TY - GEN
T1 - A Generative Cramér-Rao Bound on Frequency Estimation with Learned Measurement Distribution
AU - Habi, Hai Victor
AU - Messer, Hagit
AU - Bresler, Yoram
N1 - Publisher Copyright:
© 2022 IEEE.
PY - 2022
Y1 - 2022
N2 - 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.
AB - 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.
KW - CRB
KW - Generative model
KW - deep learning
KW - normalizing flow
KW - parameter estimation
UR - http://www.scopus.com/inward/record.url?scp=85135370245&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85135370245&partnerID=8YFLogxK
U2 - 10.1109/SAM53842.2022.9827830
DO - 10.1109/SAM53842.2022.9827830
M3 - Conference contribution
AN - SCOPUS:85135370245
T3 - Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
SP - 176
EP - 180
BT - 2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
PB - IEEE Computer Society
T2 - 12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022
Y2 - 20 June 2022 through 23 June 2022
ER -