Consistent parameter bounding identification using cross-covariance constraints on the noise

Cross-covariance constraints on the noise are introduced into bounded error identification as an alternative to the standard time-domain noise constraints. The constraints are represented by a small number of linear inequalities, which can be used in parameter bounding by linear programming. An important feature of this new type of noise bound is that under fairly general conditions the feasible parameter set converges to the true parameter vector, the noise bounds need not be tight. A procedure is presented to estimate the cross-covariance bounds on the noise from data, such that asymptotically they will be correct with any prespecified probability desired. Also another noise constraint, a bound on the amplitude of the discrete Fourier transform of the noise, is introduced into time-domain parameter bounding identification. This frequency domain constraint on the noise is analysed as well.<
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