Flexible least squares for approximately linear systems

A probability-free multicriteria approach is presented to the problem of filtering and smoothing when prior beliefs concerning dynamics and measurements take an approximately linear form. In particular, model discrepancy terms are treated as model specification errors that may not have any meaningful probabilistic description. Applications are envisioned in various fields, particularly in the social and biological sciences, where obtaining agreement among researchers regarding probability relations for discrepancy terms is difficult. The essence of the proposed flexible least squares (FLS) procedure is the cost-efficient frontier. This frontier, a curve in a two-dimensional cost plane, provides an explicit and systematic way to determine the efficient trade-offs between the separate costs incurred for dynamic and measurement specification errors. The estimated state sequences whose associated cost vectors attain the cost-efficient frontier, referred to as FLS estimates, show how the state vector could have evolved over time in a manner minimally incompatible with the prior dynamic and measurement specifications. A Fortran program, GFLS, for implementing the FLS filtering and smoothing procedure for approximately linear systems is provided