The number of wireless devices is drastically increasing, resulting in many devices contending for radio resources. In this work, we present an algorithm to detect active devices for unsourced random access, i.e., the devices are uncoordinated. The devices use a unique, but non-orthogonal preamble, known to the network, prior to sending the payload data. They do not employ any carrier sensing technique and blindly transmit the preamble and data. To detect the active users, we exploit partial channel state information (CSI), which could have been obtained through a previous channel estimate. For static devices, e.g., Internet of Things nodes, it is shown that CSI is less time-variant than assumed in many theoretical works. The presented iterative algorithm uses a maximum likelihood approach to estimate both the activity and a potential phase offset of each known device. The convergence of the proposed algorithm is evaluated. The performance in terms of probability of miss detection and false alarm is assessed for different qualities of partial CSI and different signal-to-noise ratio.