  We propose a parameter estimation protocol for generalized Pauli channels
acting on $d$-dimensional Hilbert space. The salient features of the proposed
method include product probe states and measurements, the number of measurement
configurations linear in $d$, minimal post-processing, and the scaling of the
mean square error comparable to that of the entanglement-based parameter
estimation scheme for generalized Pauli channels. We also show an effective
method to mitigate the effects of noise on the probe states to recover the
scaling of the noiseless case when the noise strength is known.
