Echo Delay Estimation to Aid Source Localization in Noisy Environments

Abstract

Time-delay estimation (TDE) finds application in a variety of problems, be it locating fractures or steering cameras towards the speaker in a multi-participant conference application. Underwater acoustic OFDM source localization is another important application of TDE. Existing underwater acoustic source localization techniques use a microphone array consisting of three or four sensors in order to effectively locate the source. Analog-to-digital (ADC) converters at these sensors call for a non-nominal investment in terms of circuitry and memory. A relatively inexpensive source localization algorithm is needed that works with the output of a single sensor. Since an inexpensive process for estimating the location of the source is desired, the ADC used at the sensor is capable only of a relatively low sampling rate. For a given delay, a low sampling rate leads to sub-sample interval delays, which the desired algorithm must be able to estimate. Prevailing TDE algorithms make some a priori assumptions about the nature of the received signal, such as Gaussianity, wide-sense stationarity, or periodicity. The desired algorithm must not be restrictive in so far as the nature of the transmitted signal is concerned.

A time-delay estimation algorithm based on the time-frequency ratio of mixtures (TFRM) method is proposed. The experimental set-up consists of two microphones/sensors placed at some distances from the source. The method accepts as input the received signal which consists of the sum of the signal received at the nearer sensor and the signal received at the farther sensor and noise. The TFRM algorithm works in the time-frequency domain and seeks to perform successive source cancellation in the received burst. The key to performing source cancellation is to estimate the ratio in which the sources combine and this ratio is estimated by means of taking a windowed mean of the ratio of the spectrograms of any two pulses in the received burst. The variance of the mean function helps identify single-source regions and regions in which the sources mix.

The performance of the TFRM algorithm is evaluated in the presence of noise and is compared against the Cramer-Rao lower bound. It is found that the variance of the estimates returned by the estimator diverge from the predictions of the Cramer-Rao inequality as the farther sensor is moved farther away. Conversely, the estimator becomes more reliable as the farther sensor is moved closer.

The time-delay estimates obtained from the TFRM algorithm are used for source localization. The problem of finding the source reduces to finding the locus of points such that the difference of its distances to the two sensors equals the time delay. By moving the pair of sensors to a different location, or having a second time delay sensor, an exact location for the source can be determined by finding the point of intersection of the two loci.

The TFRM method does not rely on a priori information about the signal. It is applicable to OFDM sources as well as sinusoidal and chirp sources.