In this paper, the problem of speech enhancement when only corrupted speech signal is available for processing is considered. For this, the Kalman filtering method is studied and compared with the Wiener filtering method. Its performance is found to be significantly better than the Wiener filtering method. A delayed-Kalman filtering method is also proposed which improves the speech enhancement performance of Kalman filter further.

The density power divergence (DPD) measure, defined in terms of a single parameter α, has proved to be a popular tool in the area of robust estimation [ 1 A. Basu, I.R. Harris, N.L. Hjort and M.C. Jones, Robust and efficient estimation by minimizing a density power divergence, Biometrika 85 (1998), pp. 549–559. doi: 10.1093/biomet/85.3.549 [Crossref], [Web of Science ®] [Google Scholar] ]. Recently, Ghosh and Basu [ 5 A. Ghosh and A. Basu, Robust estimation for independent non-homogeneous observations using density power divergence with applications to linear regression, Electron. J. Stat. 7 (2013), pp. 2420–2456. doi: 10.1214/13-EJS847 [Crossref], [Web of Science ®] [Google Scholar] ] rigorously established the asymptotic properties of the MDPDEs in case of independent non-homogeneous observations. In this paper, we present an extensive numerical study to describe the performance of the method in the case of linear regression, the most common setup under the case of non-homogeneous data. In addition, we extend the existing methods for the selection of the optimal robustness tuning parameter from the case of independent and identically distributed (i.i.d.) data to the case of non-homogeneous observations. Proper selection of the tuning parameter is critical to the appropriateness of the resulting analysis. The selection of the optimal robustness tuning parameter is explored in the context of the linear regression problem with an extensive numerical study involving real and simulated data.