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.

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