Summary: This article considers the identification problems of nonlinear systems with scarce measurements by using the instrumental variable technique. When the product of the instrumental matrix and the information matrix is a nonsingular matrix and the weak persistent excitation condition about the instrumental vector is true, the obtained parameter estimates can be unbiased consistent estimates. The key is how to choose the instrumental variables. Difficulty arises in that the system outputs are unavailable. By applying the negative gradient search, a recursive instrumental variable-based gradient algorithm is derived to estimate the parameters of the nonlinear systems with missing observed data. Moreover, the multi-innovation identification theory is introduced to further improve the parameter estimation accuracy. The simulation results illustrate that the proposed methods are effective.
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