Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Author

Mallat, Achraf ; Gezici, Sinan ; Dardari, Davide ; Craeye, Christophe ; Vandendorpe, Luc

Author_Institution

Inst. for Inf. & Commun. Technol., Electron. & Appl. Math., Univ. Catholique de Louvain, Louvain-la-Neuve, Belgium

Volume

62

Issue

21

fYear

2014

fDate

Nov.1, 2014

Firstpage

5663

Lastpage

5676

Abstract

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramér-Rao lower bound at low and medium signal-to-noise ratios (SNRs) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accuracy of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.

Keywords

deterministic algorithms; maximum likelihood estimation; mean square error methods; nonlinear estimation; time-of-arrival estimation; ALB family; Cramér-Rao lower bound; MIE; MLE; MSEA; SNR levels; TOA estimation; Taylor series expansion; ambiguity phenomena; approximate lower bound; approximate upper bounds; binary detection principle; maximum likelihood estimator; mean-squared error approximations; method of interval estimation; nonlinear deterministic parameter estimation; signal-to-noise ratios; statistics; threshold phenomena; time-of-arrival estimation; Approximation methods; Bayes methods; Materials; Maximum likelihood estimation; Signal to noise ratio; Time of arrival estimation; Nonlinear estimation; maximum likelihood estimator; mean-squared error; threshold and ambiguity phenomena; time-of-arrival; upper and lowers bounds;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2014.2355771

Filename

6894212