A multiple model least-squares estimation method

The traditional least-squares parameter estimation method involves matrix inversion and is therefore subject to numerical problems. In this paper, a multiple model least-squares (MMLS) method is proposed which is a fundamental reformulation and efficient implementation of the least-squares method. The MMLS method simultaneously produces multiple models of various orders plus the corresponding loss functions which can be used for order-determination. The order-recursive nature of the MMLS method avoids the numerical problems associated with overparameterization.