Implementation of Ensemble Kalman Filters in Stone-Soup

The Ensemble Kalman Filter is a well understood method for highly nonlinear data assimilation applications, where many other state estimators either diverge or become computationally unfeasible. Here, an implementation of the Ensemble Kalman Filter (EnKF) and the Ensemble Square Root Filter (EnSRF) is proposed for inclusion in the International Society of Information Fusion (ISIF) affiliated open source Python tracking framework Stone Soup. The unique representation of the system’s state necessitated a novel EnsembleState data type, which flexibly encapsulates many StateVector objects in a computationally efficient manner for the requisite Predictor and Updater classes. Using the existing Stone Soup metrics generator, as well as a custom implementation of the root mean squared error, we demonstrate the EnKF’s convergence to the result of the Kalman filter for two dimensional linear Gaussian tracking examples. The same situation is then repeated with a nonlinear measurement model consisting of a range and bearing measurement, to demonstrate the added versatility over the Kalman filter. It is our hope that inclusion of the EnKF and EnSRF will open the door to development and implementation of a whole class of derived algorithms.

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