  Building upon the statistical formulation for parameter estimation in the
presence of correlated noise proposed by Cireddu et al., we present an initial
study to incorporate the effects of correlated noise into the analyses of
various detector designs' performance. We consider a two L-shaped detector
configuration located in the European Union, and compare the expectation of
parameter estimation between the non-colocated and a hypothetical colocated
configurations. In our study, we posit the existence of low-frequency
correlated noise within the $5\text{ Hz}$ to $10\text{ Hz}$ range for the
colocated detector configuration, with a varying degree of correlation. In this
specific detector setup, our observations indicate an enhancement in the
precision of intrinsic parameter measurements as the degree of correlation
increases. This trend suggests that higher degrees of noise correlation may
beneficially influence the accuracy of parameter estimation. In particular,
when the noise is highly correlated, the uncertainty on chirp mass decreases by
up to $30\%$. The absence of an inter-European baseline does hinder the
estimation of the extrinsic parameters. However, given a realistic global
network with the additional detector located in the United States, the
uncertainty of extrinsic parameters is significantly reduced. This reduction is
further amplified as the degree of noise correlation increases. When noise
correlation exceeds a certain level, the colocated configuration outperforms
the non-colocated one, reducing the $90\%$ credible area of sky location by up
to $10\%$. We conclude that noise correlation significantly impacts detector
performance, potentially altering both quantitative and qualitative outcomes.
Thus, we recommend including noise correlation in comprehensive assessments of
third-generation gravitational wave detector designs.
