This command selects an objective function that corresponds to a Cauchy or Lorentzian distribution, i.e., the probability density function of the residuals r reads:
This distribution exhibits more extensive tails compared to the normal distribution, and leads therefore to a more robust estimation if outliers are present. The objective function to be minimized is given by the following equation:
This objective function can bE minimized using the standard Levenberg-Marquardt algorithm which is designed for a quadratic objective function. The objective function can be reasonably well approximated by a quadratic function, so that the Levenberg-Marquardt algorithm is usually quite efficient.
>>> assume measurement errors follow a CAUCHY distribution
>>> ANDREW | >>> L1-ESTIMATOR | >>> LEAST-SQUARES | >>> QUADRATIC-LINEAR