It has been shown that the channel state information (CSI) of a Wi-Fi system can be exploited to localize Wi-Fi devices or track trajectory of a moving target. In the existing literature, both sensing tasks are treated separately and some prior information is usually requested, including the signal fingerprints, the locations of some anchor devices in the Wi-Fi system, and etc. In the proposed WiSLAT method, however, it is shown that both sensing tasks can assist each other, such that the request on prior system information can be eliminated. Particularly, in a Wi-Fi system with an access point (AP) and at least three stations, where the locations of the stations are unknown, the WiSLAT is designed to detect the Doppler frequencies of the downlink CSI at the stations, such that their locations and the trajectory of the target with respect to the AP can be inferred. The joint detection can be conducted by searching the optimal stations' locations and target's trajectory, such that their corresponding Doppler frequencies fit the observed ones best. Due to the tremendous non-convex search space, a low-complexity sub-optimal algorithm integrating alternate optimization, extended Kalman filter and density-based clustering is proposed in WiSLAT. Experiments conducted in indoor environments demonstrate the effectiveness of WiSLAT, achieving a median trajectory-tracking error of 0.68 m.