Off the grid time delay estimation for sparse translation-invariant signals

We present a time delay estimation method for sparse translation-invariant signals, off the grid. We enforce sparsity by imposing penalties based on an atomic norm to consider signals in a continuous domain. Our formulation leads to an atomic norm minimization problem. A number of recent theoretical results demonstrate that an atomic norm minimization can be solved using a semidefinite programming (SDP). We propose to modify some parameters to solve our problem in the same manner. We demonstrate the effectiveness of the method on simulated data by comparing results of our approach to those of discretization methods. We observe that our approach has an advantage over other discretization methods, including time delay estimation off the grid, which completely obviates the basis mismatch.