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1 2007

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Structured total least norm for MISO ARX system identification

Larkowski T., Vinsonneau B., Burnham K. J.

Systems Science

2007

Vol. 33, no 4

73-83

The errors-in-variables (EIV) identification framework concerns the identification of dynamic models of systems where all the variables are corrupted by noise. The total least squares (TLS) is one of the most prominent techniques that has proven to be both robust and reliable. The structured total least norm (STLN) can be seen as a natural extension to TLS that preserves any affine structure of the joint data matrix, which is mostly the case in identification schemes. In contrast to the least squares (LS), TLS or mixed LS-TLS problems, the STLN solution cannot be expressed in a closed form, therefore, an optimization procedure is required. Note that STLN allows different norms to be considered other than the usual square norm (or 2 norm). This paper describes a direct application of the STLN approach for systems that can be represented by auto-regressive with exogenous input (ARX) multi-input single-output (MISO) models. The performance of the proposed STLN algorithm (in the case of the square norm) is compared to the LS, the bias-eliminating LS (BELS), the extended matrix LS (EMLS), the instrumental variables (IV), TLS and the compensated TLS (CTLS) methods when applied to a simulated MISO ARX system. Results, obtained from Monte Carlo simulation, show that, under the conditions considered here, STLN surpasses all other investigated techniques, attaining the best estimates of the true system parameters.