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The authors state the non-uniformly periodically sampling pattern and derives the state-space models of non-uniformly sampled-data systems with coloured noises, and further obtains the corresponding transfer function models. Difficulties of identification are that there exist unknown inner variables and unmeasurable noise terms in the information vectors. By means of the auxiliary model method, an auxiliary model based multi-innovation generalised extended stochastic gradient (SG) algorithm is presented by expanding the scalar innovation to the innovation vector and introducing the innovation length. The proposed algorithm provides higher parameter estimation accuracy and faster convergence rate than the SG algorithm due to repeatedly using the system innovation.