State and Parameter Estimation from Observed Signal Increments
It addresses the challenge of joint state and parameter estimation for Lagrangian particle tracking in stochastic velocity fields, an important problem in geophysical and environmental modeling.
The paper develops ensemble Kalman-Bucy filter algorithms for combined state and parameter estimation in continuous-time data assimilation with correlated errors, demonstrating performance on multi-scale model systems.
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. We demonstrate their performance through a series of increasingly complex multi-scale model systems.