  Recent result shows how to compute distributively and efficiently the linear
MMSE for the multiuser detection problem, using the Gaussian BP algorithm. In
the current work, we extend this construction, and show that operating this
algorithm twice on the matching inputs, has several interesting
interpretations. First, we show equivalence to computing one iteration of the
Kalman filter. Second, we show that the Kalman filter is a special case of the
Gaussian information bottleneck algorithm, when the weight parameter $\beta =
1$. Third, we discuss the relation to the Affine-scaling interior-point method
and show it is a special case of Kalman filter.
  Besides of the theoretical interest of this linking estimation,
compression/clustering and optimization, we allow a single distributed
implementation of those algorithms, which is a highly practical and important
task in sensor and mobile ad-hoc networks. Application to numerous problem
domains includes collaborative signal processing and distributed allocation of
resources in a communication network.
