Technical Report 2009-016

Expressions for the Covariance Matrix of Covariance Data

Torsten Söderström

May 2009

In several estimation methods used in system identification, a first step is to estimate the covariance functions of the measured inputs and outputs for a small set of lags. These covariance elements can be set up as a vector. The report treats the problem of deriving and computing the asymptotic covariance matrix of this vector, when the number of underlying input-output data is large. The derived algorithm is derived under fairly general assumptions. It is assumed that the input and output are linked through a linear finite-order system. Further, the input is assumed to be modelled as an ARMA model of a fixed, but arbitrary order. Finally, it is allowed that the both the input and the output are not measured directly, but with some white measurement noise, thus including typical errors-in-variables situations in the analysis.

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