Sequential Estimation of Signals under Model Uncertainty

Abstract

Two important areas of signal processing are parameter estimation of signals and signal detection. In standard textbooks they are usually addressed separately, although in many practical problems they are applied jointly. In estimation theory, it is almost always assumed that the model of the signal is known, and the objective is to estimate its parameters from noisy signal data. For example, if the observed data vector is y, where y ∈ ${R^{{n_y}}}$ , and the model of the signal is represented by a function whose analytical form is known, the goal is to estimate the signal parameters x from y, where x ∈ ${R^{{n_y}}}$ .¹ In cases when it is unclear whether there is a signal in the data, one resorts to estimation of the signal parameters under the assumption that the data contain a signal, thereafter applying a detection scheme to decide if the signal is indeed in the data.