Decentralized quantized Kalman filtering with scalable communication cost

Estimation and tracking of generally nonstationary Markov processes is of paramount importance for applications such as localization and navigation. In this context, ad hoc wireless sensor networks (WSNs) offer decentralized Kalman filtering (KF) based algorithms with documented merits over centralized alternatives. Adhering to the limited power and bandwidth resources WSNs must operate with, this paper introduces two novel decentralized KF estimators based on quantized measurement innovations. In the first quantization approach, the region of an observation is partitioned into N contiguous, nonoverlapping intervals where each partition is binary encoded using a block of m bits. Analysis and Monte Carlo simulations reveal that with minimal communication overhead, the mean-square error (MSE) of a novel decentralized KF tracker based on 2-3 bits comes stunningly close to that of the clairvoyant KF. In the second quantization approach, if intersensor communications can afford m bits at time n, then the ith bit is iteratively formed using the sign of the difference between the n th observation and its estimate based on past observations (up to time n - 1) along with previous bits (up to i - 1) of the current observation. Analysis and simulations show that KF-like tracking based on m bits of iteratively quantized innovations communicated among sensors exhibits MSE performance identical to a KF based on analog-amplitude observations applied to an observation model with noise variance increased by a factor of [1 - (1 - 2/π)^m]^-1.