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This study addresses the high‐resolution time delay estimation (TDE) via sparse parameter estimation methods. Two representative algorithms, Sparse Asymptotic Minimum Variance (SAMV) and SParse Iterative Covariance‐based Estimation are devised in both the time and frequency domains for application to the TDE of spread‐spectrum signals and their performances are analysed in various multipath environments. The authors also proposes the combined approach of SAMV and weighted RELAX, referred to as SAMV‐WRELAX, to reduce the computational load. Numerical examples demonstrate that the frequency‐domain approaches with a proper type of snapshots not only outperform the corresponding time‐domain approaches but also mitigate the problem of the noise correlation encountered in time‐domain processing. They also show that the computational load of SAMV‐WRELAX with a grid size of 0.1Tc decreases up to a few tenths of that of SAMV with a fine grid, e.g. a size of 0.01Tc, without any performance degradations. [ABSTRACT FROM AUTHOR]