  The future space-borne Laser Interferometer Space Antenna (LISA) is expected
to detect gravitational waves (GW) from Extreme Mass Ratio Inspiral (EMRI)
binaries which may live in nontrivial environments such as accretion disks. In
this work, we apply the Fisher matrix Principal Component Analysis (PCA) method
to assess how well LISA observations can jointly constrain the source
parameters and environmental densities around EMRIs. Specifically, we calculate
the Fisher matrix from the post-Newtonian parameters of an EMRI binary embedded
in a fluid with a constant density profile. We determine that the most dominant
measurable parameter combination is dominated by contributions from
environmental effects, namely, gravitational drag, accretion, and gravitational
pull (in order of contribution). The proposed reparameterization of the PN
parameters can be used to improve the power and efficiency of future detection
and parameter estimation methods.
