Interactive Kalman Filtering

Data assimilation via the extended Kalman filter can become problematic when the assimilating model is strongly nonlinear, primarily in connection with sharp, ''switchlike'' changes between different regimes of the system. The filter seems too inert to follow those switches quickly enough, a fact that can lead to a complete failure when the switches occur often enough. In this paper we replace the key feature of the filter, the use of local linearity for the error model update, with a principle that uses a more global approach through the utilization of a set of preselected regimes. The method uses all regime error models simultaneously. Being mutually incompatible, a compromise between the different error models is found through the use of a weighting function that reflects the 'closeness' of the error model to the correct model. To test the interactive Kalman filter a series of numerical experiments is performed using the double-well system and the well-known Lorenz system, and the results are compared to the extended Kalman filter. It turns out that, depending on the set of preselected regimes, the performance is worse than, comparable to, or better than that of the extended Kalman filter.