State and Parameter Estimation from Observed Signal Increments

Abstract

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.

References in corpus (1)

• Data Assimilation: A Mathematical Introduction

Cited by in corpus (5)

• McKean-Vlasov SDEs in nonlinear filtering
• Projection Filtering with Observed State Increments with Applications in Continuous-Time Circular Filtering
• Robust parameter estimation using the ensemble Kalman filter
• Analysis of the Ensemble Kalman--Bucy Filter for correlated observation noise
• Rough McKean-Vlasov dynamics for robust ensemble Kalman filtering