  In conventional distributed Kalman filtering, employing diffusion strategies,
each node transmits its state estimate to all its direct neighbors in each
iteration. In this paper we propose a partial diffusion Kalman filter (PDKF)
for state estimation of linear dynamic systems. In the PDKF algorithm every
node (agent) is allowed to share only a subset of its intermediate estimate
vectors at each iteration among its neighbors, which reduces the amount of
internode communications. We study the stability of the PDKF algorithm where
our analysis reveals that the algorithm is stable and convergent in both mean
and mean-square senses. We also investigate the steady-state mean-square
deviation (MSD) of the PDKF algorithm and derive a closed-form expression that
describes how the algorithm performs at the steady-state. Experimental results
validate the effectiveness of PDKF algorithm and demonstrate that the proposed
algorithm provides a trade-off between communication cost and estimation
performance that is extremely profitable.
