  Various coefficients of the 3.5 post-Newtonian (PN) phasing formula of
non-spinning compact binaries moving in circular orbits is fully characterized
by the two component masses. If two of these coefficients are independently
measured, the masses can be estimated. Future gravitational wave observations
could measure many of the 8 independent PN coefficients calculated to date.
These additional measurements can be used to test the PN predictions of the
underlying theory of gravity. Since all of these parameters are functions of
the two component masses, there is strong correlation between the parameters
when treated independently. Using Singular Value Decomposition of the Fisher
information matrix, we remove this correlations and obtain a new set of
parameters which are linear combinations of the original phasing coefficients.
We show that the new set of parameters can be estimated with significantly
improved accuracies which has implications for the ongoing efforts to implement
parametrised tests of PN theory in the data analysis pipelines.
