In many applications such as localization, there is a need to determine the unknown time shift D between a signal, and its time shifted version. Aligning one against the other until the two match will find D. When working with compressive sensing (CS) measurements, only linearly transformed samples of the signal and its time-shifted version are available. These CS samples conceal the explicit time shift relationship between the signals, and D can no longer be found by a simple alignment of the CS measurements. As a result, estimation of the time-difference-of-arrival (TDOA) from CS measurements requires the restoration of the original signals. The nonlinear restoration can be time consuming, and may introduce large errors when noise is present. This paper provides an alternate TDOA estimator that avoids restoration. The key is in making additional measurements to preserve the time shift relationship of the signals. This requires a slight modification of the random modulator pre-integrator, as described in the paper, which also includes a simulation example.

Additional Metadata
Keywords compressed sensing, random modulator pre-integrator, TDOA estimation
Persistent URL dx.doi.org/10.1109/CoSeRa.2015.7330307
Conference 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar, and Remote Sensing, CoSeRa 2015
Citation
Chan, Y.T. (Y. T.), Chan, F. (F.), Rajan, S, & Lee, B.H. (B. H.). (2015). Direct estimation of time difference of arrival from compressive sensing measurements. In 2015 3rd International Workshop on Compressed Sensing Theory and its Applications to Radar, Sonar, and Remote Sensing, CoSeRa 2015 (pp. 273–276). doi:10.1109/CoSeRa.2015.7330307