The problem considered is that of estimating unambiguously migrating targets observed with a wideband radar. We extend a previously described sparse Bayesian algorithm to the presence of diffuse clutter and off-grid targets. A hybrid-Gibbs sampler is formulated to jointly estimate the sparse target amplitude vector, the grid mismatch, and the (assumed) autoregressive noise. Results on synthetic and fully experimental data show that targets can be actually unambiguously estimated even if located in blind speeds.