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A constrained independent component analysis (ICA) approach is presented in this paper to address the linear instantaneous blind source separation (BSS) problem where the unknown mixing coefficients vary over time. It is assumed that the variations are small, within a specified bound, not frequent and mostly due to environmental disturbances. The separating matrix for the nominal system (which may be determined using a batch version or on-line version of natural gradient algorithm) is assumed to be known beforehand. The constrained approach leads to the modification of the contrast function based on conventional natural gradient by incorporating the assumptions as constraint. The problem is then reformulated as an unconstrained optimization problem by means of a barrier function. In situations where the mixing system is non-stationary, the natural gradient algorithm performs poorly in terms of convergence and separation ability. Numerical experiments on both synthetic signals and acoustic electromechanical signals confirm the superior performance of the proposed algorithm over the conventional natural gradient algorithm (NGA) in a non-stationary environment.