Identification of symmetric noncausal processes. (May 2019) - Lu, Qiugang; Loewen, Philip D.; Bhushan Gopaluni, R.; Forbes, Michael G.; Backström, Johan U.; Dumont, Guy A.; Davies, Michael S.
Abstract: We propose a maximum likelihood estimation approach for the identification of symmetric noncausal models. Such models are used to represent the cross-directional dynamic response of many industrial processes that are generally modeled with a high-dimensional gain matrix. Reducing the number of parameters in a noncausal model can significantly reduce the uncertainty associated with parameter estimates. We adapt the maximum likelihood method to treat symmetric noncausal models by showing that every symmetric noncausal process admits a spectrally equivalent causal model. It is then proved that the maximum likelihood estimate of this causal model converges to that of the original noncausal model. We present an iterative identification algorithm to efficiently estimate the parameters in noncausal models. Finally, we show that the parameter covariance estimate obtained from the causal model also converges to that of the noncausal model, which lays a foundation for optimal input design in noncausal processes. Several numerical examples illustrate the effectiveness of the proposed algorithm.