Abstract: ‍ ‍The goal of massive Machine Type Communications （mMTC） is to enable communications among a large number of Internet of Things （IoT） devices， enabling the creation of intelligent systems in various fields， such as industrial automation and smart transportation. In the mMTCs， only a small fraction of devices need to be in an active state to communicate with the base station， while the rest remain in a dormant state to conserve energy. For such mMTCs， the traditional authorization-based random access techniques suffer from high access failure probabilities and high signaling overhead. To this end， the concept of grant-free random access （GFRA） has emerged， and it allows for direct data transmission without waiting for authorization after the active user devices send pilot sequences. In the mMTCs based on GFRA， a critical task for the base station is to perform user device activity detection. In practical scenarios， user devices probably remain active due to consecutive activations triggered by the same event， indicating a high degree of temporal correlation between a device’s state in the current time slot and the previous one. However， this feature is ignored by classical active user detection algorithms. Exploiting this temporal correlation as prior information can reduce the error probability in detecting user device activity. Starting from this perspective， a time-information-assisted user activity detection algorithm is proposed， and it is named the coordinate descent algorithm based on maximum a posteriori probability （MAP-CD）. Specifically， the proposed algorithm begins by constructing the objective function related to user device activity detection from the perspective of maximum a posteriori probability and then expresses the state transitions in consecutive time slots using Markov chains. Next， the coordinate descent algorithm is employed to figure out the set of active user devices with the help of the covariance of received signals. Simulation results indicate that， compared with the state-of-the-art activity detection algorithms in mMTCs， the proposed MAP-CD algorithm exhibits lower error detection probabilities due to its exploitation of the temporal correlation in user activities. The MAP-CD algorithm maintains good performance， even with a short pilot sequence or an increased number of active users. Moreover， as the number of receiving antennas gradually increases， the MAP-CD algorithm also exhibits more significant performance gains.