An Improved Implementation of the Orthogonal Polynomial Modal Parameter Estimation Algorithm Using the Orthogonal Complement

The rational fraction polynomial algorithm is the entry-level model of the high-order, frequency-domain modal parameter estimation methods. However, it has some well-known issues with numerical ill-conditioning for a high model order and a wide frequency range. Among the alternatives that have been proposed over the years to address this shortcoming is a change of basis functions from power polynomials to orthogonal polynomials. While this approach does cure the numerical ill-conditioning issues, this algorithm has not yet achieved mainstream acceptance, with the reasons for this reluctance typically cited being additional complication or increased computation time. This paper introduces an improved implementation of the orthogonal polynomial algorithm that uses the orthogonal complement, coupled with QR decomposition, to greatly reduce the time of the accumulation phase. The neat trick performed by the orthogonal complement is to get all of the overdetermination possible without having to do all of the work.