State and Parameter Estimation from Observed Signal Increments

Understand

The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems.

• In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified.
• Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters.
• We take an appropriate class of McKean-Vlasov equations as the starting point to derive ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation.