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- Elvander, Filip, et al.
(författare)
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Worst-Case Uncertainty Bounds in Covariance Interpolation
- 2022
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Ingår i: 2022 30TH EUROPEAN SIGNAL PROCESSING CONFERENCE (EUSIPCO 2022). - : IEEE. ; , s. 2256-2260
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Konferensbidrag (refereegranskat)abstract
- In this work, we establish and compute worst case bounds in covariance interpolation for continuous-time stationary stochastic processes, a problem that appears in applications such as broad-band direction-of-arrival estimation and optimal sensor placement. More specifically, for two such stochastic processes whose covariance functions agree on a finite discrete set of time-lags, we would like to compute the maximal possible discrepancy of the covariance functions for real-valued time-lags outside this discrete grid. In array processing, this difference quantifies the inherent uncertainty pertaining to the discrete sampling of space determined by the array geometry. Computing this uncertainty corresponds to solving an infinite-dimensional non-convex problem. However, we herein prove that the maximal objective value may be bounded from above by a finite-dimensional convex optimization problem, allowing for efficient computation by standard methods. Furthermore, we empirically observe that for the case of signals whose spectra are supported on an interval, this upper bound is sharp, i.e., provides an exact quantification of the covariance uncertainty.
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| 2. |
- Svedberg, David, et al.
(författare)
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Determining joint periodicities in multi-time data with sampling uncertainties
- 2022
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Ingår i: 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). - : Institute of Electrical and Electronics Engineers (IEEE). - 1520-6149. - 9781665405409 - 9781665405416 ; , s. 5737-5741
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Konferensbidrag (refereegranskat)abstract
- In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, and only partially known, sampling times. The problem originates in paleoclimatology, where each data point derives from a separate ice core measurement, resulting in that even though all measurements reflect the same periodicities, the sampling times and phases differ among the data sets, with the sampling times being only approximately known. The proposed estimator exploits all available data using a sparse reconstruction framework allowing for a reliable and robust estimation of the underlying periodicities. The performance of the method is illustrated using both simulated and measured ice core data sets.
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