  Substantial improvement in accuracy of identified linear time-invariant
single-input multi-output (SIMO) dynamical models is possible when the
disturbances affecting the output measurements are spatially correlated. Using
an orthogonal representation for the modules composing the SIMO structure, in
this paper we show that the variance of a parameter estimate of a module is
dependent on the model structure of the other modules, and the correlation
structure of the disturbances. In addition, we quantify the variance-error for
the parameter estimates for finite model orders, where the effect of noise
correlation structure, model structure and signal spectra are visible. From
these results, we derive the noise correlation structure under which the
mentioned model parameterization gives the lowest variance, when one module is
identified using less parameters than the other modules.
