- Multi-sensor information fusion usually involves existence of nuisance parameters, such as the estimation error covariance at each node of the network. In this paper, we address the question of how accurately one can estimate a parameter of interest using a network of multi-sensors, subject to unknown noise intensity at the sensors. The commonly used Cramér-Rao bound (CRB) is restricted to mean-unbiased estimation of all model parameters with no distinction of their character and leads to optimistic and unachievable performance analysis. Instead, a Cramér-Rao-type bound on the mean-squared-error (MSE) is derived for the considered scenario, where the noise variances are considered as nuisance parameters. The proposed bound is based on the risk-unbiased CRB (RUCRB), which assumes risk-unbiased estimation of the parameters of interest. Simulations show that the RUCRB provides a tight and achievable performance analysis for the MSE of conventional estimators.