Time Delay Estimate Based Direction of Arrival Estimation for Speech in Reverberant Environments

Time delay estimation (TDE)-based algorithms for estimation of direction of arrival (DOA) have been most popular for use with speech signals. This is due to their simplicity and low computational requirements. Though other algorithms, like the steered response power with phase transform (SRP-PHAT), are available that perform better than TDE based algorithms, the huge computational load required for this algorithm makes it unsuitable for applications that require fast refresh rates using short frames. In addition, the estimation errors that do occur with SRP-PHAT tend to be large. This kind of performance is unsuitable for an application such as video camera steering, which is much less tolerant to large errors than it is to small errors.

We propose an improved TDE-based DOA estimation algorithm called time delay selection (TIDES) based on either minimizing the weighted least squares error (MWLSE) or minimizing the time delay separation (MWTDS). In the TIDES algorithm, we consider not only the maximum likelihood (ML) TDEs for each pair of microphones, but also other secondary delays corresponding to smaller peaks in the generalized cross-correlation (GCC). From these multiple candidate delays for each microphone pair, we form all possible combinations of time delay sets. From among these we pick one set based on one of the two criteria mentioned above and perform least squares DOA estimation using the selected set of time delays. The MWLSE criterion selects that set of time delays that minimizes the least squares error. The MWTDS criterion selects that set of time delays that has minimum distance from a statistically averaged set of time delays from previously selected time delays.

Both TIDES algorithms are shown to out-perform the ML-TDE algorithm in moderate signal to reverberation ratios. In fact, TIDES-MWTDS gives fewer large errors than even the SRP-PHAT algorithm, which makes it very suitable for video camera steering applications. Under small signal to reverberation ratio environments, TIDES-MWTDS breaks down, but TIDES-MWLSE is still shown to out-perform the algorithm based on ML-TDE.