Transient and tracking performance bounds of the sign-sign algorithm

The paper provides a rigorous tracking analysis of the sign-sign algorithm when used in the identification of a time-varying plant with a white Gaussian input. The plant parameters vary according to a random walk model. The assumptions allow nonstationarity of the plant input, plant noise, and increments of the plant parameters. Upper bounds are derived for the long-term averages of the mean of the weight misalignment norm, mean absolute error, mean square weight misalignment, and mean square error. These bounds hold for all values of the algorithm step size, all initial filter weight settings, and all degrees of nonstationarity of the plant input, plant noise, and plant parameter increments. Lower bounds of the mean square weight misalignment and mean square error are also derived. The step sizes that minimize the above bounds are derived. A transient analysis of the algorithm is done in the case of a time-invariant plant. A tight lower bound of the convergence time is derived. The above analytical results are supported by computer simulations.