This paper proposes a radio simultaneous location and mapping (radio-SLAM) scheme based on sparse multipath channel estimation. By leveraging sparse channel estimation schemes at millimeter wave bands, namely high resolution estimates of the multipath angle of arrival (AoA), time difference of arrival (TDoA), and angle of departure (AoD), we develop a radio-SLAM algorithm that operates without any requirements of clock synchronization, receiver orientation knowledge, multiple anchor points, or two-way protocols. Thanks to the AoD information obtained via compressed sensing (CS) of the channel, the proposed scheme can estimate the receiver clock offset and orientation from a single anchor transmission, achieving sub-meter accuracy in a realistic typical channel simulation.