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For sparse system identification, a μ-law memorised improved proportionate affine projection algorithm (MMIPAPA) can achieve faster convergence rate than the standard affine projection algorithm. However, the MMIPAPA with constant regularisation parameter requires a tradeoff between fast convergence speed and low steady-state error. To address the problem, proposed are two kinds of variable non-identity regularisation matrices for the MMIPAPA with a negligible additional computational cost and a stability condition for the step-size choice. Simulation results show the good misalignment performance of the proposed algorithms for both coloured and speech input.