  We consider the problem of estimating multiple analytic functions of a set of
local parameters via qubit sensors in a quantum sensor network. To address this
problem, we highlight a generalization of the sensor symmetric performance
bounds of Rubio et. al. [J. Phys. A: Math. Theor. 53 344001 (2020)] and develop
a new optimized sequential protocol for measuring such functions. We compare
the performance of both approaches to one another and to local protocols that
do not utilize quantum entanglement, emphasizing the geometric significance of
the coefficient vectors of the measured functions in determining the best
choice of measurement protocol. We show that, in many cases, especially for a
large number of sensors, the optimized sequential protocol results in more
accurate measurements than the other strategies. In addition, in contrast to
the the sensor symmetric approach, the sequential protocol is known to always
be explicitly implementable. The sequential protocol is very general and has a
wide range of metrological applications.
