Coded Kalman Filtering over MIMO Gaussian Channels with Feedback
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911093385854976 |
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| author | Han, Barron Sabag, Oron Kostina, Victoria Hassibi, Babak |
| author_facet | Han, Barron Sabag, Oron Kostina, Victoria Hassibi, Babak |
| contents | We consider the problem of remotely stabilizing a dynamical system. A sensor (encoder) co-located with the system communicates with a controller (decoder), whose goal is to stabilize the system, over a noisy communication channel with feedback. To accomplish this, the controller must estimate the system state with finite mean squared error (MSE). The vector-valued dynamical system state follows a Gauss-Markov law with additive control. The channel is a multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channel with feedback. For such a source, a linear encoder, and a MIMO AWGN channel, the minimal MSE decoder is a Kalman filter. The parameters of the Kalman filter and the linear encoder can be jointly optimized, under a power constraint at the channel input. We term the resulting encoder-decoder pair a coded Kalman filter. We establish sufficient and necessary conditions for the coded Kalman filter to achieve a finite MSE in the real-time estimation of the state. For sufficiency, we introduce a coding scheme where each unstable mode of the state is estimated using the channel outputs of a single sub-channel. We prove a coinciding necessity condition when either the source or channel is scalar and present a matrix-algebraic condition which implies the condition is necessary in general. Finally, we provide a new counter-example demonstrating that linear codes are generally sub-optimal for coding over MIMO channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17196 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coded Kalman Filtering over MIMO Gaussian Channels with Feedback Han, Barron Sabag, Oron Kostina, Victoria Hassibi, Babak Information Theory Systems and Control We consider the problem of remotely stabilizing a dynamical system. A sensor (encoder) co-located with the system communicates with a controller (decoder), whose goal is to stabilize the system, over a noisy communication channel with feedback. To accomplish this, the controller must estimate the system state with finite mean squared error (MSE). The vector-valued dynamical system state follows a Gauss-Markov law with additive control. The channel is a multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) channel with feedback. For such a source, a linear encoder, and a MIMO AWGN channel, the minimal MSE decoder is a Kalman filter. The parameters of the Kalman filter and the linear encoder can be jointly optimized, under a power constraint at the channel input. We term the resulting encoder-decoder pair a coded Kalman filter. We establish sufficient and necessary conditions for the coded Kalman filter to achieve a finite MSE in the real-time estimation of the state. For sufficiency, we introduce a coding scheme where each unstable mode of the state is estimated using the channel outputs of a single sub-channel. We prove a coinciding necessity condition when either the source or channel is scalar and present a matrix-algebraic condition which implies the condition is necessary in general. Finally, we provide a new counter-example demonstrating that linear codes are generally sub-optimal for coding over MIMO channels. |
| title | Coded Kalman Filtering over MIMO Gaussian Channels with Feedback |
| topic | Information Theory Systems and Control |
| url | https://arxiv.org/abs/2406.17196 |