  The paper provides simple formulas of Bayesian filtering for the exact
recursive computation of state conditional probability density functions given
quantized innovations signal measurements of a linear stochastic system. This
is a topic of current interest because the innovations signal should be white
and therefore efficient in its use of channel capacity and in the design and
optimization of the quantizer. Earlier approaches, which we reexamine and
characterize here, have relied on assumptions concerning densities or
approximations to yield recursive solutions, which include the
sign-of-innovations Kalman filter and a Particle filtering technique. Our
approach uses the Kalman filter innovations at the transmitter side and
provides a point of comparison for the other methods, since it is based on the
Bayesian filter. Computational examples are provided.
