Identification of Stochastic Systems Under Multiple Operating Conditions: The Vector Dependent FP-ARX Parametrization

The problem of identifying stochastic systems under multiple operating conditions, by using excitation-response signals obtained from each condition, is addressed. Each operating condition is characterized by several measurable variables forming a vector operating parameter. The problem is tackled within a novel framework consisting of postulated vector dependent functionally pooled ARX (VFP-ARX) models, proper data pooling techniques, and statistical parameter estimation. Least squares (LS) and maximum likelihood (ML) estimation methods are developed. Their strong consistency is established and their performance characteristics are assessed via a Monte Carlo study