Robust optimal filters of linear stochastic systems

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Although the Kalman filter has been the most popular and widely used optimal filter for stochastic systems in practice, it is not a robust filter and so we cannot have good results often in simulations for the systems with mismatches between the actual systems and their mathematical models (i.e., the systems with modeling errors). Chen and Patton succeeded in proposing a simple filtering algorithm ODDO which is robust and optimal and can be applicable even to the systems with modeling errors. However, we later indicated that the ODDO was derived from their incorrect basic formula. In this project, we have succeeded in establishing a correct theory of robust optimal filters for stochastic systems with unknown disturbances and developing widely applicable algorithms (iterative methods) for practical systems.