  Combining quantum and Bayesian principles leads to optimality in metrology,
but the optimisation equations involved are often hard to solve. This work
mitigates this problem with a novel class of measurement strategies for
quantities isomorphic to location parameters, which are shown to admit a
closed-form optimisation. The resulting framework admits any parameter range,
prior information, or state, and the associated estimators apply to finite
samples. As an example, the metrology of relative weights is formulated from
first principles and shown to require hyperbolic errors. The primary advantage
of this approach lies in its simplifying power: it reduces the search for good
strategies to identifying which symmetry leaves a state of maximum ignorance
invariant. This will facilitate the application of quantum metrology to
fundamental physics, where symmetries play a key role.
