It is also possible to give a sequential interpretation of the standard nudging algorithm by seeing it as a Kalman filter. Indeed, when no observations are available, the nudging method simply consists of solving the model equations, like Kalman filters. On the other hand, when some observations are available, in both nudging and Kalman filters, the model solution is corrected with the innovation vector, i.e. the difference between the observations and the corresponding model state [16].
If at any time, the nudging matrices are set in an optimal way, then the standard nudging method is equivalent to the standard Kalman filter. In the other cases, it can be seen as a suboptimal Kalman filter. However, the iterative and alternative resolutions of forward and backward models appreciably improves the efficiency of the standard nudging method.