This paper presents a matrix inequality approach to sensor fault estimation in presence of random input disturbance with unknown covariance. The input is supposed to be a correlated stationary Gaussian noise with bounded mean anisotropy. The quality criterion is defined as anisotropic norm of the system. Anisotropic norm of the system defines gain from input disturbance with bounded mean anisotropy to output. The main contribution of the paper is sensor fault estimator design that allows to estimate sensor fault with guaranteed anisotropybased disturbance attenuation level. Numerical example is given.