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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/2409.12368 |
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| _version_ | 1866917779551027200 |
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| author | Varley, Maxwell Molloy, Timothy L. Nair, Girish N. |
| author_facet | Varley, Maxwell Molloy, Timothy L. Nair, Girish N. |
| contents | Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of high-dimensional measurements and analyze state estimation in linear time-invariant systems with infinite-dimensional measurements but finite-dimensional states, both corrupted by additive noise. We propose a linear filter and derive the corresponding optimal gain functional in the sense of the minimum mean square error, analogous to the classic Kalman filter. By modeling the measurement noise as a wide-sense stationary random field, we are able to derive the optimal linear filter explicitly, in contrast to previous derivations of Kalman filters in distributed-parameter settings. Interestingly, we find that we need only impose conditions that are finite-dimensional in nature to ensure that the filter is asymptotically stable. The proposed filter is verified via simulation of a linearized system with a pinhole camera sensor. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_12368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Linear Filtering for Discrete-Time Systems with Infinite-Dimensional Measurements Varley, Maxwell Molloy, Timothy L. Nair, Girish N. Systems and Control Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of high-dimensional measurements and analyze state estimation in linear time-invariant systems with infinite-dimensional measurements but finite-dimensional states, both corrupted by additive noise. We propose a linear filter and derive the corresponding optimal gain functional in the sense of the minimum mean square error, analogous to the classic Kalman filter. By modeling the measurement noise as a wide-sense stationary random field, we are able to derive the optimal linear filter explicitly, in contrast to previous derivations of Kalman filters in distributed-parameter settings. Interestingly, we find that we need only impose conditions that are finite-dimensional in nature to ensure that the filter is asymptotically stable. The proposed filter is verified via simulation of a linearized system with a pinhole camera sensor. |
| title | Optimal Linear Filtering for Discrete-Time Systems with Infinite-Dimensional Measurements |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2409.12368 |