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We investigate a broad class of non-classical states, composed of superposedsqueezed 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 statefidelity in comparison to metrologically sensitive compass state, is more than99$\%$. Also, the variance in small shifts measurements, is found equal forboth proposed and compass states. They show similar behaviour with change inaverage photon number. In metrological application, number variance of thecompass state being small for low coherent amplitude, suggests its potential toestimate damping parameter.

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