Several proposed gravitational wave interferometers have a triangular
configuration, such as the Einstein Telescope and the Laser Interferometer
Space Antenna. For such a configuration one can construct a unique null channel
insensitive to gravitational waves from all directions. We expand on earlier
work and describe how to use the null channel formalism to estimate the power
spectral density for the Einstein Telescope interferometers with non-identical
as well as correlated noise sources. The formalism is illustrated with two
examples in the context of the Einstein Telescope, with increasing degrees of
complexity and realism. By using known mixtures of noises we show the formalism
is mathematically correct and internally consistent. Finally we highlight
future research needed to use this formalism as an ingredient for a Bayesian
estimation framework.
