  We present a study of the use and limits of the Time-Delay Interferometry
null channels for in flight estimation of the Laser Interferometer Space
Antenna instrumental noise. The paper considers how the two main limiting noise
sources, test-mass acceleration noise and interferometric phase measurement
noise, propagate through different Time-Delay Interferometry channels: the
Michelson combination X that is the most sensitive to gravitational waves, then
the less-sensitive combinations $\alpha$, and finally the null channel $\zeta$.
We note that the null channel $\zeta$, which is known to be equivalent to any
null channel, not only has a reduced sensitivity to the gravitational waves,
but also feature a larger degree of cancellation of the test mass acceleration
noise relative to the interferometry noise. This severely limits its use in
quantifying the low frequency instrumental noise in the Michelson X
combination, which is expected to be dominated by acceleration noise. However,
we show that one can still use in-flight noise estimations from $\zeta$ to put
an upper bound on the considered noises entering in the X channel, which allows
to distinguish them from a strong stochastic gravitational wave background.
