Parameter estimation for a controlled autoregressive autoregressive moving average system based on a recursive framework

In this paper, an adaptive recursive estimation scheme based on a novel recursive framework is proposed for a controlled autoregressive autoregressive moving average (CARARMA) system. A common loss function is established using the prediction error scheme, which has two shortcomings in case of interference, namely, biased estimation and minima problems. To overcome the two shortcomings, a recursive estimation scheme is proposed by using output error data with a discount factor and initial error data with a penalty operator. The former data do not involve the noise information of system data, so the biased estimation issue can be improved. The latter data include initial value information, such that the minima problem can be resolved. To achieve the target, polynomial transformation is applied to transform the CARARMA system into a particular model, then the loss function is introduced. Based on the loss function and recursive structure, a recursive estimator is developed. Moreover, the convergence of the proposed identification scheme is strictly analyzed. The advantage and practicality of the proposed estimator are evaluated by using a numerical example and real-world process.