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, in the countable infinite quantization alphabet case, the network can still achieve weak consensus with the information loss due to quantization, 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 error variance sequences as interacting particles, then model each sequence evolution as a Random Dynamical System (RDS), and further prove its stochastically bounded nature. Moreover, based on the analysis for the countable infinite quantization alphabet case, we also prove that under certain conditions the network can also achieve weak consensus, when the quantization alphabet is finite, which is more restricted and practical.