Treatment of Gross Errors Using Maximum Probability Theory

We describe a nonlinear analysis scheme capable of directly treating observations which have a non‐Gaussian error distribution. This non‐Gaussian analysis scheme is shown to be a generalization of the familiar optimum interpolation scheme and must be solved iteratively. the approach to the treatment of gross errors is compared with a more traditional approach in which a quality‐control step precedes the analysis. Simulation experiments are performed in which the observations have many of the characteristics of observations from the proposed space‐borne atmospheric laser Doppler instrument and a 50% probability of gross error. Both approaches are shown to perform well, with the non‐Gaussian analysis giving the better results.