimal estimation for linear
Gaussian systems where packets containing observations are dropped according to
an i.i.d. Bernoulli process, modeling a memoryless erasure channel. In this
case the authors show that the Kalman Filter is still the optimal estimator,
although boundedness of the error depends directly upon the channel arrival
probability, p. In particular they also prove the existence of a critical
value, pc, for such probability, below which the Kalman filter will diverge.
The authors are not able to compute the actual value of this critical
probability for general linear systems, but provide upper and lower bounds.
They are able to show that for special cases, i.e. C invertible, such critical
value coincides with the lower bound. This paper computes the value of the
critical arrival probability, under minimally restrictive conditions on the
matrices A and C.
