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A new filtering approach based on the idea of iterative learning control (ILC) is proposed for linear and non-Gaussian stochastic systems. The objective of filtering is to estimate the states of linear systems with non-Gaussian random disturbances so that the entropy of output error is made to monotonically decrease along the progress of batches of process operation. The term Batch is referred to a period of time when the process repeats itself. During a batch, the filter gain is kept fixed and state estimation is performed. Between any two adjacent batches, the filter gain is updated so that the entropy of closed-loop output error is reduced for the next batch. Analysis is carried out to explicitly determine the learning rates which lead to convergence of the overall algorithm. Experiments have been implemented on a laboratory-based process test rig to demonstrate the effectiveness of proposed filtering method.