Worst-Case Uncertainty Bounds in Covariance Interpolation

Filip Elvander, Johan Karlsson, Toon Van Waterschoot

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussaConference article in proceedingsScientificvertaisarvioitu

Abstrakti

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.
AlkuperäiskieliEnglanti
Otsikko2022 30th European Signal Processing Conference (EUSIPCO)
KustantajaIEEE
Sivut2256-2260
Sivumäärä5
ISBN (elektroninen)978-90-827970-9-1
ISBN (painettu)978-1-6654-6799-5
TilaJulkaistu - syysk. 2022
OKM-julkaisutyyppiA4 Artikkeli konferenssijulkaisussa
TapahtumaEuropean Signal Processing Conference - Belgrade, Serbia
Kesto: 29 elok. 20222 syysk. 2022
Konferenssinumero: 30
https://2022.eusipco.org/

Julkaisusarja

NimiEuropean Signal Processing Conference
ISSN (painettu)2219-5491
ISSN (elektroninen)2076-1465

Conference

ConferenceEuropean Signal Processing Conference
LyhennettäEUSIPCO
Maa/AlueSerbia
KaupunkiBelgrade
Ajanjakso29/08/202202/09/2022
www-osoite

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