This paper deals with recursive random parameter or state estimation for use in distributed tracking applications implemented with a Wireless Sensor Network (WSN). Bandwidth and energy limitations encountered with WSNs, motivate quantization of individual sensor observations before their digital transmission to the fusion center, where tracking is to be performed. Recent results investigating the intertwining between quantization and batch parameter estimation with WSNs, hint that quantization to a single bit per sensor may lead to a small penalty in state estimation variance. Relying on a dynamical model, we derive a Kalman-like Filter (KF) based on what we term "sign- differential" quantization, and establish that for all cases of practical interest, its asymptotic variance comes surprisingly close to the asymptotic variance of the clairvoyant minimum mean-square error KF state estimator which is based on the original (analog) observations. In a nutshell, this paper establishes the rather unexpected result that tracking with a WSN can simply rely on sensor observations quantized to a single bit.