It Is Better to Take Few Accurate Measurements rather than Many Noisy Ones ∗

Linear pre-filtering (projection) of the measurement space is often used in parameter estimation to reduce the dimensionality, and hence the complexity, of the (generally non-linear) processor. We examine the tradeoff between the number and the accuracy of the measurements, as reflected by the Fisher Information after the prefilter. We observe the following phenomena. Taking twice as much but half as accurate measurements does not preserve the Fisher information after the prefiletr, unless the measurement noise is Gaussian. Thus, when the processor dimension is fixed and the noise is not Gaussian, it is better to take few accurate measurements rather than many noisy ones.