Consistent estimation in an implicit quadratic measurement error model

An adjusted least squares estimator is derived that yields a consistent estimate of the parameters of an implicit quadratic measurement error model. In addition, a consistent estimator for the measurement error noise variance is proposed. Important assumptions are: (1) all errors are uncorrelated identically distributed and (2) the error distribution is normal. The estimators for the quadratic measurement error model are used to estimate consistently conic sections and ellipsoids. Simulation examples, comparing the adjusted least squares estimator with the ordinary least squares method and the orthogonal regression method, are shown for the ellipsoid fitting problem.

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