  This paper is concerned with developing a novel distributed Kalman filtering
algorithm over wireless sensor networks based on randomized consensus strategy.
Compared with the centralized algorithm, distributed filtering techniques
require less computation per sensor and lead to more robust estimation since
they simply use the information from the neighboring nodes in the network.
However, poor local sensor estimation caused by limited observability and
network topology changes which interfere the global consensus are challenging
issues. Motivated by this observation, we propose a novel randomized
gossip-based distributed Kalman filtering algorithm. Information exchange and
computation in the proposed algorithm can be carried out in an arbitrarily
connected network of nodes. In addition, the computational burden can be
distributed for a sensor which communicates with a stochastically selected
neighbor at each clock step under schemes of gossip algorithm. In this case,
the error covariance matrix changes stochastically at every clock step, thus
the convergence is considered in a probabilistic sense. We provide the mean
square convergence analysis of the proposed algorithm. Under a sufficient
condition, we show that the proposed algorithm is quite appealing as it
achieves better mean square error performance theoretically than the
noncooperative decentralized Kalman filtering algorithm. Besides, considering
the limited computation, communication, and energy resources in the wireless
sensor networks, we propose an optimization problem which minimizes the average
expected state estimation error based on the proposed algorithm. To solve the
proposed problem efficiently, we transform it into a convex optimization
problem. And a sub-optimal solution is attained. Examples and simulations are
provided to illustrate the theoretical results.
