Direction Finding for Transient Acoustic Source Based on Biased TDOA Measurement

A sound localization system consisting of a number of spatially distributed sensors can be employed to estimate the source bearing by measuring the relative time-difference-of-arrival (TDOA) of the transient acoustic signal. However, sensor measurements may contain nonnegligible consistent systematic biases, resulting in significant direction finding estimation error. In this paper, an efficient expectation-maximization (EM) algorithm is proposed for accurately estimating the direction-of-arrival (DOA) of the signal from a far field source in the presence of biased TDOA measurements. The unknown biases are treated as hidden variables, and nonlinear least square estimators are developed to jointly estimate the biases and DOA parameters for both the reference-free mode and the reference mode. TDOA error distribution is investigated and four different distributions [Gaussian distribution, Laplace distribution, Gaussian-Laplace distribution, and generalized normal distribution (GND)] are employed to fit the experimental data. It is observed that GND is the best for modeling the biased TDOA errors in terms of cumulative distribution function fitting root mean square error, while Laplace distribution offers a good tradeoff between the accuracy and complexity. Both the simulation and field experimental results demonstrate that the proposed EM-based estimators can considerably outperform the existing algorithms.