  I propose a quantum sensor based on driven-dissipative quantum system for the
joint estimation of two conjugated variables characterizing the phase space
displacement. The quantum probe consists of lattice system with two level atoms
and bosonic modes which interact via dipolar coupling. Interplay between the
coherent dynamics and dissipative processes of losses of bosonic excitations
leads to a steady state which exhibits a non-analytical behaviour. I show that
close to the dissipative phase transition the sensitivity of one of the
conjugated parameters either the magnitude of the phase of the displacement can
be significantly enhanced. Moreover, I show that the sum of the measurement
uncertainties of the two parameters can overcome the standard quantum limit.
