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We consider the problem of estimating the output of an unknown discrete-time linear time-invariant system and identifying a model of the system, where only measurements via a nonlinear dynamic sensor with known dynamics are available. The main result of this paper is a rank-constrained semidefinite program, which provides an equivalent characterization of this identification and estimation problem. This extends existing results from Wiener system identification to the more general case that the nonlinear block exhibits dynamic behavior, which is a commonly found scenario in practical applications. Notably, the result can be applied in the presence of nonlinear sensors with general non-invertible system dynamics. Two examples are used to illustrate the applicability of our approach.
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A Non-Convex Approach To Joint Sensor Calibration And Spectrum Estimation
Blind sensor calibration for spectrum estimation is the problem of estimating the unknown sensor calibration parameters as well as the parameters-of-interest of the impinging signals simultaneously from snapshots of measurements obtained from an array of sensors. In this paper, we consider blind phase and gain calibration (BPGC) problem for direction-of-arrival estimation with multiple snapshots of measurements obtained from an uniform array of sensors, where each sensor is perturbed by an unknown gain and phase parameter. Due to the unknown sensor and signal parameters, BPGC problem is a highly nonlinear problem. Assuming that the sources are uncorrelated, the covariance matrix of the measurements in a perfectly calibrated array is a Toeplitz matrix. Leveraging this fact, we first change the nonlinear problem to a linear problem considering certain rank-one positive semidefinite matrix, and then suggest a non-convex optimization approach to find the factor of the rank-one matrix under a unit norm constraint to avoid trivial solutions. Numerical experiments demonstrate that our proposed non-convex optimization approach provides better or competitive recovery performance than existing methods in the literature, without requiring any tuning parameters.
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- Award ID(s):
- 1818571
- PAR ID:
- 10078982
- Date Published:
- Journal Name:
- 2018 IEEE Statistical Signal Processing Workshop (SSP)
- Page Range / eLocation ID:
- 398 to 402
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/SSP.2018.8450691
