The maximum of CRLB of time delay estimation

Author

Fei Wang ; Hailin Li ; Weijie Xia ; Jianjiang Zhou

Author_Institution

Coll. of Electron. & Inf. Eng., Nanjing Univ. of Aeronaut. & Astronaut., Nanjing, China

fYear

2014

fDate

15-17 Dec. 2014

Firstpage

1

Lastpage

4

Abstract

Cramer-Rao lower bound (CRLB) is very significant to evaluate parameter´s estimation results. This paper proposes to study the maximum of CRLB of time delay estimation (TDE) under certain signal to noise ratio, when we only need to get a reasonable range of estimation variance to test the validity of an algorithm without knowing the exact formula of signal, or to design a waveform which is difficult to be located. First, we deduce the estimation variance of time delay using the principle of least squares. Then, through comparing to CRLB in frequency domain, we know that they are same to express the lower variance bound for unbiased TDE. Finally, with time-frequency uncertainty principle, we could know that Gaussian envelope is the waveform to maximize CRLB of TDE under certain signal to noise ratio. Simulations also illustrate that Gaussian envelope is close to the maximum of CRLB of time delay.

Keywords

delay estimation; least squares approximations; time-frequency analysis; CRLB; Cramer-Rao lower bound; Gaussian envelope; TDE; estimation variance range; frequency domain; least squares principle; lower variance bound; parameter estimation evaluation; signal to noise ratio; time delay estimation; time-frequency uncertainty principle; Delay effects; Estimation error; Mathematical model; Radar; Signal to noise ratio; Time-frequency analysis; CRLB; Gaussian envelope; time delay estimation;

fLanguage

English

Publisher

ieee

Conference_Titel

Signal Processing and Communication Systems (ICSPCS), 2014 8th International Conference on

Conference_Location

Gold Coast, QLD

Type

conf

DOI

10.1109/ICSPCS.2014.7021095

Filename

7021095