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The success of the ensemble Kalman filter has triggered a strong interest inexpanding its scope beyond classical state estimation problems. In this paper,we focus on continuous-time data assimilation where the model and measurementerrors are correlated and both states and parameters need to be identified.Such scenarios arise from noisy and partial observations of Lagrangianparticles which move under a stochastic velocity field involving unknownparameters. We take an appropriate class of McKean-Vlasov equations as thestarting point to derive ensemble Kalman-Bucy filter algorithms for combinedstate and parameter estimation. We demonstrate their performance through aseries of increasingly complex multi-scale model systems.

State and Parameter Estimation from Observed Signal Increments