Abstract: A multi-task joint estimation algorithm for both the channel and impulsive noise is proposed to improve the sparse recovery performance under time-varying channels to address the ice-induced impulsive noise in underwater acoustic channels in polar environments. The received data blocks are divided into sub-blocks, and the time correlation between the sub-block channel data is utilized to design the algorithm. Impulsive noise is further incorporated into the multi-task sparse Bayesian learning channel estimation model and an iterative algorithm is derived for joint estimation of the channel and impulsive noise using the variational Bayesian method. An adaptive scheme is introduced for the weighted factors in the channel message passing between data sub-blocks. Key weight factors are optimized to further improve the channel estimation accuracy during the Turbo iterative process, effectively mitigating error propagation. The algorithm has been validated using experimental data from the eleventh Chinese Arctic expedition’s sub-ice acoustic communication experiment. The results demonstrate that the proposed algorithm effectively suppresses the interference from impulsive noise, shows superior performance in preventing error propagation. For high-order modulation data over a communication distance of 11 km in a single-input-single-output system, the proposed algorithm achieves an average bit error rate reduction of 92.5% after five iterations compared to algorithms without pulse noise elimination.