The pwpfit Toolbox for Polynomial and Piece-wise Polynomial Data Fitting

Cunis, Torbjørn

doi:10.1016/j.ifacol.2018.09.204

Cited by 2 publications

(5 citation statements)

References 9 publications

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“…y −i dy. (13) Provided that, g(u) = −g(l) = v, and i 1 > 0 is an odd-integer, and i 2 > 0 is an even-integer, then, for i = i 1 and i = i 2 , respectively,…”

Section: Definitionmentioning

confidence: 99%

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Polynomial Distributions and Transformations

Loskot

2023

Mathematics

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Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rather than to assume polynomials for only approximating known or empirically estimated distributions. Polynomial distributions offer great modeling flexibility and mathematical tractability. However, unlike canonical distributions, polynomial functions may have non-negative values in the intervals of support for some parameter values; their parameter numbers are usually much larger than for canonical distributions, and the interval of support must be finite. Hence, polynomial distributions are defined here assuming three forms of a polynomial function. Transformations and approximations of distributions and histograms by polynomial distributions are also considered. The key properties of the polynomial distributions are derived in closed form. A piecewise polynomial distribution construction is devised to ensure that it is non-negative over the support interval. A goodness-of-fit measure is proposed to determine the best order of the approximating polynomial. Numerical examples include the estimation of parameters of the polynomial distributions and generating polynomially distributed samples.

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“…y −i dy. (13) Provided that, g(u) = −g(l) = v, and i 1 > 0 is an odd-integer, and i 2 > 0 is an even-integer, then, for i = i 1 and i = i 2 , respectively,…”

Section: Definitionmentioning

confidence: 99%

“…The problem of fitting a polynomial into a finite number of data samples has been investigated in the classic reference [12]. The polynomial curve fitting methods are often available in various software packages [13]. Modeling times series data by piecewise polynomials is considered in [14,15].…”

Section: Introductionmentioning

confidence: 99%

Polynomial Distributions and Transformations

Loskot

2023

Mathematics

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“…As the observations form a discrete set, an optimization approach over X 1,2 would be fair and just, thus yielding an ideal model. With piecewise polynomial fitting keeping most properties of polynomial regression, it has been proven numerically in [22] that the inaccuracy of a fitted erroneous signal is reduced: given data pairs (x i , z i ) i by (4) with ∼ N (0, σ) and a piecewise fit f , the standard deviation of f to the true values, γ(x) − f (x), is smaller than the measurement error σ.…”

Section: B Piecewise Polynomial Fittingmentioning

confidence: 99%

“…The computation of the zero constraint is not illustrated in Fig. 1 but is given, regardless the constraint of continuity, by [22,Alg. 3] and precedes the solution of the LSQ problem.…”

Section: With the Definition Pmentioning

confidence: 99%

“…Motivated by the practical problems encountered with mini-UAs flight control and guidance, civil aircraft fault detection and isolation, and upset recovery, we aim to derive a simple yet powerful aerodynamic model still suitable for functional analysis. A novel approach for piecewise polynomial modeling aerodynamic coefficients, the pwpfit toolbox for MATLAB, was recently proposed in [22]. Here, we have proven feasibility of fitting both a piecewise polynomial model and its joint surface using linear least-square (LSQ) optimization techniques.…”

Section: Introductionmentioning

confidence: 99%

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