  Using commodity WiFi data for applications such as indoor localization,
object identification and tracking and channel sounding has recently gained
considerable attention. We study the problem of channel impulse response (CIR)
estimation from commodity WiFi channel state information (CSI). The accuracy of
a CIR estimation method in this setup is limited by both the available channel
bandwidth as well as various CSI distortions induced by the underlying
hardware. We propose a multi-band splicing method that increases channel
bandwidth by combining CSI data across multiple frequency bands. In order to
compensate for the CSI distortions, we develop a per-band processing algorithm
that is able to estimate the distortion parameters and remove them to yield the
"clean" CSI. This algorithm incorporates the atomic norm denoising sparse
recovery method to exploit channel sparsity. Splicing clean CSI over M
frequency bands, we use orthogonal matching pursuit (OMP) as an estimation
method to recover the sparse CIR with high (M-fold) resolution. Unlike previous
works in the literature, our method does not appeal to any limiting assumption
on the CIR (other than the widely accepted sparsity assumption) or any ad hoc
processing for distortion removal. We show, empirically, that the proposed
method outperforms the state of the art in terms of localization accuracy.
