This note provides an error bound on an estimate resulting from a simple fusion scheme combining individual estimates based on measurements of different sensing mechanisms. An important benefit of the bound is that it requires only knowledge of the individual sensor covariances rather than the complete inter-sensor covariance structure. An example drawn from a previous paper is presented to assess the benefit to the accuracy of emitter location using a Doppler sensor for which the error bound is applied to the estimate of a set of local states entering the Doppler sensor model as parameters.