Uplink sensing in integrated sensing and communications (ISAC) systems, such as Perceptive Mobile Networks, is challenging due to the clock asynchronism between transmitter and receiver. Existing solutions typically require the presence of a dominating line-of-sight path and the knowledge of transmitter location at the receiver. In this paper, relaxing these requirements, we propose a novel and effective uplink sensing scheme with the assistance of static anchor points. Two major algorithms are proposed in the scheme. The first algorithm estimates the relative timing and carrier frequency offsets due to clock asynchronism, with respect to those at a randomly selected reference snapshot. Theoretical performance analysis is provided for the algorithm. The estimates from the first algorithm are then used to compensate for the offsets and generate the angle-Doppler maps. Using the maps, the second algorithm identifies the anchor points, and then locates the UE and dynamic targets. Feasibility of UE localization is also analyzed. Simulation results are provided and demonstrate the effectiveness of the proposed algorithms.