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• W2964202295 abstract "In this paper, we focus on sensor placement in linear dynamic estimation, where the objective is to place a small number of sensors in a system of interdependent states so to design an estimator with a desired estimation performance. In particular, we consider a linear time-variant system that is corrupted with process and measurement noise, and study how the selection of its sensors affects the estimation error of the corresponding Kalman filter over a finite observation interval. Our contributions are threefold: First, we prove that the minimum mean square error of the Kalman filter decreases only linearly as the number of sensors increases. That is, adding extra sensors so to reduce this estimation error is ineffective, a fundamental design limit. Similarly, we prove that the number of sensors grows linearly with the system's size for fixed minimum mean square error and number of output measurements over an observation interval; this is another fundamental limit, especially for systems where the system's size is large. Second, we prove that the log det of the error covariance of the Kalman filter, which captures the volume of the corresponding confidence ellipsoid, with respect to the system's initial condition and process noise is a supermodular and non-increasing set function in the choice of the sensor set. Therefore, it exhibits the diminishing returns property. Third, we provide an efficient approximation algorithm that selects a small number sensors so to optimize the Kalman filter with respect to this estimation error —the worst-case performance guarantees of this algorithm are provided as well." @default.
• W2964202295 created "2019-07-30" @default.
• W2964202295 creator A5029243115 @default.
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• W2964202295 date "2016-07-01" @default.
• W2964202295 modified "2023-10-01" @default.
• W2964202295 title "Sensor placement for optimal Kalman filtering: Fundamental limits, submodularity, and algorithms" @default.
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• W2964202295 doi "https://doi.org/10.1109/acc.2016.7524914" @default.
• W2964202295 hasPublicationYear "2016" @default.
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