Simplify the RFM based on the Anti-ill-posed Algorithms

摘要

In recent years, the Rational Function Model (RFM) is more and more popular because of its generalization, high accuracy and simplification. And it gradually replaced the traditional rigorous physical models. The classical form of Rational Function Model is usually expressed as ratios of polynomials whose term's maximum power are limited to 3. Although the maximum power of each term is limited, the terms of a polynomial with 3 power in the model are 20, and the total terms of one RFM will be up to 80, which brings heavy calculation. Meanwhile, it needs 39 control points to solve the RFM, but it is difficult to collect so many control points artificially. So this paper aims to simplify the RFM. The paper can mainly be divided into three parts. Firstly, the development of RFM is introduced and its advantages and disadvantages are discussed. Secondly, the classical method, iterative least squares solution, for solving RFM is detailed described, and three anti-ill-posed algorithms for overcoming the RFM's ill-posed problem are introduced. Lastly, using experimental results to prove it is feasible to simplify the RFM.