Compressive Time Delay Estimation using Interpolation

We show that compressive sensing (CS) applied to time delay estimation (TDE) simultaneously enables a reduction in the sampling frequency and preserves good estimation precision. With CS, we seek to recover signals and parameters from an under-determined system of linear equations by assuming sparsity in a known dictionary. A common problem in CS is that the observed signals may not be sparsely representable in the dictionary. This problem also occurs in TDE as the delay parameter is a continuous parameter. We remedy this issue by combining CS with interpolation.