  This work presents distributed algorithms for estimation of time-varying
random fields over multi-agent/sensor networks. A network of sensors makes
sparse and noisy local measurements of the dynamic field. Each sensor aims to
obtain unbiased distributed estimates of the entire field with bounded
mean-squared error (MSE) based on its own local observations and its neighbors'
estimates. This work develops three novel distributed estimators:
Pseudo-Innovations Kalman Filter (PIKF), Distributed Information Kalman Filter
(DIKF) and Consensus+Innovations Kalman Filter (CIKF). We design the gain
matrices such that the estimators achieve unbiased estimates with bounded MSE
under minimal assumptions on the local observation and network communication
models. This work establishes trade-offs between these three distributed
estimators and demonstrates how they outperform existing solutions. We validate
our results through extensive numerical evaluations.
