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Substantial improvement in accuracy of identified linear time-invariantsingle-input multi-output (SIMO) dynamical models is possible when thedisturbances affecting the output measurements are spatially correlated. Usingan orthogonal representation for the modules composing the SIMO structure, inthis paper we show that the variance of a parameter estimate of a module isdependent on the model structure of the other modules, and the correlationstructure of the disturbances. In addition, we quantify the variance-error forthe parameter estimates for finite model orders, where the effect of noisecorrelation structure, model structure and signal spectra are visible. Fromthese results, we derive the noise correlation structure under which thementioned model parameterization gives the lowest variance, when one module isidentified using less parameters than the other modules.

Variance Analysis of Linear SIMO Models with Spatially Correlated Noise