Taylor series adaptive processing

Many signal processing applications require estimating and tracking a quantity that is inherently nonstationary. Such quantities may be matrices (e.g., a covariance matrix or an image), vectors (e.g., a weight vector or an eigenvector), or scalars. This paper considers the use of Taylor series expansions to enhance tracking. The potential benefits of this approach include: (1) a reduction in computational burden, (2) a reduction in required memory size and/or communication bandwidth (via an implicit compression of the quantity of interest), (3) interpolation through "gaps" in the available data, and (4) increased fidelity due to the explicit incorporation of "nonstationarity" into the model. Sensor array processing examples are used to illustrate the approach.