Compass state: Effect of squeezing and displacement on the Fock space

We investigate a broad class of non-classical states, composed of superposed squeezed and displaced number states. The phase space structure is analysed, keeping in mind, Heisenberg limited sensitivity in parameter estimation. Appropriate squeezing and displacement parameters are identified, wherein state fidelity in comparison to metrologically sensitive compass state, is more than 99$\mathrm{\%}$. Also, the variance in small shifts measurements, is found equal for both proposed and compass states. They show similar behaviour with change in average photon number. In metrological application, number variance of the compass state being small for low coherent amplitude, suggests its potential to estimate damping parameter.