Distributed Kalman Filtering with quantized sensing state

This paper studies a Quantized Gossip-based Interactive Kalman Filtering (QGIKF) algorithm implemented in a wireless sensor network, where the sensors exchange their quantized states with neighbors via inter-sensor communications. We show that with the information loss due to quantization, the network can still achieve weak consensus, i.e., the estimation error variance sequence at a randomly selected sensor can converge weakly (in distribution) to a unique invariant measure. To prove the weak convergence, we first interpret the error variance sequence evolution as the interacting particle, then formulate the sequence as a Random Dynamical System (RDS), and finally prove that it is stochastically bounded.