In massive Machine Type Communications（mMTC） uplink grand-free Non Orthogonal Multiple Access（NOMA） systems

active users usually transmit data in consecutive time slots with high probability. In order to make full use of the time correlation between adjacent time slots

this paper proposes an Improved Dynamic Adaptive（IDA） multi-user detection algorithm

which combines the reconstruction idea of the existing compressed sensing algorithm with time correlation to achieve joint detection of active users and data. In the process of estimating the support set

an adaptive threshold-assisted strategy is added to select atoms

and the power function variable step size method is used to improve the accuracy of the sparsity estimation and optimize the iteration termination conditions. The simulation results show that compared with the greedy reconstruction algorithm and the Dynamic Compressed Sensing（DCS） algorithm

the IDA algorithm has better signal detection performance in the absence of a priori sparseness.