Lp normed minimization with applications to linear predictive modeling for sinusoidal frequency estimation

Abstract Robust time series modeling is an active area of research within many disciplines. For estimating the frequency of sinusoids from relatively short data records linear predictive methods have proven successful in numerous applications. Typically, least squares based solutions are invoked to calculate the model coefficients required to form frequency estimates for reasons of mathematical tractability and computational efficiency. The least squares error criteria equally weights all modeling errors and may produced biased frequency location estimates if the data are contaminated by impulsive noise or if transient components such as multipath are present. It is well known that a least absolute deviation error criteria may aid in generating a robust parametric model in such situations. Iterative algorithms possess the advantage of being able to generate L p normed solutions. It is natural to consider the behavior of the prediction error filter roots as the solution iterates from some initial state (e.g. a least squares solution) to the L p normed solution. Of particular interest may be the behavior of any extraneous roots introduced by overmodeling. By plotting prediction error filter roots in the complex z -plane at each iteration step, we have generated graphical data somewhat analogous to a root locus plot. From this approach we gain insight into the transient and steady behavior of the iterative algorithm. Additionally, the robustness of an L p normed solution when estimating the frequency of sinusoids from data contaminated by impulsive noise is demonstrated.