@TECHREPORT\{IMM2007-05316,
    author       = "L. E. Christiansen and H. A. Nielsen and T. S. Nielsen and H. Madsen",
    title        = "Automatic selection of tuning parameters in wind power prediction",
    year         = "2007",
    number       = "",
    series       = "IMM-Technical Report-2007-12",
    institution  = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5316-full.html",
    abstract     = "This document presents frameworks for on-line tuning of adaptive estimation procedures. First, introducing unbounded optimization of variable forgetting factor recursive least squares (RLS) using steepest descent and Gauss-Newton methods. Second, adaptive optimization of the bandwidth in conditional parametric {ARX-}models.

It was found that the steepest descent approach was more suitable in the examples considered. Further a large increase in the stability when using the proposed transformation of the forgetting factor as compared to the standard approach using a clipper function is observed. This becomes increasingly important when the optimal forgetting factor approaches unity.

Adaptive estimation in conditional parametric models are also considered. A similar approach is used to develop a procedure for on-line tuning of the bandwidth independently for each fitting point. Both Gaussian and tri-cube weight functions have been used and for many applications the tri-cube weight function with a lower bound on the bandwidth is preferred.

Overall this work documents that automatic tuning of adaptiveness of tuning parameters is indeed feasible and makes it easier to initialize these classes of systems, e.g. when predicting the power production from new wind farms."
}