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 distributed 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 a novel distributed KF estimator based on quantized measurement innovations. The quantized observations and the distributed nature of the iteratively quantized KF algorithm are amenable to the resource constraints of the ad hoc WSNs. 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. With minimal communication overhead, the mean square error (MSE) of the distributed KF-like tracker based on 2-3 bits is almost indistinguishable from that of the clairvoyant KF.