This is an extention to my other question. My sampling frequency is only about 2x my tone frequency. I want to estimate time delay of arrival using this signal. I am generating the tone signal so I know its properties. Can I use compressed sensing to reconstruct my tone wave received by the sensors and get a good time delay estimate? An answer with some matlab code would be brilliant.
A colleague of mine has investigated time delay estimation using compressed sensing in this paper: http://vbn.aau.dk/en/publications/compressive-parameter-estimation-for-sparse-translationinvariant-signals-using-polar-interpolation(56d35506-d4ae-4296-9a36-7ec95b1160c7).html You can find the accompanying Matlab code here: http://www.sparsesampling.com/cpe/
You should try to measure the phase of the signals, since so you can average out errors. Phase difference is proportional to time delay, but wraps.