  We seek to characterize the estimation performance of a sensor network where
the individual sensors exhibit the phenomenon of drift, i.e., a gradual change
of the bias. Though estimation in the presence of random errors has been
extensively studied in the literature, the loss of estimation performance due
to systematic errors like drift have rarely been looked into. In this paper, we
derive closed-form Fisher Information matrix and subsequently Cram\'er-Rao
bounds (upto reasonable approximation) for the estimation accuracy of
drift-corrupted signals. We assume a polynomial time-series as the
representative signal and an autoregressive process model for the drift. When
the Markov parameter for drift \rho<1, we show that the first-order effect of
drift is asymptotically equivalent to scaling the measurement noise by an
appropriate factor. For \rho=1, i.e., when the drift is non-stationary, we show
that the constant part of a signal can only be estimated inconsistently
(non-zero asymptotic variance). Practical usage of the results are demonstrated
through the analysis of 1) networks with multiple sensors and 2) bandwidth
limited networks communicating only quantized observations.
