Covariance, one of the most widely accepted mathematical tool for similarity measurement relies heavily on the assumption of Gaussian distribution noise model. Along with many other second‐order statistics based methods, its performance deteriorates significantly in the presence of impulsive noise. Therefore, in this study, a generalised covariance function named bounded non‐linear covariance (BNC) is put forward to handle relative problems in the presence of noise with non‐Gaussian and heavy‐tailed distribution. Meanwhile, the projection approximation subspace tracking‐like algorithm based on BNC is proposed as well. Simulations have verified its performances over existing methods, especially the robustness to impulsive noise.