Estimation of colored plant noise using Kalman filter based deconvolution

In many deconvolution problems, the signal to be estimated is modeled as the input to a known plant and assumed white. There are, however, situations in which this signal is not white. A simple iterative scheme for estimating colored sequences is presented. In this scheme, the colored plant noise is modeled as the output of a shaping filter excited by white noise. The shaping filter is considered as part of the plant while applying Mendel´s minimum variance deconvolution (MVD) algorithm based on the Kalman filter to estimate the plant noise. To begin with, the shaping filter is just an identity filter. The estimated plant noise is then used to update its coefficients iteratively until the change in the coefficient values is small. The iterative scheme has been tested using simulated data under different conditions, and is found to perform quite well under certain situations.<>