A probabilistic approach to time delay estimation

Time delay estimation is a very general problem with wide range of applications. When noisy repetitive signals are observed, the noise cancellation is achieved by averaging perfectly aligned signals. A time delay estimator is developed for determining time delay between signals received on different trials in the presence of uncorrelated noise. The estimator is based on a probabilistic generative model for delayed signals, and tries to find the delay and the source signal simultaneously so that maximum likelihood is achieved. An iterative method based on the Expectation-Maximization algorithm is used for finding maximum likelihood estimate of parameters. The estimator has been tested on three types of synthetic signals. The result shows that it can tolerate 5 to 10dB more noise while achieving the same performance as cross-correlation estimator.