Discrete Smoothing Filters for Correlated Noise

A discrete polynomial smoother may be defined in the following terms. Consider the random process R(nT), where n is an integer and T is the period of the samples at which the process wall be of interest.* The process will be thought of as comprising a desired component R(nT), and a noise component R(nT). It will be assumed that R(nT) can be satisfactorily approximated by an rth degree polynomial in nT, R(nT). Further, assume that R(nT) is a random process that is widesense stationary with respect to the sampling instants nT. The foregoing situation would occur, for example, in the tracking of a moving object whose true position could be represented as an rth degree polynomial in time, and whose measured position included a random error. We will assume that E[R(nT)] = 0 (1)