Closed-Form Formulae for Time-Difference-of-Arrival Estimation

Author

So, Hing Cheung ; Chan, Yiu Tong ; Chan, Frankie Kit Wing

Author_Institution

Dept. of Electron. Eng., City Univ. of Hong Kong, Kowloon

Volume

56

Issue

6

fYear

2008

fDate

6/1/2008 12:00:00 AM

Firstpage

2614

Lastpage

2620

Abstract

For a positioning system with L sensors, a maximum of L(L-1)/2 distinct time-difference-of-arrival (TDOA) measurements, which are referred to as the full TDOA set, can be obtained. In this paper, closed-form expressions regarding optimum conversion of the full TDOA set to the nonredundant TDOA set, which corresponds to (L-1) TDOA measurements with respect to a common reference receiver, in the case of white signal source and noise, are derived. The most interesting finding is that optimum conversion can be achieved via the standard least squares estimation procedure. Furthermore, the Cramer-Rao lower bound for TDOA-based positioning is produced in closed-form, which will be useful for optimum sensor array design.

Keywords

array signal processing; least squares approximations; sensor arrays; time-of-arrival estimation; white noise; Cramer-Rao lower bound; TDOA-based positioning system; closed-form formulae; least squares estimation procedure; optimum sensor array design; time-difference-of-arrival estimation; white noise; white signal source; Closed-form solution; Delay effects; Delay estimation; Gaussian processes; Least squares approximation; Microphone arrays; Position measurement; Sensor arrays; Sensor systems; Time difference of arrival; Optimum processing; source localization; time delay estimation;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2007.914342

Filename

4524057