Effective filtering approach for joint parameter-state estimation in SDEs via Rao-Blackwellization and modularization

For joint parameter-state estimation problems, classical particle filters often suffer from sample degeneracy or problems related to artificial noise, stemming from the particles representing unknown parameters. To address this challenge, this paper provides a novel filtering approach that avoids generating such particles by utilizing Rao-Blackwellization, which therefore provides more accurate estimates. Moreover, our method employs a modularization approach when integrating out the parameters, significantly reducing the computational complexity. All these designs ensure the superior performance of our method. Finally, a couple of numerical examples are presented to illustrate the superior performance of our method compared with several existing approaches.