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**Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model.**
*(English)*
Zbl 1177.65095

Summary: In order to reduce computational burden and improve the convergence rate of identification algorithms, an auxiliary model based multi-innovation stochastic gradient (AM-MISG) algorithm is derived for the multiple-input single-output systems by means of the auxiliary model identification idea and multi-innovation identification theory. The basic idea is to replace the unknown outputs of the fictitious subsystems in the information vector with the outputs of the auxiliary models and to present an auxiliary model based stochastic gradient algorithm, and then to derive the AM-MISG algorithm by expanding the scalar innovation to innovation vector and introducing the innovation length. The simulation example shows that the proposed algorithms work quite well.

### MSC:

65K10 | Numerical optimization and variational techniques |

### Keywords:

parameter estimation; multi-innovation identification theory; auxiliary models; stochastic gradient; output error systems; multivariable systems; numerical example; convergence; multi-innovation stochastic gradient algorithm
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\textit{Y. Liu} et al., Appl. Math. Comput. 215, No. 4, 1477--1483 (2009; Zbl 1177.65095)

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### References:

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