Hidden Markov Model for multidimensional wavefront tracking

In subsurface sensing, the estimation of the delays (wavefronts) of the backscattered wavefields is a very time-consuming, mostly manual task. We propose delay estimation by exploiting the continuity of the wavefronts modeled as a Markov chain. Each wavefront is a realization of Brownian motion with a correlation that depends on the distance between each source/receiver pair. Therefore, the delay profiles can be tracked with any known method by assuming that the ordered sequence of signals is described by a hidden Markov model (HMM). Linear array provides the most natural data-ordering, and in this case the tracking algorithms can preserve the target/tracker association. However, when measurements are multidimensional, the volume-slicing strategies, that are able to get a linear array of (virtually) ordered signals, select the measurements independently of the target. When different estimates along slices are merged mis-ties can occur easily. Since data-ordering is a main issue for irregularly positioned sources and receivers, we propose a region growing tracking technique that orders (for each specified target) the data while tracking. The ordering is based on the maximum a posteriori probability of detection. Experiments based on multidimensional measurements show that this region growing tracking algorithm based on HMM preserves the target/tracker association.