The Nesterov accelerated gradient algorithm for CARMA models with lost input data based on interpolation method

In this paper, an interpolation-based Nesterov accelerated gradient (INAG) algorithm is proposed for controlled autoregressive and moving average (CARMA) models with random lost input data. The algorithm uses the auxiliary model to replace unmeasurable noise terms with their estimates and applies the interpolation mothod to fill in the missing input data. Based on these interpolated data, the parameters can be estimated with better accuracy. Furthermore, the Nesterov accelerated gradient (NAG) method is introduced which not only improves the accuracy of parameter estimation but also increases the convergence rates. A simulation example is used to verify the effectiveness of the proposed algorithm.