Evaluation of Time-Difference-of-Arrival Error of Acoustic Beacons Caused by Velocity of Microphone Array

Abstract

In this paper, we described a criterion of estimating the quality of time-difference-of-arrival (TDOA) estimation with a moving microphone array. The microphone array was supposed to receive a known signal from an acoustic beacon which transmitted a binary code with binary phase shift keying (BPSK). The movement of the microphone array may cause two kinds of error on the TDOA estimation; physical change of TDOA caused by the movement, and apparent change caused by the lower correlation values of Doppler-shifted signals. For evaluating the latter error, we employed the peak to average power ratio (PAPR) of the cross correlation function. The Doppler effect on TDOA error were evaluated with a computer simulation. The microphone array was moved at -2 to 2 m/s, covering the velocity range of indoor mobile robot. Besides the velocity, following three parameters of the sound were investigated. The types of the code for evaluation were chosen as M-, Gold and Kasami sequences, carrier frequencies were 0-40 kHz, and chip rates of the binary code were 0.5 - 20 kHz. As the results, it was confirmed that if PAPR is lower than a certain value, 40 in this simulation, the peak detection of the cross correlation is difficult and it results in high and unpredictable TDOA errors. Higher chip rates and lower carrier frequencies showed better resilience against the Doppler effect. The proposed criterion may infer the maximum velocities at which TDOA can be estimated without any measure against the Doppler effect for realistic parameters. This criterion would contribute to the on-line evaluation of the quality of TDOA, which may be beneficial for estimating sound direction of arrival.