  We consider non-local sensing of scalar signals with specific spatial
dependence in the Bayesian regime. We design schemes that allow one to achieve
optimal scaling and are immune to noise sources with a different spatial
dependence than the signal. This is achieved by using a sensor array of
spatially separated sensors and constructing a multi-dimensional decoherence
free subspace. While in the Fisher regime with sharp prior and multiple
measurements only the spectral range $\Delta$ is important, in single-shot
sensing with broad prior the number of available energy levels $L$ is crucial.
We study the influence of $L$ and $\Delta$ also in intermediate scenarios, and
show that these quantities can be optimized separately in our setting. This
provides us with a flexible scheme that can be adapted to different situations,
and is by construction insensitive to given noise sources.
