Conjugate continuous-discrete projection filter via sparse-Grid quadrature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918329368707072 |
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| author | Emzir, Muhammad F. Sawlan, Zaid A. Ferik, Sami El |
| author_facet | Emzir, Muhammad F. Sawlan, Zaid A. Ferik, Sami El |
| contents | In this article, we study the continuous-discrete projection filter for exponential-family manifolds with conjugate likelihoods. We first derive the local projection error of the prediction step of the continuous-discrete projection filter. We then derive the exact Bayesian update algorithm for a class of discrete measurement processes with additive Gaussian noise. To control the stiffness of the natural parameters' ordinary differential equations, we introduce a regularization method via projection to the Fisher information metric's eigenspace. Lastly, we apply the proposed method to approximate the filtering density of a modified Van der Pol oscillator problem and a coupled stochastic FitzHugh--Nagumo system. The proposed projection filter shows superior performance compared to several state-of-the-art parametric continuous-discrete filtering methods. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_17324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conjugate continuous-discrete projection filter via sparse-Grid quadrature Emzir, Muhammad F. Sawlan, Zaid A. Ferik, Sami El Optimization and Control In this article, we study the continuous-discrete projection filter for exponential-family manifolds with conjugate likelihoods. We first derive the local projection error of the prediction step of the continuous-discrete projection filter. We then derive the exact Bayesian update algorithm for a class of discrete measurement processes with additive Gaussian noise. To control the stiffness of the natural parameters' ordinary differential equations, we introduce a regularization method via projection to the Fisher information metric's eigenspace. Lastly, we apply the proposed method to approximate the filtering density of a modified Van der Pol oscillator problem and a coupled stochastic FitzHugh--Nagumo system. The proposed projection filter shows superior performance compared to several state-of-the-art parametric continuous-discrete filtering methods. |
| title | Conjugate continuous-discrete projection filter via sparse-Grid quadrature |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.17324 |