Off-the-Grid Compressive Time Delay Estimation via Manifold-Based Optimization

The time delay estimation (TDE) of some known waveforms from sampled data is of great interest in the area of signal processing, e.g., wireless communication, radar, and sonar. Classical algorithms, such as matched filters, multiple signal classification always work under the Nyquist sampling rate determined by the bandwidth of the waveform. With the assumption of sparsity, the novel compressive sensing (CS)-based algorithms are proposed in recent studies, which theoretically reduce the sampling rate but preserve the same accuracy. Yet these novel algorithms often suffer from the-so-called off-the-grid issue (or basis mismatch) and do not perform as well as expectations. This letter proposes a manifold-based optimization strategy to improve the CS-based TDE algorithms in order to solve this issue and improve the estimation accuracy and the resolution. The proposed algorithm not only achieve a much higher accuracy but also works under a much lower sampling rate compared with the state-of-the-art CS-based algorithms.