What is the ensemble Kalman filter and how well does it work?

In this paper we described the ensemble Kalman filter algorithm. This approach to nonlinear Kalman filtering is a Monte Carlo procedure, which has been widely used in weather forecasting applications. Our goal was to apply the ensemble Kalman filter to representative examples to quantify the tradeoff between estimation accuracy and ensemble size. For all of the linear and nonlinear examples that we considered, the ensemble Kalman filter worked successfully once a threshold ensemble size was reached. In future work we will investigate the factors that determine this threshold value.