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Matlab code associated with manuscript "Lognormal and Mixed Gaussian–Lognormal Kalman Filters"
(Colorado State University. Libraries, 2022) Fletcher, Steven
In this paper we shall present the derivation of two new forms of the Kalman filter equations; the first is for a pure lognormally distributed random variable, while the second set of Kalman filter equations will be for a combination of Gaussian and lognormally distributed random variables. We shall show that the appearance is similar to that of the Gaussian based equations, but that the analytical state is a multivariate median and not the mean. We shall show results of the mixed distribution Kalman filter with the Lorenz 1963 model with lognormal errors for the background and observations of the $z$ component, and compare them to results and forecasts from a traditional Gaussian based Kalman filter and show that under certain circumstances the new approach produces more accurate results.