Matlab code associated with manuscript "Lognormal and Mixed Gaussian–Lognormal Kalman Filters" - Fletcher, Steven (Colorado State University. Libraries, 2022)
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.
This is a MATLAB m file that implements the mixed Gaussian-lognormal Kalman filter (MXKF) with the Lorenz 1963 model for lognormally distributed background and observational errors for the z component, Gaussian distributed background and observational errors for the x and y components, and compares this against the performance of the current Extended Kalman Filter (EKF). The code has four command line prompts to run, and produces two sets of figure: The first figure is of the trajectories of the z and x components for the true, MXKF, and the EKF, along with the observations, while the second plots contains the analysis errors for the z and x solutions from the MXKF and EKJF.
Cooperative Institute for Research in the Atmosphere
Keywords: Non-Gaussian Kalman Filter; Extended Kalman Filter; Lorenz 63 model