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Multiple Model Parameter Estimation

Handling many models simultaneously is a desired feature in least-squares estimation. This is typically handled by reducing the maximum order case to a triangular set of equations and then solving the triangular equations for different orders. In this paper, we suggest an alternative method called the multiple model least-squares (MMLS), which is based on a single matrix factorization and directly gives all lower order models, including the parameter estimates and loss functions. The factorization structure of the MMLS estimator improves numerical performance and thus problems such as those associated with overparameterization are avoided. The MMLS method can be used as a replacement/update of the conventional implementation of the least-squares method