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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2403.04712 |
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| _version_ | 1866914707894435840 |
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| author | Teng, Sangli Zhang, Harry Jin, David Jasour, Ashkan Ghaffari, Maani Carlone, Luca |
| author_facet | Teng, Sangli Zhang, Harry Jin, David Jasour, Ashkan Ghaffari, Maani Carlone, Luca |
| contents | This paper develops a new filtering approach for state estimation in polynomial systems corrupted by arbitrary noise, which commonly arise in robotics. We first consider a batch setup where we perform state estimation using all data collected from the initial to the current time. We formulate the batch state estimation problem as a Polynomial Optimization Problem (POP) and relax the assumption of Gaussian noise by specifying a finite number of moments of the noise. We solve the resulting POP using a moment relaxation and prove that under suitable conditions on the rank of the relaxation, (i) we can extract a provably optimal estimate from the moment relaxation, and (ii) we can obtain a belief representation from the dual (sum-of-squares) relaxation. We then turn our attention to the filtering setup and apply similar insights to develop a GMKF for recursive state estimation in polynomial systems with arbitrary noise. The GMKF formulates the prediction and update steps as POPs and solves them using moment relaxations, carrying over a possibly non-Gaussian belief. In the linear-Gaussian case, GMKF reduces to the standard Kalman Filter. We demonstrate that GMKF performs well under highly non-Gaussian noise and outperforms common alternatives, including the Extended and Unscented Kalman Filter, and their variants on matrix Lie group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04712 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | GMKF: Generalized Moment Kalman Filter for Polynomial Systems with Arbitrary Noise Teng, Sangli Zhang, Harry Jin, David Jasour, Ashkan Ghaffari, Maani Carlone, Luca Robotics Systems and Control This paper develops a new filtering approach for state estimation in polynomial systems corrupted by arbitrary noise, which commonly arise in robotics. We first consider a batch setup where we perform state estimation using all data collected from the initial to the current time. We formulate the batch state estimation problem as a Polynomial Optimization Problem (POP) and relax the assumption of Gaussian noise by specifying a finite number of moments of the noise. We solve the resulting POP using a moment relaxation and prove that under suitable conditions on the rank of the relaxation, (i) we can extract a provably optimal estimate from the moment relaxation, and (ii) we can obtain a belief representation from the dual (sum-of-squares) relaxation. We then turn our attention to the filtering setup and apply similar insights to develop a GMKF for recursive state estimation in polynomial systems with arbitrary noise. The GMKF formulates the prediction and update steps as POPs and solves them using moment relaxations, carrying over a possibly non-Gaussian belief. In the linear-Gaussian case, GMKF reduces to the standard Kalman Filter. We demonstrate that GMKF performs well under highly non-Gaussian noise and outperforms common alternatives, including the Extended and Unscented Kalman Filter, and their variants on matrix Lie group. |
| title | GMKF: Generalized Moment Kalman Filter for Polynomial Systems with Arbitrary Noise |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2403.04712 |