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In this paper, Kalman and Least Mean Square based filters are used for colored noise corrupted speech enhancement. Unlike previous studies a second speech signal has been utilized as colored noise which represents the situation where two persons are talking concurrently. Such a setup will help analyse the performance of speech enhancement algorithms when there are more than one speech components in the signal to be analysed and main speech signal has to be recovered. Final Prediction Error method has been employed for determining the model parameters, Speech was modeled with AR model and selected methods has been tested for their performance in terms of mean square error. The experimental results show that dual Kalman filter, which estimates both state and parameters concurently, has produced lower mean square error values when compared to joint and single Kalman filters. Joint Kalman filter, on the other hand, produced lower mean square error than single Kalman filter. Finally, it was observed that, the performance of LMS based filters was not adequate for the enhancement of colored noise corrupted speech.