A Gaussian mixture ensemble transform filter for vector observations
Santosh Nannuru, Mark Coates, Arnaud Doucet · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2013
The ensemble Kalman filter relies on a Gaussian approximation being a reasonably accurate representation of the filtering distribution. Reich recently introduced a Gaussian mixture ensemble transform filter which can address scenarios where the prior can be modeled using a Gaussian mixture. Reichs derivation is suitable for a scalar measurement or a vector of uncorrelated measurements. We extend the derivation to the case of vector observations with arbitrary correlations. We illustrate through numerical simulation that implementation is challenging, because the filter is prone to instability.