A Generative Cramér-Rao Bound on Frequency Estimation with Learned Measurement Distribution

Hai Victor Habi, Hagit Messer, Yoram Bresler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The estimation of the frequency of a single tone signal is a classical problem. The Cramér-Rao lower bound (CRB) on the frequency estimates has been well studied for the case of additive Gaussian noise. In practical applications, however, the probability density function of the noise is rarely Gaussian, or known. Moreover, non-linear effects, as quantization, are often present, making the Gaussian CRB unreachable. In this paper we propose a data-driven approach for evaluating the CRB on frequency estimation with unknown noise and other degradation. Using a learned normalizing flow model, we model the distribution of the measurements by a neural network and obtain an approximate CRB, referred to as a Generative CRB (GCRB). We demonstrate the GCRB on frequency estimation both in cases where the CRB has been previously evaluated, showing the accuracy of the GCRB empirically, and on complex cases where the CRB cannot be evaluated analytically or numerically.

Original languageEnglish (US)
Title of host publication2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
PublisherIEEE Computer Society
Pages176-180
Number of pages5
ISBN (Electronic)9781665406338
DOIs
StatePublished - 2022
Event12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022 - Trondheim, Norway
Duration: Jun 20 2022Jun 23 2022

Publication series

NameProceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
Volume2022-June
ISSN (Electronic)2151-870X

Conference

Conference12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
Country/TerritoryNorway
CityTrondheim
Period6/20/226/23/22

Keywords

  • CRB
  • deep learning
  • Generative model
  • normalizing flow
  • parameter estimation

ASJC Scopus subject areas

  • Signal Processing
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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