Power minimisation approach is an effective interference suppression algorithm for satellite navigation systems. It forms automatically deep nulls in the direction-of-arrival (DOA) of interferences without prior information about the DOAs of satellite signals and interferences. However, it cannot provide flat gains for other directions. Thus, the desired satellite signals may be partly suppressed when they locate in the shallow nulls. By combining eigenvalue thresholding method and l1-norm constraint, a new interference suppression algorithm is proposed for satellite navigation systems that would provide approximately flat gains in all directions except that of interferences. However, the l1-norm constraint leads to a non-smooth optimisation problem which cannot be solved by the conventional gradient-based algorithm. After that, by utilising the proximal operator, an iterative algorithm is proposed. The simulations demonstrate the effectiveness of the proposed algorithm.

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