engleski

Fitting an elliptical paraboloid with the known shape to the empirical data

The goal of this paper is to fit an elliptical paraboloid of the known shape to the empirical data by finding the analytical solution for an optimal vertex position in the weighted least squares sense. The model of the elliptical paraboloid is formed as the quadratic form (X'AX) in two variables (x0 and y0) where the matrix A denotes the known positive-definite symmetric matrix that defines the paraboloid's shape while the matrix X contains the distances of input samples from the unknown position of the vertex (x0, y0) which is being estimated. To fit such a model to the data contaminated with additive Gaussian noise, our objective function minimizes the weighted sum of squared residuals between the model and the target for all input samples to obtain an unbiased solution of minimal variance with optimal unit weights.

Elliptical paraboloid fitting ; Weighted least squares method ; Resultant ; Parameter estimation

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